Chinese_Economic_Influence_in_Africa.ipynb

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      "metadata": {
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          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ]
        }
      ],
      "source": [
        "%matplotlib inline\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "import io\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "pd.set_option('display.max_columns', 500)\n",
        "\n",
        "import scipy.stats as stats\n",
        "from scipy.stats import kendalltau, pearsonr, spearmanr\n",
        "import statsmodels.api as sm\n",
        "from statsmodels.formula.api import ols\n",
        "\n",
        "from datetime import datetime, date"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import files\n",
        "\n",
        "africa = files.upload()\n",
        "investment = files.upload()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 394
        },
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        "outputId": "e5a36a3b-eefd-46cc-d62e-387c62bba56f"
      },
      "execution_count": null,
      "outputs": [
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            "\u001b[0;32m/usr/local/lib/python3.7/dist-packages/google/colab/files.py\u001b[0m in \u001b[0;36m_upload_files\u001b[0;34m(multiple)\u001b[0m\n\u001b[1;32m    121\u001b[0m   result = _output.eval_js(\n\u001b[1;32m    122\u001b[0m       'google.colab._files._uploadFiles(\"{input_id}\", \"{output_id}\")'.format(\n\u001b[0;32m--> 123\u001b[0;31m           input_id=input_id, output_id=output_id))\n\u001b[0m\u001b[1;32m    124\u001b[0m   \u001b[0mfiles\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_collections\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdefaultdict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_six\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbinary_type\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    125\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
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    {
      "cell_type": "code",
      "source": [
        "africa_df = pd.read_csv(io.BytesIO(africa[\"ObservationData_lavlqce.csv\"]))\n",
        "investmentdf = pd.read_excel(io.BytesIO(investment[\"FDIData_10Jan2022.xlsx\"]), header = [0, 1])"
      ],
      "metadata": {
        "id": "MpAtRIdXos5t",
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          "base_uri": "https://localhost:8080/"
        },
        "outputId": "12e09eaa-bdea-4888-bbee-1ba5ed4c1436"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/openpyxl/worksheet/_reader.py:312: UserWarning: Unknown extension is not supported and will be removed\n",
            "  warn(msg)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "investmentdf.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 336
        },
        "id": "Xt50agTFoxvd",
        "outputId": "ca7993d0-48c3-4a96-8117-8f8886ac81df"
      },
      "execution_count": null,
      "outputs": [
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          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "  Chinese FDI Stock in African Countries                                \\\n",
              "                      US$ mn, unadjusted Regional Algeria Angola Benin   \n",
              "0                                   1990      NaN     NaN    NaN   NaN   \n",
              "1                                   1991      NaN     NaN    NaN   NaN   \n",
              "2                                   1992      NaN     NaN    NaN   NaN   \n",
              "3                                   1993      NaN     NaN    NaN   NaN   \n",
              "4                                   1994      NaN     NaN    NaN   NaN   \n",
              "\n",
              "                                                                      \\\n",
              "  Botswana Burkina Faso Burundi Cameroon Cape Verde CAR Chad Comoros   \n",
              "0      NaN          NaN     NaN      NaN        NaN NaN  NaN     NaN   \n",
              "1      NaN          NaN     NaN      NaN        NaN NaN  NaN     NaN   \n",
              "2      NaN          NaN     NaN      NaN        NaN NaN  NaN     NaN   \n",
              "3      NaN          NaN     NaN      NaN        NaN NaN  NaN     NaN   \n",
              "4      NaN          NaN     NaN      NaN        NaN NaN  NaN     NaN   \n",
              "\n",
              "                                                                               \\\n",
              "  Congo, Rep. Congo, Dem. Rep. Cote d'Ivoire Djibouti Egypt Equatorial Guinea   \n",
              "0         NaN              NaN           NaN      NaN   NaN               NaN   \n",
              "1         NaN              NaN           NaN      NaN   NaN               NaN   \n",
              "2         NaN              NaN           NaN      NaN   NaN               NaN   \n",
              "3         NaN              NaN           NaN      NaN   NaN               NaN   \n",
              "4         NaN              NaN           NaN      NaN   NaN               NaN   \n",
              "\n",
              "                                                                           \\\n",
              "  Eritrea Ethiopia Fmr. Sudan Gabon The Gambia Ghana Guinea Guinea-Bissau   \n",
              "0     NaN      NaN        NaN   NaN        NaN   NaN    NaN           NaN   \n",
              "1     NaN      NaN        NaN   NaN        NaN   NaN    NaN           NaN   \n",
              "2     NaN      NaN        NaN   NaN        NaN   NaN    NaN           NaN   \n",
              "3     NaN      NaN        NaN   NaN        NaN   NaN    NaN           NaN   \n",
              "4     NaN      NaN        NaN   NaN        NaN   NaN    NaN           NaN   \n",
              "\n",
              "                                                                           \\\n",
              "  Kenya Lesotho Liberia Libya Madagascar Malawi Mali Mauritania Mauritius   \n",
              "0   NaN     NaN     NaN   NaN        NaN    NaN  NaN        NaN       NaN   \n",
              "1   NaN     NaN     NaN   NaN        NaN    NaN  NaN        NaN       NaN   \n",
              "2   NaN     NaN     NaN   NaN        NaN    NaN  NaN        NaN       NaN   \n",
              "3   NaN     NaN     NaN   NaN        NaN    NaN  NaN        NaN       NaN   \n",
              "4   NaN     NaN     NaN   NaN        NaN    NaN  NaN        NaN       NaN   \n",
              "\n",
              "                                                                               \\\n",
              "  Morocco Mozambique Namibia Niger Nigeria Rwanda Sao Tome & Principe Senegal   \n",
              "0     NaN        NaN     NaN   NaN     NaN    NaN                 NaN     NaN   \n",
              "1     NaN        NaN     NaN   NaN     NaN    NaN                 NaN     NaN   \n",
              "2     NaN        NaN     NaN   NaN     NaN    NaN                 NaN     NaN   \n",
              "3     NaN        NaN     NaN   NaN     NaN    NaN                 NaN     NaN   \n",
              "4     NaN        NaN     NaN   NaN     NaN    NaN                 NaN     NaN   \n",
              "\n",
              "                                                                           \\\n",
              "  Seychelles Sierra Leone Somalia South Africa South Sudan Sudan Eswatini   \n",
              "0        NaN          NaN     NaN          NaN         NaN   NaN      NaN   \n",
              "1        NaN          NaN     NaN          NaN         NaN   NaN      NaN   \n",
              "2        NaN          NaN     NaN          NaN         NaN   NaN      NaN   \n",
              "3        NaN          NaN     NaN          NaN         NaN   NaN      NaN   \n",
              "4        NaN          NaN     NaN          NaN         NaN   NaN      NaN   \n",
              "\n",
              "                                                                          \\\n",
              "  Tanzania Togo Tunisia Uganda Western Sahara Zambia Zimbabwe Zimbabwe.1   \n",
              "0      NaN  NaN     NaN    NaN            NaN    NaN      NaN        NaN   \n",
              "1      NaN  NaN     NaN    NaN            NaN    NaN      NaN        NaN   \n",
              "2      NaN  NaN     NaN    NaN            NaN    NaN      NaN        NaN   \n",
              "3      NaN  NaN     NaN    NaN            NaN    NaN      NaN        NaN   \n",
              "4      NaN  NaN     NaN    NaN            NaN    NaN      NaN        NaN   \n",
              "\n",
              "                               \n",
              "  Total, US$ mn Total, US$ bn  \n",
              "0           NaN           NaN  \n",
              "1           NaN           NaN  \n",
              "2           NaN           NaN  \n",
              "3           NaN           NaN  \n",
              "4           NaN           NaN  "
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              "  <thead>\n",
              "    <tr>\n",
              "      <th></th>\n",
              "      <th colspan=\"61\" halign=\"left\">Chinese FDI Stock in African Countries</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th></th>\n",
              "      <th>US$ mn, unadjusted</th>\n",
              "      <th>Regional</th>\n",
              "      <th>Algeria</th>\n",
              "      <th>Angola</th>\n",
              "      <th>Benin</th>\n",
              "      <th>Botswana</th>\n",
              "      <th>Burkina Faso</th>\n",
              "      <th>Burundi</th>\n",
              "      <th>Cameroon</th>\n",
              "      <th>Cape Verde</th>\n",
              "      <th>CAR</th>\n",
              "      <th>Chad</th>\n",
              "      <th>Comoros</th>\n",
              "      <th>Congo, Rep.</th>\n",
              "      <th>Congo, Dem. Rep.</th>\n",
              "      <th>Cote d'Ivoire</th>\n",
              "      <th>Djibouti</th>\n",
              "      <th>Egypt</th>\n",
              "      <th>Equatorial Guinea</th>\n",
              "      <th>Eritrea</th>\n",
              "      <th>Ethiopia</th>\n",
              "      <th>Fmr. Sudan</th>\n",
              "      <th>Gabon</th>\n",
              "      <th>The Gambia</th>\n",
              "      <th>Ghana</th>\n",
              "      <th>Guinea</th>\n",
              "      <th>Guinea-Bissau</th>\n",
              "      <th>Kenya</th>\n",
              "      <th>Lesotho</th>\n",
              "      <th>Liberia</th>\n",
              "      <th>Libya</th>\n",
              "      <th>Madagascar</th>\n",
              "      <th>Malawi</th>\n",
              "      <th>Mali</th>\n",
              "      <th>Mauritania</th>\n",
              "      <th>Mauritius</th>\n",
              "      <th>Morocco</th>\n",
              "      <th>Mozambique</th>\n",
              "      <th>Namibia</th>\n",
              "      <th>Niger</th>\n",
              "      <th>Nigeria</th>\n",
              "      <th>Rwanda</th>\n",
              "      <th>Sao Tome &amp; Principe</th>\n",
              "      <th>Senegal</th>\n",
              "      <th>Seychelles</th>\n",
              "      <th>Sierra Leone</th>\n",
              "      <th>Somalia</th>\n",
              "      <th>South Africa</th>\n",
              "      <th>South Sudan</th>\n",
              "      <th>Sudan</th>\n",
              "      <th>Eswatini</th>\n",
              "      <th>Tanzania</th>\n",
              "      <th>Togo</th>\n",
              "      <th>Tunisia</th>\n",
              "      <th>Uganda</th>\n",
              "      <th>Western Sahara</th>\n",
              "      <th>Zambia</th>\n",
              "      <th>Zimbabwe</th>\n",
              "      <th>Zimbabwe.1</th>\n",
              "      <th>Total, US$ mn</th>\n",
              "      <th>Total, US$ bn</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>1990</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
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              "      <td>NaN</td>\n",
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              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1991</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1992</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1993</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1994</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-f3e10100-17d7-4395-ab89-ebb7fa7a0fc0')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
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              "                                                     [key], {});\n",
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              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
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            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Looks like there is some good info for the years we're concerned with. Let's make these Chinese investment numbers easier to work with by creating a newly formatted dataframe. For any NaN values, we'll assume non-investment by setting the value to a very small number like .01 -- this is a workaround in order to be able to log-transform the data, while still retaining a value small enough to essentially indicate non-investment that year. "
      ],
      "metadata": {
        "id": "J39H0eoqKAjf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "idf = pd.DataFrame()\n",
        "idf[\"Country\"] = investmentdf.iloc[0]\n",
        "idf[\"2003_invest\"] = investmentdf.iloc[13]\n",
        "idf[\"2004_invest\"] = investmentdf.iloc[14]\n",
        "idf[\"2005_invest\"] = investmentdf.iloc[15]\n",
        "idf[\"2006_invest\"] = investmentdf.iloc[16]\n",
        "idf[\"2007_invest\"] = investmentdf.iloc[17]\n",
        "idf[\"2008_invest\"] = investmentdf.iloc[18]\n",
        "idf[\"2009_invest\"] = investmentdf.iloc[19]\n",
        "idf[\"2010_invest\"] = investmentdf.iloc[20]\n",
        "idf[\"2011_invest\"] = investmentdf.iloc[21]\n",
        "idf[\"2012_invest\"] = investmentdf.iloc[22]\n",
        "idf[\"2013_invest\"] = investmentdf.iloc[23]\n",
        "idf[\"2014_invest\"] = investmentdf.iloc[24]\n",
        "idf[\"2015_invest\"] = investmentdf.iloc[25]\n",
        "idf[\"2016_invest\"] = investmentdf.iloc[26]\n",
        "idf[\"2017_invest\"] = investmentdf.iloc[27]\n",
        "idf[\"2018_invest\"] = investmentdf.iloc[28]\n",
        "idf[\"2019_invest\"] = investmentdf.iloc[29]\n",
        "idf[\"2020_invest\"] = investmentdf.iloc[30]\n",
        "idf.dropna(how = 'all')\n",
        "cleaner_invest = idf.iloc[2:]\n",
        "cleaner_invest.reset_index(inplace=True)\n",
        "cleaner_invest = cleaner_invest.drop(['level_0', 'Country'], axis = 1)\n",
        "cleaner_invest.rename(columns = {'level_1':'Country'}, inplace = True)\n",
        "cleaner_invest = cleaner_invest.dropna(how = 'all')"
      ],
      "metadata": {
        "id": "h00DKELFKMTR"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Checking the other dataframe, let's modify it to suit our needs by changing the year column to each year being a separate column."
      ],
      "metadata": {
        "id": "JZQkFK5aXPp_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "africa_df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "id": "lWPTn7cOo4_2",
        "outputId": "4bbe4275-932d-4b1a-88ee-d8a93b39c826"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "  Country  Year  Real per Capita GDP Growth Rate (annual %)  \\\n",
              "0  Malawi  1980                                         NaN   \n",
              "1  Malawi  1981                                      -13.06   \n",
              "2  Malawi  1982                                       -0.93   \n",
              "3  Malawi  1983                                        1.56   \n",
              "4  Malawi  1984                                        0.54   \n",
              "\n",
              "   Real GDP growth (annual %)  Gross domestic product, (constant prices US$)  \\\n",
              "0                         NaN                                        3038.14   \n",
              "1                      -10.81                                        2709.74   \n",
              "2                        1.44                                        2748.84   \n",
              "3                        4.21                                        2864.70   \n",
              "4                        3.92                                        2976.95   \n",
              "\n",
              "   Gross domestic product, current prices (current US$)  \\\n",
              "0                                            2236.36      \n",
              "1                                            2236.40      \n",
              "2                                            2113.68      \n",
              "3                                            2203.66      \n",
              "4                                            2157.88      \n",
              "\n",
              "   Final consumption expenditure  (current US$)  \\\n",
              "0                                       1104.30   \n",
              "1                                       1091.26   \n",
              "2                                       1002.45   \n",
              "3                                       1037.06   \n",
              "4                                       1028.95   \n",
              "\n",
              "   General government final consumption expenditure (current US$)  \\\n",
              "0                                             238.76                \n",
              "1                                             221.16                \n",
              "2                                             206.82                \n",
              "3                                             200.81                \n",
              "4                                             189.62                \n",
              "\n",
              "   Household final consumption expenditure (current US$)  \\\n",
              "0                                             865.54       \n",
              "1                                             870.10       \n",
              "2                                             795.63       \n",
              "3                                             836.26       \n",
              "4                                             839.34       \n",
              "\n",
              "   Gross capital formation (current US$)  \\\n",
              "0                                 306.24   \n",
              "1                                 218.14   \n",
              "2                                 252.58   \n",
              "3                                 278.87   \n",
              "4                                 155.58   \n",
              "\n",
              "   Gross capital formation, Private sector  (current US$)  \\\n",
              "0                                              90.26        \n",
              "1                                              91.70        \n",
              "2                                             153.01        \n",
              "3                                             176.89        \n",
              "4                                              37.64        \n",
              "\n",
              "   Gross capital formation, Public sector  (current US$)  \\\n",
              "0                                             215.98       \n",
              "1                                             126.44       \n",
              "2                                              99.57       \n",
              "3                                             101.98       \n",
              "4                                             117.94       \n",
              "\n",
              "   Exports of goods and services (current US$)  \\\n",
              "0                                       307.48   \n",
              "1                                       317.66   \n",
              "2                                       265.46   \n",
              "3                                       253.84   \n",
              "4                                       342.72   \n",
              "\n",
              "   Imports of goods and services (current US$)  \\\n",
              "0                                       480.36   \n",
              "1                                       389.37   \n",
              "2                                       340.40   \n",
              "3                                       346.54   \n",
              "4                                       319.23   \n",
              "\n",
              "   Final consumption expenditure  (% of GDP)  \\\n",
              "0                                      49.38   \n",
              "1                                      48.80   \n",
              "2                                      47.43   \n",
              "3                                      47.06   \n",
              "4                                      47.68   \n",
              "\n",
              "   General government final consumption expenditure (% of GDP)  \\\n",
              "0                                              10.68             \n",
              "1                                               9.89             \n",
              "2                                               9.78             \n",
              "3                                               9.11             \n",
              "4                                               8.79             \n",
              "\n",
              "   Household final consumption expenditure  (% of GDP)  \\\n",
              "0                                              38.70     \n",
              "1                                              38.91     \n",
              "2                                              37.64     \n",
              "3                                              37.95     \n",
              "4                                              38.90     \n",
              "\n",
              "   Gross capital formation (% of GDP)  \\\n",
              "0                               13.69   \n",
              "1                                9.75   \n",
              "2                               11.95   \n",
              "3                               12.65   \n",
              "4                                7.21   \n",
              "\n",
              "   Gross capital formation, Private sector (% GDP)  \\\n",
              "0                                             4.04   \n",
              "1                                             4.10   \n",
              "2                                             7.24   \n",
              "3                                             8.03   \n",
              "4                                             1.74   \n",
              "\n",
              "   Gross capital formation, Public sector (% GDP)  \\\n",
              "0                                            9.66   \n",
              "1                                            5.65   \n",
              "2                                            4.71   \n",
              "3                                            4.63   \n",
              "4                                            5.47   \n",
              "\n",
              "   Exports of goods and services (% of GDP)  \\\n",
              "0                                     13.75   \n",
              "1                                     14.20   \n",
              "2                                     12.56   \n",
              "3                                     11.52   \n",
              "4                                     15.88   \n",
              "\n",
              "   Imports of goods and services (% of GDP)  \\\n",
              "0                                     21.48   \n",
              "1                                     17.41   \n",
              "2                                     16.10   \n",
              "3                                     15.73   \n",
              "4                                     14.79   \n",
              "\n",
              "   Central government, Fiscal Balance (Current US $)  \\\n",
              "0                                            -142.96   \n",
              "1                                            -133.47   \n",
              "2                                            -119.21   \n",
              "3                                             -96.80   \n",
              "4                                             -78.94   \n",
              "\n",
              "   Central government, total revenue and grants  (Current US $)  \\\n",
              "0                                             298.61              \n",
              "1                                             276.61              \n",
              "2                                             254.71              \n",
              "3                                             250.68              \n",
              "4                                             239.30              \n",
              "\n",
              "   Central government, total expenditure and net lending  (Current US $)  \\\n",
              "0                                             441.57                       \n",
              "1                                             410.09                       \n",
              "2                                             373.92                       \n",
              "3                                             347.48                       \n",
              "4                                             318.24                       \n",
              "\n",
              "   Central government, Fiscal Balance (% of GDP)  \\\n",
              "0                                          -6.39   \n",
              "1                                          -5.97   \n",
              "2                                          -5.64   \n",
              "3                                          -4.39   \n",
              "4                                          -3.66   \n",
              "\n",
              "   Central government, total revenue and grants  (% of GDP)  \\\n",
              "0                                              13.35          \n",
              "1                                              12.37          \n",
              "2                                              12.05          \n",
              "3                                              11.38          \n",
              "4                                              11.09          \n",
              "\n",
              "   Central government, total expenditure and net lending  (% of GDP)  \\\n",
              "0                                              19.75                   \n",
              "1                                              18.34                   \n",
              "2                                              17.69                   \n",
              "3                                              15.77                   \n",
              "4                                              14.75                   \n",
              "\n",
              "   Current account balance (Net, BoP, cur. US$)  \\\n",
              "0                                       -207.07   \n",
              "1                                        -86.71   \n",
              "2                                        -91.15   \n",
              "3                                       -103.94   \n",
              "4                                          3.88   \n",
              "\n",
              "   Current account balance (As % of GDP)  \\\n",
              "0                                  -9.26   \n",
              "1                                  -3.88   \n",
              "2                                  -4.31   \n",
              "3                                  -4.72   \n",
              "4                                   0.18   \n",
              "\n",
              "   Inflation, consumer prices (annual %)  \n",
              "0                                    NaN  \n",
              "1                                  12.01  \n",
              "2                                   9.52  \n",
              "3                                  13.77  \n",
              "4                                  19.74  "
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              "      <th>Country</th>\n",
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              "      <th>Real per Capita GDP Growth Rate (annual %)</th>\n",
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              "      <th>Final consumption expenditure  (% of GDP)</th>\n",
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              "      <th>Household final consumption expenditure  (% of GDP)</th>\n",
              "      <th>Gross capital formation (% of GDP)</th>\n",
              "      <th>Gross capital formation, Private sector (% GDP)</th>\n",
              "      <th>Gross capital formation, Public sector (% GDP)</th>\n",
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              "      <th>Imports of goods and services (% of GDP)</th>\n",
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              "      <th>Central government, Fiscal Balance (% of GDP)</th>\n",
              "      <th>Central government, total revenue and grants  (% of GDP)</th>\n",
              "      <th>Central government, total expenditure and net lending  (% of GDP)</th>\n",
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              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Malawi</td>\n",
              "      <td>1980</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>3038.14</td>\n",
              "      <td>2236.36</td>\n",
              "      <td>1104.30</td>\n",
              "      <td>238.76</td>\n",
              "      <td>865.54</td>\n",
              "      <td>306.24</td>\n",
              "      <td>90.26</td>\n",
              "      <td>215.98</td>\n",
              "      <td>307.48</td>\n",
              "      <td>480.36</td>\n",
              "      <td>49.38</td>\n",
              "      <td>10.68</td>\n",
              "      <td>38.70</td>\n",
              "      <td>13.69</td>\n",
              "      <td>4.04</td>\n",
              "      <td>9.66</td>\n",
              "      <td>13.75</td>\n",
              "      <td>21.48</td>\n",
              "      <td>-142.96</td>\n",
              "      <td>298.61</td>\n",
              "      <td>441.57</td>\n",
              "      <td>-6.39</td>\n",
              "      <td>13.35</td>\n",
              "      <td>19.75</td>\n",
              "      <td>-207.07</td>\n",
              "      <td>-9.26</td>\n",
              "      <td>NaN</td>\n",
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              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Malawi</td>\n",
              "      <td>1981</td>\n",
              "      <td>-13.06</td>\n",
              "      <td>-10.81</td>\n",
              "      <td>2709.74</td>\n",
              "      <td>2236.40</td>\n",
              "      <td>1091.26</td>\n",
              "      <td>221.16</td>\n",
              "      <td>870.10</td>\n",
              "      <td>218.14</td>\n",
              "      <td>91.70</td>\n",
              "      <td>126.44</td>\n",
              "      <td>317.66</td>\n",
              "      <td>389.37</td>\n",
              "      <td>48.80</td>\n",
              "      <td>9.89</td>\n",
              "      <td>38.91</td>\n",
              "      <td>9.75</td>\n",
              "      <td>4.10</td>\n",
              "      <td>5.65</td>\n",
              "      <td>14.20</td>\n",
              "      <td>17.41</td>\n",
              "      <td>-133.47</td>\n",
              "      <td>276.61</td>\n",
              "      <td>410.09</td>\n",
              "      <td>-5.97</td>\n",
              "      <td>12.37</td>\n",
              "      <td>18.34</td>\n",
              "      <td>-86.71</td>\n",
              "      <td>-3.88</td>\n",
              "      <td>12.01</td>\n",
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              "      <th>2</th>\n",
              "      <td>Malawi</td>\n",
              "      <td>1982</td>\n",
              "      <td>-0.93</td>\n",
              "      <td>1.44</td>\n",
              "      <td>2748.84</td>\n",
              "      <td>2113.68</td>\n",
              "      <td>1002.45</td>\n",
              "      <td>206.82</td>\n",
              "      <td>795.63</td>\n",
              "      <td>252.58</td>\n",
              "      <td>153.01</td>\n",
              "      <td>99.57</td>\n",
              "      <td>265.46</td>\n",
              "      <td>340.40</td>\n",
              "      <td>47.43</td>\n",
              "      <td>9.78</td>\n",
              "      <td>37.64</td>\n",
              "      <td>11.95</td>\n",
              "      <td>7.24</td>\n",
              "      <td>4.71</td>\n",
              "      <td>12.56</td>\n",
              "      <td>16.10</td>\n",
              "      <td>-119.21</td>\n",
              "      <td>254.71</td>\n",
              "      <td>373.92</td>\n",
              "      <td>-5.64</td>\n",
              "      <td>12.05</td>\n",
              "      <td>17.69</td>\n",
              "      <td>-91.15</td>\n",
              "      <td>-4.31</td>\n",
              "      <td>9.52</td>\n",
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              "      <th>3</th>\n",
              "      <td>Malawi</td>\n",
              "      <td>1983</td>\n",
              "      <td>1.56</td>\n",
              "      <td>4.21</td>\n",
              "      <td>2864.70</td>\n",
              "      <td>2203.66</td>\n",
              "      <td>1037.06</td>\n",
              "      <td>200.81</td>\n",
              "      <td>836.26</td>\n",
              "      <td>278.87</td>\n",
              "      <td>176.89</td>\n",
              "      <td>101.98</td>\n",
              "      <td>253.84</td>\n",
              "      <td>346.54</td>\n",
              "      <td>47.06</td>\n",
              "      <td>9.11</td>\n",
              "      <td>37.95</td>\n",
              "      <td>12.65</td>\n",
              "      <td>8.03</td>\n",
              "      <td>4.63</td>\n",
              "      <td>11.52</td>\n",
              "      <td>15.73</td>\n",
              "      <td>-96.80</td>\n",
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              "      <td>-4.39</td>\n",
              "      <td>11.38</td>\n",
              "      <td>15.77</td>\n",
              "      <td>-103.94</td>\n",
              "      <td>-4.72</td>\n",
              "      <td>13.77</td>\n",
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              "      <th>4</th>\n",
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              "      <td>1984</td>\n",
              "      <td>0.54</td>\n",
              "      <td>3.92</td>\n",
              "      <td>2976.95</td>\n",
              "      <td>2157.88</td>\n",
              "      <td>1028.95</td>\n",
              "      <td>189.62</td>\n",
              "      <td>839.34</td>\n",
              "      <td>155.58</td>\n",
              "      <td>37.64</td>\n",
              "      <td>117.94</td>\n",
              "      <td>342.72</td>\n",
              "      <td>319.23</td>\n",
              "      <td>47.68</td>\n",
              "      <td>8.79</td>\n",
              "      <td>38.90</td>\n",
              "      <td>7.21</td>\n",
              "      <td>1.74</td>\n",
              "      <td>5.47</td>\n",
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              "      <td>14.79</td>\n",
              "      <td>-78.94</td>\n",
              "      <td>239.30</td>\n",
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              "      <td>14.75</td>\n",
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              "      <td>0.18</td>\n",
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          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Now years are columns, very good. "
      ],
      "metadata": {
        "id": "73ydC5MqXUIK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "africa_df = (africa_df.loc[(africa_df['Year'] >= 2003) & (africa_df['Year'] <= 2020)])\n",
        "africa_df = africa_df.reset_index().pivot(columns='Year', index='Country', values=['Real GDP growth (annual %)', 'Gross domestic product, (constant prices US$)'])\n",
        "africa_df.reset_index(inplace=True)\n",
        "africa_df.head()"
      ],
      "metadata": {
        "colab": {
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        "id": "PG6E8nq7EyKE",
        "outputId": "d72a7a4b-ea6c-49e5-d729-887c8e98978d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "           Country Real GDP growth (annual %)                              \\\n",
              "Year                                     2003   2004   2005   2006   2007   \n",
              "0          Algeria                       7.24   4.34   5.94   1.74   3.44   \n",
              "1           Angola                       2.99  10.95  15.03  11.55  14.01   \n",
              "2            Benin                       3.44   4.43   1.71   3.95   5.99   \n",
              "3         Botswana                       4.63   2.71   4.56   8.36   8.28   \n",
              "4     Burkina Faso                       8.04   4.48   8.73   6.03   4.44   \n",
              "\n",
              "                                                                            \\\n",
              "Year   2008  2009  2010      2011      2012       2013      2014      2015   \n",
              "0      2.44  1.64  3.64  2.900000  3.400000   2.840000  3.800000  3.700000   \n",
              "1     11.17  0.86  4.86  3.471981  8.542147   4.954590  4.822626  0.943576   \n",
              "2      4.89  2.32  2.12  2.964000  4.811000   7.191000  6.358000  1.778000   \n",
              "3      6.25 -7.65  8.56  6.000000  4.456145  11.343397  4.149262 -1.697935   \n",
              "4      5.63  2.96  8.44  6.600000  6.452672   5.792585  4.326846  3.921229   \n",
              "\n",
              "                                                        \\\n",
              "Year      2016      2017      2018      2019      2020   \n",
              "0     3.200000  1.300000  1.400000  0.800000 -4.737985   \n",
              "1    -2.580097 -0.147207 -2.003577 -0.600000 -4.520618   \n",
              "2     3.340000  5.672000  6.697000  6.865687  2.311357   \n",
              "3     4.303767  2.903998  4.478837  2.966126 -8.899091   \n",
              "4     5.957977  6.203489  6.731236  5.699435 -0.206372   \n",
              "\n",
              "     Gross domestic product, (constant prices US$)                        \\\n",
              "Year                                          2003       2004       2005   \n",
              "0                                        128419.81  133993.23  141952.43   \n",
              "1                                         43913.67   48723.48   56046.09   \n",
              "2                                          5434.86    5675.60    5772.74   \n",
              "3                                          9527.29    9785.08   10230.96   \n",
              "4                                          6052.52    6323.97    6875.95   \n",
              "\n",
              "                                                                            \\\n",
              "Year       2006       2007       2008       2009       2010           2011   \n",
              "0     144422.40  149390.53  153035.66  155545.45  161207.30  165882.311300   \n",
              "1      62518.11   71276.98   79235.77   79916.18   83799.48   86708.987140   \n",
              "2       6000.60    6359.82    6671.03    6825.75    6970.24    7176.838523   \n",
              "3      11086.67   12004.30   12754.01   11778.03   12786.65   13553.850930   \n",
              "4       7290.73    7614.50    8042.89    8281.25    8980.02    9572.706573   \n",
              "\n",
              "                                                                  \\\n",
              "Year           2012           2013           2014           2015   \n",
              "0     171522.309900  176393.543500  183096.498100  189871.068500   \n",
              "1      94115.796580   98778.848870  103542.582900  104519.585400   \n",
              "2       7522.116224    8063.031602    8575.679151    8728.154727   \n",
              "3      14157.830110   15763.808980   16417.890750   16139.125570   \n",
              "4      10190.401970   10780.689650   11247.153440   11688.180060   \n",
              "\n",
              "                                                                              \n",
              "Year           2016           2017          2018          2019          2020  \n",
              "0     195946.942700  198494.253000  201273.17250  202883.35790  193270.77580  \n",
              "1     101822.878500  101672.987700   99635.89131   99038.07596   94560.94247  \n",
              "2       9019.675095    9531.271066   10169.58029   10867.79180   11118.98528  \n",
              "3      16833.716010   17322.566730   18098.41618   18635.23794   16976.87120  \n",
              "4      12384.559110   13152.833920   14038.18216   14838.27922   14807.65720  "
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              "  <thead>\n",
              "    <tr>\n",
              "      <th></th>\n",
              "      <th>Country</th>\n",
              "      <th colspan=\"18\" halign=\"left\">Real GDP growth (annual %)</th>\n",
              "      <th colspan=\"18\" halign=\"left\">Gross domestic product, (constant prices US$)</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Year</th>\n",
              "      <th></th>\n",
              "      <th>2003</th>\n",
              "      <th>2004</th>\n",
              "      <th>2005</th>\n",
              "      <th>2006</th>\n",
              "      <th>2007</th>\n",
              "      <th>2008</th>\n",
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              "      <th>2011</th>\n",
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              "      <th>2015</th>\n",
              "      <th>2016</th>\n",
              "      <th>2017</th>\n",
              "      <th>2018</th>\n",
              "      <th>2019</th>\n",
              "      <th>2020</th>\n",
              "      <th>2003</th>\n",
              "      <th>2004</th>\n",
              "      <th>2005</th>\n",
              "      <th>2006</th>\n",
              "      <th>2007</th>\n",
              "      <th>2008</th>\n",
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              "      <th>2019</th>\n",
              "      <th>2020</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Algeria</td>\n",
              "      <td>7.24</td>\n",
              "      <td>4.34</td>\n",
              "      <td>5.94</td>\n",
              "      <td>1.74</td>\n",
              "      <td>3.44</td>\n",
              "      <td>2.44</td>\n",
              "      <td>1.64</td>\n",
              "      <td>3.64</td>\n",
              "      <td>2.900000</td>\n",
              "      <td>3.400000</td>\n",
              "      <td>2.840000</td>\n",
              "      <td>3.800000</td>\n",
              "      <td>3.700000</td>\n",
              "      <td>3.200000</td>\n",
              "      <td>1.300000</td>\n",
              "      <td>1.400000</td>\n",
              "      <td>0.800000</td>\n",
              "      <td>-4.737985</td>\n",
              "      <td>128419.81</td>\n",
              "      <td>133993.23</td>\n",
              "      <td>141952.43</td>\n",
              "      <td>144422.40</td>\n",
              "      <td>149390.53</td>\n",
              "      <td>153035.66</td>\n",
              "      <td>155545.45</td>\n",
              "      <td>161207.30</td>\n",
              "      <td>165882.311300</td>\n",
              "      <td>171522.309900</td>\n",
              "      <td>176393.543500</td>\n",
              "      <td>183096.498100</td>\n",
              "      <td>189871.068500</td>\n",
              "      <td>195946.942700</td>\n",
              "      <td>198494.253000</td>\n",
              "      <td>201273.17250</td>\n",
              "      <td>202883.35790</td>\n",
              "      <td>193270.77580</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Angola</td>\n",
              "      <td>2.99</td>\n",
              "      <td>10.95</td>\n",
              "      <td>15.03</td>\n",
              "      <td>11.55</td>\n",
              "      <td>14.01</td>\n",
              "      <td>11.17</td>\n",
              "      <td>0.86</td>\n",
              "      <td>4.86</td>\n",
              "      <td>3.471981</td>\n",
              "      <td>8.542147</td>\n",
              "      <td>4.954590</td>\n",
              "      <td>4.822626</td>\n",
              "      <td>0.943576</td>\n",
              "      <td>-2.580097</td>\n",
              "      <td>-0.147207</td>\n",
              "      <td>-2.003577</td>\n",
              "      <td>-0.600000</td>\n",
              "      <td>-4.520618</td>\n",
              "      <td>43913.67</td>\n",
              "      <td>48723.48</td>\n",
              "      <td>56046.09</td>\n",
              "      <td>62518.11</td>\n",
              "      <td>71276.98</td>\n",
              "      <td>79235.77</td>\n",
              "      <td>79916.18</td>\n",
              "      <td>83799.48</td>\n",
              "      <td>86708.987140</td>\n",
              "      <td>94115.796580</td>\n",
              "      <td>98778.848870</td>\n",
              "      <td>103542.582900</td>\n",
              "      <td>104519.585400</td>\n",
              "      <td>101822.878500</td>\n",
              "      <td>101672.987700</td>\n",
              "      <td>99635.89131</td>\n",
              "      <td>99038.07596</td>\n",
              "      <td>94560.94247</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Benin</td>\n",
              "      <td>3.44</td>\n",
              "      <td>4.43</td>\n",
              "      <td>1.71</td>\n",
              "      <td>3.95</td>\n",
              "      <td>5.99</td>\n",
              "      <td>4.89</td>\n",
              "      <td>2.32</td>\n",
              "      <td>2.12</td>\n",
              "      <td>2.964000</td>\n",
              "      <td>4.811000</td>\n",
              "      <td>7.191000</td>\n",
              "      <td>6.358000</td>\n",
              "      <td>1.778000</td>\n",
              "      <td>3.340000</td>\n",
              "      <td>5.672000</td>\n",
              "      <td>6.697000</td>\n",
              "      <td>6.865687</td>\n",
              "      <td>2.311357</td>\n",
              "      <td>5434.86</td>\n",
              "      <td>5675.60</td>\n",
              "      <td>5772.74</td>\n",
              "      <td>6000.60</td>\n",
              "      <td>6359.82</td>\n",
              "      <td>6671.03</td>\n",
              "      <td>6825.75</td>\n",
              "      <td>6970.24</td>\n",
              "      <td>7176.838523</td>\n",
              "      <td>7522.116224</td>\n",
              "      <td>8063.031602</td>\n",
              "      <td>8575.679151</td>\n",
              "      <td>8728.154727</td>\n",
              "      <td>9019.675095</td>\n",
              "      <td>9531.271066</td>\n",
              "      <td>10169.58029</td>\n",
              "      <td>10867.79180</td>\n",
              "      <td>11118.98528</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Botswana</td>\n",
              "      <td>4.63</td>\n",
              "      <td>2.71</td>\n",
              "      <td>4.56</td>\n",
              "      <td>8.36</td>\n",
              "      <td>8.28</td>\n",
              "      <td>6.25</td>\n",
              "      <td>-7.65</td>\n",
              "      <td>8.56</td>\n",
              "      <td>6.000000</td>\n",
              "      <td>4.456145</td>\n",
              "      <td>11.343397</td>\n",
              "      <td>4.149262</td>\n",
              "      <td>-1.697935</td>\n",
              "      <td>4.303767</td>\n",
              "      <td>2.903998</td>\n",
              "      <td>4.478837</td>\n",
              "      <td>2.966126</td>\n",
              "      <td>-8.899091</td>\n",
              "      <td>9527.29</td>\n",
              "      <td>9785.08</td>\n",
              "      <td>10230.96</td>\n",
              "      <td>11086.67</td>\n",
              "      <td>12004.30</td>\n",
              "      <td>12754.01</td>\n",
              "      <td>11778.03</td>\n",
              "      <td>12786.65</td>\n",
              "      <td>13553.850930</td>\n",
              "      <td>14157.830110</td>\n",
              "      <td>15763.808980</td>\n",
              "      <td>16417.890750</td>\n",
              "      <td>16139.125570</td>\n",
              "      <td>16833.716010</td>\n",
              "      <td>17322.566730</td>\n",
              "      <td>18098.41618</td>\n",
              "      <td>18635.23794</td>\n",
              "      <td>16976.87120</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Burkina Faso</td>\n",
              "      <td>8.04</td>\n",
              "      <td>4.48</td>\n",
              "      <td>8.73</td>\n",
              "      <td>6.03</td>\n",
              "      <td>4.44</td>\n",
              "      <td>5.63</td>\n",
              "      <td>2.96</td>\n",
              "      <td>8.44</td>\n",
              "      <td>6.600000</td>\n",
              "      <td>6.452672</td>\n",
              "      <td>5.792585</td>\n",
              "      <td>4.326846</td>\n",
              "      <td>3.921229</td>\n",
              "      <td>5.957977</td>\n",
              "      <td>6.203489</td>\n",
              "      <td>6.731236</td>\n",
              "      <td>5.699435</td>\n",
              "      <td>-0.206372</td>\n",
              "      <td>6052.52</td>\n",
              "      <td>6323.97</td>\n",
              "      <td>6875.95</td>\n",
              "      <td>7290.73</td>\n",
              "      <td>7614.50</td>\n",
              "      <td>8042.89</td>\n",
              "      <td>8281.25</td>\n",
              "      <td>8980.02</td>\n",
              "      <td>9572.706573</td>\n",
              "      <td>10190.401970</td>\n",
              "      <td>10780.689650</td>\n",
              "      <td>11247.153440</td>\n",
              "      <td>11688.180060</td>\n",
              "      <td>12384.559110</td>\n",
              "      <td>13152.833920</td>\n",
              "      <td>14038.18216</td>\n",
              "      <td>14838.27922</td>\n",
              "      <td>14807.65720</td>\n",
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          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Let's merge the two together and take a look."
      ],
      "metadata": {
        "id": "qAKk-527XXaX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "merged_df = pd.merge(left = cleaner_invest, right = africa_df, left_on = \"Country\", right_on = \"Country\", how = \"inner\")\n",
        "merged_df = merged_df.dropna()\n",
        "merged_df.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 446
        },
        "id": "AsmnYFveSdXk",
        "outputId": "2ae26653-b7e4-4d23-ba47-3c8167840ea8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:1: FutureWarning: merging between different levels is deprecated and will be removed in a future version. (1 levels on the left,2 on the right)\n",
            "  \"\"\"Entry point for launching an IPython kernel.\n",
            "/usr/local/lib/python3.7/dist-packages/pandas/core/generic.py:4150: PerformanceWarning: dropping on a non-lexsorted multi-index without a level parameter may impact performance.\n",
            "  obj = obj._drop_axis(labels, axis, level=level, errors=errors)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    Country 2003_invest 2004_invest 2005_invest 2006_invest 2007_invest  \\\n",
              "0   Algeria         5.7       34.49      171.21      247.37      393.89   \n",
              "1    Angola         0.3        0.47        8.79       37.23       78.46   \n",
              "2     Benin        7.71       20.51        19.0       22.12        35.6   \n",
              "3  Botswana         2.1         3.8       18.12       25.52       43.39   \n",
              "5   Burundi         0.0        0.02         0.0        1.65        1.65   \n",
              "\n",
              "  2008_invest 2009_invest 2010_invest 2011_invest 2012_invest 2013_invest  \\\n",
              "0      508.82      751.26      937.26     1059.45     1305.33     1497.21   \n",
              "1       68.89      195.54      351.77      400.59      1245.1     1634.74   \n",
              "2       53.15       54.01       39.33       40.03        47.6       49.91   \n",
              "3       65.26      119.25      178.52      200.38      220.15       230.9   \n",
              "5        1.65        4.64        6.51         7.2         8.7        9.79   \n",
              "\n",
              "  2014_invest 2015_invest 2016_invest 2017_invest 2018_invest 2019_invest  \\\n",
              "0     2451.57     2531.55     2552.48     1833.66     2062.86     1775.35   \n",
              "1     1214.04     1268.29     1633.21     2260.16     2299.19     2890.73   \n",
              "2       69.17       87.31      102.51      104.37      103.99       91.44   \n",
              "3      262.13      321.08       437.5      296.87      258.16      186.28   \n",
              "5       13.24       12.37       12.42       10.29       12.52         8.2   \n",
              "\n",
              "  2020_invest  (Real GDP growth (annual %), 2003)  \\\n",
              "0   1643.5174                                7.24   \n",
              "1     2690.09                                2.99   \n",
              "2       75.46                                3.44   \n",
              "3      190.43                                4.63   \n",
              "5       10.52                               -1.22   \n",
              "\n",
              "   (Real GDP growth (annual %), 2004)  (Real GDP growth (annual %), 2005)  \\\n",
              "0                                4.34                                5.94   \n",
              "1                               10.95                               15.03   \n",
              "2                                4.43                                1.71   \n",
              "3                                2.71                                4.56   \n",
              "5                                4.83                                0.91   \n",
              "\n",
              "   (Real GDP growth (annual %), 2006)  (Real GDP growth (annual %), 2007)  \\\n",
              "0                                1.74                                3.44   \n",
              "1                               11.55                               14.01   \n",
              "2                                3.95                                5.99   \n",
              "3                                8.36                                8.28   \n",
              "5                                5.42                                3.50   \n",
              "\n",
              "   (Real GDP growth (annual %), 2008)  (Real GDP growth (annual %), 2009)  \\\n",
              "0                                2.44                                1.64   \n",
              "1                               11.17                                0.86   \n",
              "2                                4.89                                2.32   \n",
              "3                                6.25                               -7.65   \n",
              "5                                4.86                                3.81   \n",
              "\n",
              "   (Real GDP growth (annual %), 2010)  (Real GDP growth (annual %), 2011)  \\\n",
              "0                                3.64                            2.900000   \n",
              "1                                4.86                            3.471981   \n",
              "2                                2.12                            2.964000   \n",
              "3                                8.56                            6.000000   \n",
              "5                                5.12                            4.032602   \n",
              "\n",
              "   (Real GDP growth (annual %), 2012)  (Real GDP growth (annual %), 2013)  \\\n",
              "0                            3.400000                            2.840000   \n",
              "1                            8.542147                            4.954590   \n",
              "2                            4.811000                            7.191000   \n",
              "3                            4.456145                           11.343397   \n",
              "5                            4.400000                            4.900000   \n",
              "\n",
              "   (Real GDP growth (annual %), 2014)  (Real GDP growth (annual %), 2015)  \\\n",
              "0                            3.800000                            3.700000   \n",
              "1                            4.822626                            0.943576   \n",
              "2                            6.358000                            1.778000   \n",
              "3                            4.149262                           -1.697935   \n",
              "5                            4.200000                           -0.400000   \n",
              "\n",
              "   (Real GDP growth (annual %), 2016)  (Real GDP growth (annual %), 2017)  \\\n",
              "0                            3.200000                            1.300000   \n",
              "1                           -2.580097                           -0.147207   \n",
              "2                            3.340000                            5.672000   \n",
              "3                            4.303767                            2.903998   \n",
              "5                            3.200000                            3.800000   \n",
              "\n",
              "   (Real GDP growth (annual %), 2018)  (Real GDP growth (annual %), 2019)  \\\n",
              "0                            1.400000                            0.800000   \n",
              "1                           -2.003577                           -0.600000   \n",
              "2                            6.697000                            6.865687   \n",
              "3                            4.478837                            2.966126   \n",
              "5                            4.200000                            4.100000   \n",
              "\n",
              "   (Real GDP growth (annual %), 2020)  \\\n",
              "0                           -4.737985   \n",
              "1                           -4.520618   \n",
              "2                            2.311357   \n",
              "3                           -8.899091   \n",
              "5                           -3.274460   \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2003)  \\\n",
              "0                                          128419.81       \n",
              "1                                           43913.67       \n",
              "2                                            5434.86       \n",
              "3                                            9527.29       \n",
              "5                                            1538.53       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2004)  \\\n",
              "0                                          133993.23       \n",
              "1                                           48723.48       \n",
              "2                                            5675.60       \n",
              "3                                            9785.08       \n",
              "5                                            1612.89       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2005)  \\\n",
              "0                                          141952.43       \n",
              "1                                           56046.09       \n",
              "2                                            5772.74       \n",
              "3                                           10230.96       \n",
              "5                                            1627.53       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2006)  \\\n",
              "0                                          144422.40       \n",
              "1                                           62518.11       \n",
              "2                                            6000.60       \n",
              "3                                           11086.67       \n",
              "5                                            1715.70       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2007)  \\\n",
              "0                                          149390.53       \n",
              "1                                           71276.98       \n",
              "2                                            6359.82       \n",
              "3                                           12004.30       \n",
              "5                                            1775.75       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2008)  \\\n",
              "0                                          153035.66       \n",
              "1                                           79235.77       \n",
              "2                                            6671.03       \n",
              "3                                           12754.01       \n",
              "5                                            1862.08       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2009)  \\\n",
              "0                                          155545.45       \n",
              "1                                           79916.18       \n",
              "2                                            6825.75       \n",
              "3                                           11778.03       \n",
              "5                                            1933.08       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2010)  \\\n",
              "0                                          161207.30       \n",
              "1                                           83799.48       \n",
              "2                                            6970.24       \n",
              "3                                           12786.65       \n",
              "5                                            2032.14       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2011)  \\\n",
              "0                                      165882.311300       \n",
              "1                                       86708.987140       \n",
              "2                                        7176.838523       \n",
              "3                                       13553.850930       \n",
              "5                                        2114.083126       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2012)  \\\n",
              "0                                      171522.309900       \n",
              "1                                       94115.796580       \n",
              "2                                        7522.116224       \n",
              "3                                       14157.830110       \n",
              "5                                        2207.102783       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2013)  \\\n",
              "0                                      176393.543500       \n",
              "1                                       98778.848870       \n",
              "2                                        8063.031602       \n",
              "3                                       15763.808980       \n",
              "5                                        2315.250820       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2014)  \\\n",
              "0                                      183096.498100       \n",
              "1                                      103542.582900       \n",
              "2                                        8575.679151       \n",
              "3                                       16417.890750       \n",
              "5                                        2412.491354       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2015)  \\\n",
              "0                                      189871.068500       \n",
              "1                                      104519.585400       \n",
              "2                                        8728.154727       \n",
              "3                                       16139.125570       \n",
              "5                                        2402.841389       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2016)  \\\n",
              "0                                      195946.942700       \n",
              "1                                      101822.878500       \n",
              "2                                        9019.675095       \n",
              "3                                       16833.716010       \n",
              "5                                        2479.732313       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2017)  \\\n",
              "0                                      198494.253000       \n",
              "1                                      101672.987700       \n",
              "2                                        9531.271066       \n",
              "3                                       17322.566730       \n",
              "5                                        2573.962141       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2018)  \\\n",
              "0                                      201273.172500       \n",
              "1                                       99635.891310       \n",
              "2                                       10169.580290       \n",
              "3                                       18098.416180       \n",
              "5                                        2682.068551       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2019)  \\\n",
              "0                                      202883.357900       \n",
              "1                                       99038.075960       \n",
              "2                                       10867.791800       \n",
              "3                                       18635.237940       \n",
              "5                                        2792.033362       \n",
              "\n",
              "   (Gross domestic product, (constant prices US$), 2020)  \n",
              "0                                      193270.775800      \n",
              "1                                       94560.942470      \n",
              "2                                       11118.985280      \n",
              "3                                       16976.871200      \n",
              "5                                        2700.609345      "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-696e3b46-9842-4b2a-9ecb-5086e326bf5c\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Country</th>\n",
              "      <th>2003_invest</th>\n",
              "      <th>2004_invest</th>\n",
              "      <th>2005_invest</th>\n",
              "      <th>2006_invest</th>\n",
              "      <th>2007_invest</th>\n",
              "      <th>2008_invest</th>\n",
              "      <th>2009_invest</th>\n",
              "      <th>2010_invest</th>\n",
              "      <th>2011_invest</th>\n",
              "      <th>2012_invest</th>\n",
              "      <th>2013_invest</th>\n",
              "      <th>2014_invest</th>\n",
              "      <th>2015_invest</th>\n",
              "      <th>2016_invest</th>\n",
              "      <th>2017_invest</th>\n",
              "      <th>2018_invest</th>\n",
              "      <th>2019_invest</th>\n",
              "      <th>2020_invest</th>\n",
              "      <th>(Real GDP growth (annual %), 2003)</th>\n",
              "      <th>(Real GDP growth (annual %), 2004)</th>\n",
              "      <th>(Real GDP growth (annual %), 2005)</th>\n",
              "      <th>(Real GDP growth (annual %), 2006)</th>\n",
              "      <th>(Real GDP growth (annual %), 2007)</th>\n",
              "      <th>(Real GDP growth (annual %), 2008)</th>\n",
              "      <th>(Real GDP growth (annual %), 2009)</th>\n",
              "      <th>(Real GDP growth (annual %), 2010)</th>\n",
              "      <th>(Real GDP growth (annual %), 2011)</th>\n",
              "      <th>(Real GDP growth (annual %), 2012)</th>\n",
              "      <th>(Real GDP growth (annual %), 2013)</th>\n",
              "      <th>(Real GDP growth (annual %), 2014)</th>\n",
              "      <th>(Real GDP growth (annual %), 2015)</th>\n",
              "      <th>(Real GDP growth (annual %), 2016)</th>\n",
              "      <th>(Real GDP growth (annual %), 2017)</th>\n",
              "      <th>(Real GDP growth (annual %), 2018)</th>\n",
              "      <th>(Real GDP growth (annual %), 2019)</th>\n",
              "      <th>(Real GDP growth (annual %), 2020)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2003)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2004)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2005)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2006)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2007)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2008)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2009)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2010)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2011)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2012)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2013)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2014)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2015)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2016)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2017)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2018)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2019)</th>\n",
              "      <th>(Gross domestic product, (constant prices US$), 2020)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Algeria</td>\n",
              "      <td>5.7</td>\n",
              "      <td>34.49</td>\n",
              "      <td>171.21</td>\n",
              "      <td>247.37</td>\n",
              "      <td>393.89</td>\n",
              "      <td>508.82</td>\n",
              "      <td>751.26</td>\n",
              "      <td>937.26</td>\n",
              "      <td>1059.45</td>\n",
              "      <td>1305.33</td>\n",
              "      <td>1497.21</td>\n",
              "      <td>2451.57</td>\n",
              "      <td>2531.55</td>\n",
              "      <td>2552.48</td>\n",
              "      <td>1833.66</td>\n",
              "      <td>2062.86</td>\n",
              "      <td>1775.35</td>\n",
              "      <td>1643.5174</td>\n",
              "      <td>7.24</td>\n",
              "      <td>4.34</td>\n",
              "      <td>5.94</td>\n",
              "      <td>1.74</td>\n",
              "      <td>3.44</td>\n",
              "      <td>2.44</td>\n",
              "      <td>1.64</td>\n",
              "      <td>3.64</td>\n",
              "      <td>2.900000</td>\n",
              "      <td>3.400000</td>\n",
              "      <td>2.840000</td>\n",
              "      <td>3.800000</td>\n",
              "      <td>3.700000</td>\n",
              "      <td>3.200000</td>\n",
              "      <td>1.300000</td>\n",
              "      <td>1.400000</td>\n",
              "      <td>0.800000</td>\n",
              "      <td>-4.737985</td>\n",
              "      <td>128419.81</td>\n",
              "      <td>133993.23</td>\n",
              "      <td>141952.43</td>\n",
              "      <td>144422.40</td>\n",
              "      <td>149390.53</td>\n",
              "      <td>153035.66</td>\n",
              "      <td>155545.45</td>\n",
              "      <td>161207.30</td>\n",
              "      <td>165882.311300</td>\n",
              "      <td>171522.309900</td>\n",
              "      <td>176393.543500</td>\n",
              "      <td>183096.498100</td>\n",
              "      <td>189871.068500</td>\n",
              "      <td>195946.942700</td>\n",
              "      <td>198494.253000</td>\n",
              "      <td>201273.172500</td>\n",
              "      <td>202883.357900</td>\n",
              "      <td>193270.775800</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Angola</td>\n",
              "      <td>0.3</td>\n",
              "      <td>0.47</td>\n",
              "      <td>8.79</td>\n",
              "      <td>37.23</td>\n",
              "      <td>78.46</td>\n",
              "      <td>68.89</td>\n",
              "      <td>195.54</td>\n",
              "      <td>351.77</td>\n",
              "      <td>400.59</td>\n",
              "      <td>1245.1</td>\n",
              "      <td>1634.74</td>\n",
              "      <td>1214.04</td>\n",
              "      <td>1268.29</td>\n",
              "      <td>1633.21</td>\n",
              "      <td>2260.16</td>\n",
              "      <td>2299.19</td>\n",
              "      <td>2890.73</td>\n",
              "      <td>2690.09</td>\n",
              "      <td>2.99</td>\n",
              "      <td>10.95</td>\n",
              "      <td>15.03</td>\n",
              "      <td>11.55</td>\n",
              "      <td>14.01</td>\n",
              "      <td>11.17</td>\n",
              "      <td>0.86</td>\n",
              "      <td>4.86</td>\n",
              "      <td>3.471981</td>\n",
              "      <td>8.542147</td>\n",
              "      <td>4.954590</td>\n",
              "      <td>4.822626</td>\n",
              "      <td>0.943576</td>\n",
              "      <td>-2.580097</td>\n",
              "      <td>-0.147207</td>\n",
              "      <td>-2.003577</td>\n",
              "      <td>-0.600000</td>\n",
              "      <td>-4.520618</td>\n",
              "      <td>43913.67</td>\n",
              "      <td>48723.48</td>\n",
              "      <td>56046.09</td>\n",
              "      <td>62518.11</td>\n",
              "      <td>71276.98</td>\n",
              "      <td>79235.77</td>\n",
              "      <td>79916.18</td>\n",
              "      <td>83799.48</td>\n",
              "      <td>86708.987140</td>\n",
              "      <td>94115.796580</td>\n",
              "      <td>98778.848870</td>\n",
              "      <td>103542.582900</td>\n",
              "      <td>104519.585400</td>\n",
              "      <td>101822.878500</td>\n",
              "      <td>101672.987700</td>\n",
              "      <td>99635.891310</td>\n",
              "      <td>99038.075960</td>\n",
              "      <td>94560.942470</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Benin</td>\n",
              "      <td>7.71</td>\n",
              "      <td>20.51</td>\n",
              "      <td>19.0</td>\n",
              "      <td>22.12</td>\n",
              "      <td>35.6</td>\n",
              "      <td>53.15</td>\n",
              "      <td>54.01</td>\n",
              "      <td>39.33</td>\n",
              "      <td>40.03</td>\n",
              "      <td>47.6</td>\n",
              "      <td>49.91</td>\n",
              "      <td>69.17</td>\n",
              "      <td>87.31</td>\n",
              "      <td>102.51</td>\n",
              "      <td>104.37</td>\n",
              "      <td>103.99</td>\n",
              "      <td>91.44</td>\n",
              "      <td>75.46</td>\n",
              "      <td>3.44</td>\n",
              "      <td>4.43</td>\n",
              "      <td>1.71</td>\n",
              "      <td>3.95</td>\n",
              "      <td>5.99</td>\n",
              "      <td>4.89</td>\n",
              "      <td>2.32</td>\n",
              "      <td>2.12</td>\n",
              "      <td>2.964000</td>\n",
              "      <td>4.811000</td>\n",
              "      <td>7.191000</td>\n",
              "      <td>6.358000</td>\n",
              "      <td>1.778000</td>\n",
              "      <td>3.340000</td>\n",
              "      <td>5.672000</td>\n",
              "      <td>6.697000</td>\n",
              "      <td>6.865687</td>\n",
              "      <td>2.311357</td>\n",
              "      <td>5434.86</td>\n",
              "      <td>5675.60</td>\n",
              "      <td>5772.74</td>\n",
              "      <td>6000.60</td>\n",
              "      <td>6359.82</td>\n",
              "      <td>6671.03</td>\n",
              "      <td>6825.75</td>\n",
              "      <td>6970.24</td>\n",
              "      <td>7176.838523</td>\n",
              "      <td>7522.116224</td>\n",
              "      <td>8063.031602</td>\n",
              "      <td>8575.679151</td>\n",
              "      <td>8728.154727</td>\n",
              "      <td>9019.675095</td>\n",
              "      <td>9531.271066</td>\n",
              "      <td>10169.580290</td>\n",
              "      <td>10867.791800</td>\n",
              "      <td>11118.985280</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Botswana</td>\n",
              "      <td>2.1</td>\n",
              "      <td>3.8</td>\n",
              "      <td>18.12</td>\n",
              "      <td>25.52</td>\n",
              "      <td>43.39</td>\n",
              "      <td>65.26</td>\n",
              "      <td>119.25</td>\n",
              "      <td>178.52</td>\n",
              "      <td>200.38</td>\n",
              "      <td>220.15</td>\n",
              "      <td>230.9</td>\n",
              "      <td>262.13</td>\n",
              "      <td>321.08</td>\n",
              "      <td>437.5</td>\n",
              "      <td>296.87</td>\n",
              "      <td>258.16</td>\n",
              "      <td>186.28</td>\n",
              "      <td>190.43</td>\n",
              "      <td>4.63</td>\n",
              "      <td>2.71</td>\n",
              "      <td>4.56</td>\n",
              "      <td>8.36</td>\n",
              "      <td>8.28</td>\n",
              "      <td>6.25</td>\n",
              "      <td>-7.65</td>\n",
              "      <td>8.56</td>\n",
              "      <td>6.000000</td>\n",
              "      <td>4.456145</td>\n",
              "      <td>11.343397</td>\n",
              "      <td>4.149262</td>\n",
              "      <td>-1.697935</td>\n",
              "      <td>4.303767</td>\n",
              "      <td>2.903998</td>\n",
              "      <td>4.478837</td>\n",
              "      <td>2.966126</td>\n",
              "      <td>-8.899091</td>\n",
              "      <td>9527.29</td>\n",
              "      <td>9785.08</td>\n",
              "      <td>10230.96</td>\n",
              "      <td>11086.67</td>\n",
              "      <td>12004.30</td>\n",
              "      <td>12754.01</td>\n",
              "      <td>11778.03</td>\n",
              "      <td>12786.65</td>\n",
              "      <td>13553.850930</td>\n",
              "      <td>14157.830110</td>\n",
              "      <td>15763.808980</td>\n",
              "      <td>16417.890750</td>\n",
              "      <td>16139.125570</td>\n",
              "      <td>16833.716010</td>\n",
              "      <td>17322.566730</td>\n",
              "      <td>18098.416180</td>\n",
              "      <td>18635.237940</td>\n",
              "      <td>16976.871200</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Burundi</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.02</td>\n",
              "      <td>0.0</td>\n",
              "      <td>1.65</td>\n",
              "      <td>1.65</td>\n",
              "      <td>1.65</td>\n",
              "      <td>4.64</td>\n",
              "      <td>6.51</td>\n",
              "      <td>7.2</td>\n",
              "      <td>8.7</td>\n",
              "      <td>9.79</td>\n",
              "      <td>13.24</td>\n",
              "      <td>12.37</td>\n",
              "      <td>12.42</td>\n",
              "      <td>10.29</td>\n",
              "      <td>12.52</td>\n",
              "      <td>8.2</td>\n",
              "      <td>10.52</td>\n",
              "      <td>-1.22</td>\n",
              "      <td>4.83</td>\n",
              "      <td>0.91</td>\n",
              "      <td>5.42</td>\n",
              "      <td>3.50</td>\n",
              "      <td>4.86</td>\n",
              "      <td>3.81</td>\n",
              "      <td>5.12</td>\n",
              "      <td>4.032602</td>\n",
              "      <td>4.400000</td>\n",
              "      <td>4.900000</td>\n",
              "      <td>4.200000</td>\n",
              "      <td>-0.400000</td>\n",
              "      <td>3.200000</td>\n",
              "      <td>3.800000</td>\n",
              "      <td>4.200000</td>\n",
              "      <td>4.100000</td>\n",
              "      <td>-3.274460</td>\n",
              "      <td>1538.53</td>\n",
              "      <td>1612.89</td>\n",
              "      <td>1627.53</td>\n",
              "      <td>1715.70</td>\n",
              "      <td>1775.75</td>\n",
              "      <td>1862.08</td>\n",
              "      <td>1933.08</td>\n",
              "      <td>2032.14</td>\n",
              "      <td>2114.083126</td>\n",
              "      <td>2207.102783</td>\n",
              "      <td>2315.250820</td>\n",
              "      <td>2412.491354</td>\n",
              "      <td>2402.841389</td>\n",
              "      <td>2479.732313</td>\n",
              "      <td>2573.962141</td>\n",
              "      <td>2682.068551</td>\n",
              "      <td>2792.033362</td>\n",
              "      <td>2700.609345</td>\n",
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            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Renaming the columns so that they are easier to work with. "
      ],
      "metadata": {
        "id": "Nc6_iIvAXcqr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mdf = merged_df.rename(columns={merged_df.columns[19]: '2003_growthGDP', merged_df.columns[20]: '2004_growthGDP', merged_df.columns[21]: '2005_growthGDP', merged_df.columns[22]: '2006_growthGDP', merged_df.columns[23]: '2007_growthGDP',\n",
        "                                merged_df.columns[24]: '2008_growthGDP', merged_df.columns[25]: '2009_growthGDP', merged_df.columns[26]: '2010_growthGDP', merged_df.columns[27]: '2011_growthGDP', merged_df.columns[28]: '2012_growthGDP', \n",
        "                                merged_df.columns[29]: '2013_growthGDP', merged_df.columns[30]: '2014_growthGDP', merged_df.columns[31]: '2015_growthGDP', merged_df.columns[32]: '2016_growthGDP', merged_df.columns[33]: '2017_growthGDP',\n",
        "                                merged_df.columns[34]: '2018_growthGDP', merged_df.columns[35]: '2019_growthGDP', merged_df.columns[36]: '2020_growthGDP', merged_df.columns[37]: '2003_realGDP', merged_df.columns[38]: '2004_realGDP', \n",
        "                                merged_df.columns[39]: '2005_realGDP', merged_df.columns[40]: '2006_realGDP', merged_df.columns[41]: '2007_realGDP', merged_df.columns[42]: '2008_realGDP', merged_df.columns[43]: '2009_realGDP',\n",
        "                                merged_df.columns[44]: '2010_realGDP', merged_df.columns[45]: '2011_realGDP', merged_df.columns[46]: '2012_realGDP', merged_df.columns[47]: '2013_realGDP', merged_df.columns[48]: '2014_realGDP', \n",
        "                                merged_df.columns[49]: '2015_realGDP', merged_df.columns[50]: '2016_realGDP', merged_df.columns[51]: '2017_realGDP', merged_df.columns[52]: '2018_realGDP', merged_df.columns[53]: '2019_realGDP', \n",
        "                                merged_df.columns[54]: '2020_realGDP'})"
      ],
      "metadata": {
        "id": "-UkpspGfWKke"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Making an average of all of our fields and appending them to the end of the dataframe."
      ],
      "metadata": {
        "id": "tl-9xF8dQtUK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "mdf['average_invest'] = mdf.iloc[:, 1:18].astype(float).mean(axis=1)\n",
        "mdf['average_growthGDP'] = mdf.iloc[:, 19:36].astype(float).mean(axis=1)\n",
        "mdf['average_realGDP'] = mdf.iloc[:, 37:54].astype(float).mean(axis=1)"
      ],
      "metadata": {
        "id": "_Jj18l3XrA79"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x = ['Country', 'average_invest', 'average_realGDP']\n",
        "avg_mdf = mdf[x]\n",
        "avg_mdf.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "sxiS6JvfDkP7",
        "outputId": "5e621ea0-c5ae-4b3a-ea7b-619d25325706"
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      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    Country  average_invest  average_realGDP\n",
              "0   Algeria     1183.497647    167842.956906\n",
              "1    Angola      916.911765     83250.905551\n",
              "2     Benin       55.750588      7609.692852\n",
              "3  Botswana      168.788824     13933.849012\n",
              "5   Burundi        6.520588      2122.192108"
            ],
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              "      <td>1183.497647</td>\n",
              "      <td>167842.956906</td>\n",
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              "      <th>2</th>\n",
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              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Burundi</td>\n",
              "      <td>6.520588</td>\n",
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              "                                                     [key], {});\n",
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      "cell_type": "markdown",
      "source": [
        "Check for outliers beyond our Z score range of 3 (absolute value). Essentially no more than three standard deviations away, making corrections where needed. "
      ],
      "metadata": {
        "id": "ppsvZdbUFJ5m"
      }
    },
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        "mdf.boxplot(column = ['average_invest'])"
      ],
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          "height": 284
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        "id": "eMVH6nv_FJUZ",
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      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fdcb5176250>"
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          },
          "metadata": {},
          "execution_count": 52
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "use = ['average_invest', 'average_realGDP']\n",
        "#find absolute value of z-score for each observation\n",
        "z = np.abs(stats.zscore(mdf[use]))\n",
        "\n",
        "#only keep rows in dataframe with all z-scores less than absolute value of 3 \n",
        "mdf = mdf[use][(z<3).all(axis=1)]"
      ],
      "metadata": {
        "id": "pSu-ex1JFVYQ"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "mdf.boxplot(column = ['average_invest'])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 284
        },
        "id": "ujks6VydF8Bi",
        "outputId": "f89cbd4e-98f9-464c-c1eb-0f51c7b5ee41"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fdcae4f9e50>"
            ]
          },
          "metadata": {},
          "execution_count": 54
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Linear assumption is met, however fit could be better with some transformations."
      ],
      "metadata": {
        "id": "asqPWvK_SCLq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "g = sns.lmplot(x='average_invest',y='average_realGDP',data=mdf,\n",
        "          ci=0,line_kws={'color':'r','lw':3},scatter_kws={'color':'k','s':5})\n",
        "\n",
        "ax = g.axes[0,0]\n",
        "ax.set_xlim((0,1100))\n",
        "ax.set_ylim((0,60000))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 391
        },
        "id": "hFgmSHLLOI1Y",
        "outputId": "2be4b646-cf17-44b3-ab4b-a83b4d1c734f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.0, 60000.0)"
            ]
          },
          "metadata": {},
          "execution_count": 56
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Transforming the x variable seems somewhat better, but not great."
      ],
      "metadata": {
        "id": "y845YQ-8SKst"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "g = sns.lmplot(x='average_invest',y='average_realGDP',data=mdf,\n",
        "          ci=0,line_kws={'color':'r','lw':3},scatter_kws={'color':'k','s':5})\n",
        "\n",
        "ax = g.axes[0,0]\n",
        "ax.set_xlim((1,1100))\n",
        "ax.set_ylim((0,10000))\n",
        "ax.set_xscale('log')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 377
        },
        "id": "SfKvFjVhRntW",
        "outputId": "b6e145f9-dd6d-4deb-b7e9-327ef59fda49"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Transforming the y variable produces really promising results - we'll test model with this."
      ],
      "metadata": {
        "id": "YapfgpoQSRm1"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "g = sns.lmplot(x='average_invest',y='average_realGDP',data=mdf,\n",
        "          ci=0,line_kws={'color':'r','lw':3},scatter_kws={'color':'k','s':5})\n",
        "\n",
        "ax = g.axes[0,0]\n",
        "ax.set_xlim((0,1100))\n",
        "ax.set_ylim((900,1000000))\n",
        "ax.set_yscale('log')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 375
        },
        "id": "dYF2wiXzPo6i",
        "outputId": "8ead4c36-fe06-4397-e43e-00eae9e79c94"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 360x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "feature_df = mdf[['average_invest']]\n",
        "label_df = mdf['average_realGDP']\n",
        "logLabel_df = label_df.apply(np.log)"
      ],
      "metadata": {
        "id": "gCLaP_GQnVFY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def linear_regression_assumptions(features, label, feature_names=None):\n",
        "    \"\"\"\n",
        "    Tests a linear regression on the model to see if assumptions are being met\n",
        "    \"\"\"\n",
        "    from sklearn.linear_model import LinearRegression\n",
        "    \n",
        "    # Setting feature names to x1, x2, x3, etc. if they are not defined\n",
        "    if feature_names is None:\n",
        "        feature_names = ['X'+str(feature+1) for feature in range(features.shape[1])]\n",
        "    \n",
        "    print('Fitting linear regression')\n",
        "    # Multi-threading if the dataset is a size where doing so is beneficial\n",
        "    if features.shape[0] < 100000:\n",
        "        model = LinearRegression(n_jobs=-1)\n",
        "    else:\n",
        "        model = LinearRegression()\n",
        "        \n",
        "    model.fit(features, label)\n",
        "    \n",
        "    # Returning linear regression R^2 and coefficients before performing diagnostics\n",
        "    r2 = model.score(features, label)\n",
        "    print()\n",
        "    print('R^2:', r2, '\\n')\n",
        "    print('Coefficients')\n",
        "    print('-------------------------------------')\n",
        "    print('Intercept:', model.intercept_)\n",
        "    \n",
        "    for feature in range(len(model.coef_)):\n",
        "        print('{0}: {1}'.format(feature_names[feature], model.coef_[feature]))\n",
        "\n",
        "    print('\\nPerforming linear regression assumption testing')\n",
        "    \n",
        "    # Creating predictions and calculating residuals for assumption tests\n",
        "    predictions = model.predict(features)\n",
        "    df_results = pd.DataFrame({'Actual': label, 'Predicted': predictions})\n",
        "    df_results['Residuals'] = abs(df_results['Actual']) - abs(df_results['Predicted'])\n",
        "\n",
        "    \n",
        "    def linear_assumption():\n",
        "        \"\"\"\n",
        "        Linearity: Assumes there is a linear relationship between the predictors and\n",
        "                   the response variable. If not, either a polynomial term or another\n",
        "                   algorithm should be used.\n",
        "        \"\"\"\n",
        "        print('\\n=======================================================================================')\n",
        "        print('Assumption 1: Linear Relationship between the Target and the Features')\n",
        "        \n",
        "        print('Checking with a scatter plot of actual vs. predicted. Predictions should follow the diagonal line.')\n",
        "        \n",
        "        # Plotting the actual vs predicted values\n",
        "        sns.lmplot(x='Actual', y='Predicted', data=df_results, fit_reg=False, size=7)\n",
        "        \n",
        "        # Plotting the diagonal line\n",
        "        line_coords = np.arange(df_results.min().min(), df_results.max().max())\n",
        "        plt.plot(line_coords, line_coords,  # X and y points\n",
        "                 color='darkorange', linestyle='--')\n",
        "        plt.title('Actual vs. Predicted')\n",
        "        plt.show()\n",
        "        print('If non-linearity is apparent, consider adding a polynomial term')\n",
        "        \n",
        "        \n",
        "    def normal_errors_assumption(p_value_thresh=0.05):\n",
        "        \"\"\"\n",
        "        Normality: Assumes that the error terms are normally distributed. If they are not,\n",
        "        nonlinear transformations of variables may solve this.\n",
        "               \n",
        "        This assumption being violated primarily causes issues with the confidence intervals\n",
        "        \"\"\"\n",
        "        from statsmodels.stats.diagnostic import normal_ad\n",
        "        print('\\n=======================================================================================')\n",
        "        print('Assumption 2: The error terms are normally distributed')\n",
        "        print()\n",
        "    \n",
        "        print('Using the Anderson-Darling test for normal distribution')\n",
        "\n",
        "        # Performing the test on the residuals\n",
        "        p_value = normal_ad(df_results['Residuals'])[1]\n",
        "        print('p-value from the test - below 0.05 generally means non-normal:', p_value)\n",
        "    \n",
        "        # Reporting the normality of the residuals\n",
        "        if p_value < p_value_thresh:\n",
        "            print('Residuals are not normally distributed')\n",
        "        else:\n",
        "            print('Residuals are normally distributed')\n",
        "    \n",
        "        # Plotting the residuals distribution\n",
        "        plt.subplots(figsize=(12, 6))\n",
        "        plt.title('Distribution of Residuals')\n",
        "        sns.distplot(df_results['Residuals'])\n",
        "        plt.show()\n",
        "    \n",
        "        print()\n",
        "        if p_value > p_value_thresh:\n",
        "            print('Assumption satisfied')\n",
        "        else:\n",
        "            print('Assumption not satisfied')\n",
        "            print()\n",
        "            print('Confidence intervals will likely be affected')\n",
        "            print('Try performing nonlinear transformations on variables')\n",
        "        \n",
        "        \n",
        "    def multicollinearity_assumption():\n",
        "        \"\"\"\n",
        "        Multicollinearity: Assumes that predictors are not correlated with each other. If there is\n",
        "                           correlation among the predictors, then either remove prepdictors with high\n",
        "                           Variance Inflation Factor (VIF) values or perform dimensionality reduction\n",
        "                           \n",
        "                           This assumption being violated causes issues with interpretability of the \n",
        "                           coefficients and the standard errors of the coefficients.\n",
        "        \"\"\"\n",
        "        from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
        "        print('\\n=======================================================================================')\n",
        "        print('Assumption 3: Little to no multicollinearity among predictors')\n",
        "        \n",
        "        # Plotting the heatmap\n",
        "        plt.figure(figsize = (10,8))\n",
        "        sns.heatmap(pd.DataFrame(features, columns=feature_names).corr(), annot=True)\n",
        "        plt.title('Correlation of Variables')\n",
        "        plt.show()\n",
        "\n",
        "        print('Variance Inflation Factors (VIF)')\n",
        "        print('> 10: An indication that multicollinearity may be present')\n",
        "        print('> 100: Certain multicollinearity among the variables')\n",
        "        print('-------------------------------------')\n",
        "       \n",
        "       \n",
        "    def autocorrelation_assumption():\n",
        "        \"\"\"\n",
        "        Autocorrelation: Assumes that there is no autocorrelation in the residuals. If there is\n",
        "                         autocorrelation, then there is a pattern that is not explained due to\n",
        "                         the current value being dependent on the previous value.\n",
        "                         This may be resolved by adding a lag variable of either the dependent\n",
        "                         variable or some of the predictors.\n",
        "        \"\"\"\n",
        "        from statsmodels.stats.stattools import durbin_watson\n",
        "        print('\\n=======================================================================================')\n",
        "        print('Assumption 4: No Autocorrelation')\n",
        "        print('\\nPerforming Durbin-Watson Test')\n",
        "        print('Values of 1.5 < d < 2.5 generally show that there is no autocorrelation in the data')\n",
        "        print('0 to 2< is positive autocorrelation')\n",
        "        print('>2 to 4 is negative autocorrelation')\n",
        "        print('-------------------------------------')\n",
        "        durbinWatson = durbin_watson(df_results['Residuals'])\n",
        "        print('Durbin-Watson:', durbinWatson)\n",
        "        if durbinWatson < 1.5:\n",
        "            print('Signs of positive autocorrelation', '\\n')\n",
        "            print('Assumption not satisfied', '\\n')\n",
        "            print('Consider adding lag variables')\n",
        "        elif durbinWatson > 2.5:\n",
        "            print('Signs of negative autocorrelation', '\\n')\n",
        "            print('Assumption not satisfied', '\\n')\n",
        "            print('Consider adding lag variables')\n",
        "        else:\n",
        "            print('Little to no autocorrelation', '\\n')\n",
        "            print('Assumption satisfied')\n",
        "\n",
        "            \n",
        "    def homoscedasticity_assumption():\n",
        "        \"\"\"\n",
        "        Homoscedasticity: Assumes that the errors exhibit constant variance\n",
        "        \"\"\"\n",
        "        print('\\n=======================================================================================')\n",
        "        print('Assumption 5: Homoscedasticity of Error Terms')\n",
        "        print('Residuals should have relative constant variance')\n",
        "        \n",
        "        # Plotting the residuals\n",
        "        plt.subplots(figsize=(12, 6))\n",
        "        ax = plt.subplot(111)  # To remove spines\n",
        "        plt.scatter(x=df_results.index, y=df_results.Residuals, alpha=0.5)\n",
        "        plt.plot(np.repeat(0, df_results.index.max()), color='darkorange', linestyle='--')\n",
        "        ax.spines['right'].set_visible(False)  # Removing the right spine\n",
        "        ax.spines['top'].set_visible(False)  # Removing the top spine\n",
        "        plt.title('Residuals')\n",
        "        plt.show() \n",
        "        print('If heteroscedasticity is apparent, confidence intervals and predictions will be affected')\n",
        "        \n",
        "        \n",
        "    linear_assumption()\n",
        "    normal_errors_assumption()\n",
        "    multicollinearity_assumption()\n",
        "    autocorrelation_assumption()\n",
        "    homoscedasticity_assumption()"
      ],
      "metadata": {
        "id": "EaLFNAuAEYcm"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "linear_regression_assumptions(feature_df, logLabel_df)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "ihvHIlTrl7bb",
        "outputId": "09b5b614-d622-473b-def9-fed197f26b25"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Fitting linear regression\n",
            "\n",
            "R^2: 0.37217562567369944 \n",
            "\n",
            "Coefficients\n",
            "-------------------------------------\n",
            "Intercept: 6.402322057521211\n",
            "X1: 0.5765357903237072\n",
            "\n",
            "Performing linear regression assumption testing\n",
            "\n",
            "=======================================================================================\n",
            "Assumption 1: Linear Relationship between the Target and the Features\n",
            "Checking with a scatter plot of actual vs. predicted. Predictions should follow the diagonal line.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/regression.py:581: UserWarning: The `size` parameter has been renamed to `height`; please update your code.\n",
            "  warnings.warn(msg, UserWarning)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ],
            "image/png": 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1TkGeYUCPjh12eG7ofbLjKOObmbj7XDMb2ODuCcDI5Ne3AnOA72U6i4hIe5Gxi0W4w2NfheIyOPIn0KHrTp++bT/szkUFOywaK9+4laqauljtk70rGT980IhQp2D1dveVya8/Ano39UQzm2xm881sfnl5edukExHJci09xWqnW4W6w1NXwivXQV11SjmaOo/5kqMHZdX5zaGuNR38PGmPVq41uXrN3ae4+3B3H15WVtaGyUREstf25bihqpq3V23k/TWVrKusbrJYdllEz/8cXvgVHPgfcMzPwZpc7/SJps5j/saoz2TV+c0ZPXywE6H27v7YzHZ395VmtjuQ2X+KiIi0MyOH9uIa4BcPL+L9NVUU5OXRt1sR1XX1Te6jvX0RAZQU5lNZXcv1c5cwsuouePoq2OdcOO6PKRX09lkaK9+47ZO9M6GuNR1qJH0/sG2lwfnAfYFyiIjkrJFDe1HasQMDe3RkSO/OdCku3OkIcKdbhXboBp+ZCGNv/vcS7XYk1B7hbXEK1h3As8DeZrbCzC4GfgEcb2ZvA6OSt0VEJM2as0d3Y0WUX1MRFdGwc+GkuyCvfV48MdQe4W2xuntSEw8dl+nXFhHJFS1dWbxtdXUqq6gvHTGYq+9fSGV1LcUFCfateZar/Se8Pexv0ROaMcWda7YdPmj1Dm3NpB3HRERirjX7bDf3e7f9Y6C04jmuzf8eNV32otN5TzPn/eo2P/2oHdG2oCIi2WrSlHmfGg035wIVzd6j++MX4a5joePucPZc5iwjfRfjkMY0WdLt8+CCiEgWaWpl8durNjJpyrydjm6bPU2+YTlMHRMtFJs4C0p6cf3ceU2v+lZJZ1T7W6InIpJlGlvQtWbzVjZuqd3p5hot2oCjcx846Gtwxmzo0g9o3uIzSS+VtIhIzDW2snjt5hpKS3Z+gYpmbcCx6UNYtyQ6veqon0DpkE8eCnX6kaikRURir7Fduzp1SNCz084vUJHyCLhyNUw9HqaNg/raT71+qNOPRMekRUSyQsPduRpbTNZwdLvt9Ku6ev/kghYACTMmTZkXHZ8e1AGmjYX1S+C0hxs9DzrU6Uei1d0iIlkplVOr5ixexXenvkJFZQ3uTl3y133CoFeXDnRK1HB32TV0WzcfJtwHg8cFfEftWpOruzXdLSKShZq6cMX2o9uRQ3vRo2Mh+Qmj3qMmKEzkkZ/IY0NVLZckbqXL2udh3O0q6JjSdLeISJZK5QIVm6rr2KusE29+vJGEGWaG41TX1TM1/0Je2ro/J/hIrt/FqVwShkbSIiI5rF9pCas3baWu3tlSW091bQ3nFUyja6KaFZUJZmz8LBf/7QVeXlZBwmiz6yRLalTSIiI57IjB3SnfVJ285fxXyQ1c1fFGxhU+yaqN1dTU1ZEww4GV66Myb4vrJEtqVNIiIjns2SVr6dW5kOKCBJd3vI0LS2ZwU9UEbq8cRVmnQjAjL/lR7/UsW1vJsrWVvLSsQqPpGFBJi4jksOUVlfTo2IHLu8/g6yX/ZGr1WH5eeQl19dAhP4/CRB7uUFtXT209nywwM9C0dwxo4ZiItDstvexjNupXWsLmjauZ4HfyYPUIflj5NfIsjzxzPli3hdKSAtZV1VBbH52fZcn/3a1rEYk80/7cgWkkLSLtSov2s85il44YzLq6jpyx4X+5YvO3qfcEDvTsWAjAxq217NG1iG07ZnTIz2OPbkV0LirQ/twxoJG0iLQr2+9nDTl+Rad37mfkqn9xzfhvc+ntW6jHKUwYPTsV0aW4gOLCBB9t2Eq9Q5eifDp2SNCzU9En397c/bmbM0ORydmMXJopUUmLSE5r+Av7rY83sHvX4h2ek20jxpRKaOlj8MCZUHYgI4/4EYf0L/3UNqL5iTwO6V/KHZMP/2SGobK6docdzFLdn3v7HdC2n6G4Bhq9fGaqz23Jn02mfnYImu4WkZzV2NT2pq11rN60dYfnZdMVnVKarv/wWbhvQnQlq9MehoKSXV4kI5UdzHamOVfcatbVuZopkz87BI2kRSRnNTa13b1jAWs319CxQ36LRoyh7XK6ftUr0dWsOu4Op8+E4u5AahfJSGUHs6Ysr6ikW3HBDvc1NUPRnOdmMkc2UEmLSM5q7Bd2j44dqKlzenUuavUVnUIc+9xlCa1/D4q6wxmzodPuOzyvNSW8K9uuuLWzq3K15LmZzJENVNIikrOa+oU9pFdn7ph8eKt+dmPHPr8z9RXKOnVg49baZpV2c8q+qfc0oFu0Wpshp0QXy0gUpvV1d+XSEYNTPqbdnOdmMkc20DFpEclZuzoO2xoNj33W1jnrKmt4b/XmZp3a1dxTwhp7T53r1nA9F8Obd0VPSrGg03kqWnOOabf2+He6cmQDXU9aRHLattFia6e2Gzr6l4/TrbgAs2j7jyXlm6ipq8eBobt1AaCyupZenYt2OmqfNGXep0bGu/q+7d/T3t1q+D/7Fp2qlsLEWdDnyJTyt+R1JWOavJ60prtFJKdl6jhsw2nn6rr6T67XvE0qC5ZastDpk/dUvRGmHg+r3oVTH0y5oFv6utL2VNIiIi3Q8NhnIi+a8i7r3OGT5zS2YKnhceBOhdFx02YvdKqrhnsnwEfz4eR7YMCoZuXPtQVWuUrHpEVEWqDhsc+B3UsoLSkgkWdNHv9u7Djwms3VrK+qaf5x87wC2P1wGHsL7DWh2fkzebxe0kfHpEVE0mRXx7+bOg5cmMijW0nhTo+bb/vZH1RsZP+ulZwx8oi07M6VieP10mw6Ji0ikmm7Ov7d1HHg9VU1PPzNEU1+379P94IfFPyBwzY/xfn33wQc3apSzeR505IeKmkRkTbS0uPA0ele8J95UxhbP4N/5n2J8uoufOPOl+lSXJD1F5GQpumYtIi0K3MWr2LSlHkc/cvHmTRlXpteorKlx4GXV1RyYd7tnFp/JzPyTucvteezemM1ldV17eJym+2ZSlpE2o3Q15Ju6UYbZ3R6hnPrb+KxvLHckPgG5RurwaJrP+fCRSSkaZruFpF2Iw7Xkm7JceCDR57L9Q8tZSpn0yFhbKmtI8+Mnp3+fbqXznHOTRpJi0i7sbyikuKCxA73xbrcls6GrRsYse9A9h7/U3p27sj6qho6FubTo2MhXbZbhKZznHOTRtIi0m5k1QYeSx6C+06B/S+BUX/eYQS+bdo+Vy4iIU3TSFpE2o2s2cBj+ZMw43TouT8c8/NPPZxrF5GQpmkzExFpV2K/gcdH8+HuY6FTHzhrLpSUhU4kmafNTEREIOYbeLjDzC9DcU+YOFsFLSppEZHYMINT7oX6OujcJ3QaiQGVtIjkjIZXmIrdVHZTNq6A126EI66GLgNCp5EY0cIxEckJoTcqabHK8uia0C/+FtZpMxLZkUpaRHLC9huVZM0uXFvWwT1jYMNSOPVBKN0rdCKJGZW0iOSErNuopGYzTD8RVr8OJ0+DvseETiQxpJIWkZzQr7SEqpq6He6L7UYlAKsWQPkrcOIdMGhs6DQSUyppEckJWbNRyTZ9joJL3oPPnB46icSYSlpEckJW7MLl9fDIRfD6zdFtnQctu6BTsEQkZ8R+o5LHvwELb4ZuMR3dS+xoJC0i0haevgoW/AmGfxcOuyp0GskSKmkRkUx77hfw/M/hgEthxC+jncVEUqCSFhHJtPoaGPpFOO5PKmhplqDHpM3sW8AlgAOvARe6+5aQmURE0qZ6ExR2giN+GC0aM42LpHmC/Y0xsz7AN4Dh7r4fkADODpVHRCSt3p4ONw6G8tei2ypoaYHQf2vygWIzywdKgA8D5xERab33Z8GDZ0O3PaHroNBpJIsFK2l3/wD4DbAMWAmsd/eZDZ9nZpPNbL6ZzS8vL2/rmCIizfPBv+C+U6D7UDjtoWi6W6SFQk53lwITgEHAHkBHMzu34fPcfYq7D3f34WVlOvFfRGJszSKYNg4694XTZ0JRaehEkuVCTnePAt5z93J3rwGmAUcGzCMi0jpdB8E+58DE2dCxd+g0kgNCru5eBhxuZiVAFXAcMD9gHhGRltmwFAo6Q3F3GPXn0GkkhwQraXd/zsymAi8BtcDLwJRQeUREWmTTh3DXsdC5H5z5hM6DTtGcxau4fu4SlldU0q+0hEtHDI7vlq4BmbuHzpCy4cOH+/z5GmyLSExUrYF/fh42vA9nPAa7HxY6UVaYs3gVV9+/kIKEUVyQoKqmjpo6j98FUdpOk/+yC30KlohIdtq6Ae4ZC+vegVNmqKCb4fq5SyhIGCWF+ZhFnwsSxvVzl4SOFjsqaRGRlnj861C+AMbfDf2/EDpNVlleUUlxQWKH+4oLEqyoqAyUKL5U0iIiLXH0z2D8PbDn+NBJsk6/0hKqaup2uK+qpo6+pSWBEsWXSlpEJFX1dfDK9dHnzn1gr5NDJ8pKl44YTE2dU1ldi3v0uabOuXSErrPdkEpaRCQVXg+zJsPsr8CSB0OnyWojh/bimpP3pVfnItZX1dCrc1F7XjS2U0GvgiUikhXcYc634fW/wuFXfzKC1mlELTdyaC/9WaVAJS0isivP/Bhe+h0rBn6Z774+luVPP06nwgRrNlfTpbiAbsUFrNq4havvX8g1oPKRtNF0t4jIzmxYBvN/w8q+kzjn3bNYtWkr3YoLeH9tJRWVNdTVu04jkoxRSYuI7EyX/nDuC1y+7mvkJxKfnNtbV+/kGZRv3PrJU3UakaSbSlpEpDGL/wkL/hJ93WMYy9Zt3eHc3sJE9Ouzuq7+k/t0GpGkm0paRKShdx+Ah8+FN/8ZnW7Fp8/t7dmpA/UOCTOdRiQZo5IWEdnesidgxkQoOwhOuR/yotFzw3N78xNGt5ICBvXsqNOIJGO0ultEZJuVz8G9J0O3veD0R6BDl08eGjm0F9cQ7Tu9oqKSvqUl/PDEYSplySiVtIjINh+9AB17w8RZUNzjUw/r3F5payppERGvB8uDg/8T9rsQCjqGTiQC6Ji0iLR3G5bB3w6CFU9Ht1XQEiMaSYtI+7X5Y5g6CipXqZwlllTSIpJzUtpTe0sF3DMaNn4AE2dC74PDhBXZCU13i0hOmbN4FVffv5BVG7fssKf2nMWr/v2k6k0wbRysXQwT7oU+R4ULLLITKmkRySnXz11CQcI+2b6z0T21E4XRaVYn3gkDjw8XVmQXNN0tIjlleUUl3YoLdrjvkz2162qgekN0etW4vwdKKJI6jaRFJKc03L4Toj21+3UrgkcugDuPhhpdBEOyg0paRHJKw+07oz216/l19ymw+B8w7Hwo0EUwJDuopEUkp4wc2otrTt6XXp2Loj21O3XgtiHT6LPsVjj0SjjsytARRVKmY9IiknN22L5zwZ/hsT/BgV+Fo38WNphIM6mkRSS3DTk92qzkiKvBLHQakWbRdLeI5Kblc6LV3B17w5E/jvbmFsky+lsrIrnnralw93Hw/M9DJxFpFZW0iOSW9x6BB78Iux8Owy8PnUakVVTSIpI7VjwF958GPfaFUx/URTMk66mkRSQ31G6NRtBdBkQXzCjqFjqRSKtpdbeI5Ib8DnDKvVDSG0rKQqcRSQuNpEUku61bAq9cF33d+7PQuW/YPCJppJG0iGSvjR/A1FGwdX10PrRG0JJjVNIikp0qy2Hq8VC1Gs54TAUtOUklLSLZZ+t6uGcsbHgPTn8Udvtc6EQiGaGSFpHss3Q2rHkdTp4OfUeETiOSMSppEck+nzkddnsHuvQLnUQko7S6W0SyQ30tPPwlWPpYdFsFLe2ASlpE4s/r4dGL4Y2/R9PcIu2ESlpE4s0dHr8M3vgbHPkTOOSy0IlE2oxKWkTi7V8/hAV/hM9eDof/MHQakTalkhaR+PJ62PQB7P9l+PyvwSx0IpE2pdXdIhJPtVuj/bjH3BRNeaugpR3SSFpE4mfR7XDrfrBxBVge5CVCJxIJQiUtIvHyzn3w8PnQuR8U9wydRiQolbSIxMfS2fDAmbDbcDjlPsgvCp1IJCiVtIjEw0cvwL0ToHRvOPUhKOwcOpFIcCppEYmHroNhz5Nh4kwo7h46jUgsBC1pM+tmZlPNbLGZLTKzI0LmEZEA1r8freQu7gEn3QEddwudSCQ2Qo+kfwc84u5DgQOBRYHziEhb2rAU7jwGZl4cOolILAU7T9rMugIjgBbq8Y4AAB9dSURBVAsA3L0aqA6VR0Ta2KaVcPdxULMJhn83dBqRWAo5kh4ElAM3m9nLZnajmXVs+CQzm2xm881sfnl5edunFJH0q1oL94yGzR/BaQ9BrwNDJxKJpZAlnQ8cAvzF3Q8GNgNXNnySu09x9+HuPrysrKytM4pIJjz0Rah4CybcB3toKYpIU0JuC7oCWOHuzyVvT6WRkhaRHDTiV7BxOQw4LnQSkVgLNpJ294+A5Wa2d/Ku44A3QuURkQyrq4HF/4z24S47AAafGDqRSOyFvsDG14HbzawQWAJcGDiPiGRCfR08fB68+U/oMgD2ODx0IpGsELSk3X0BMDxkBhHJMHeY/ZWooI/5pQpapBlCnyctIrnMHZ68HF67EQ67Cg69InQikayikhaRzFm1AF76HRz8dTjqv0OnEck6oY9Ji0gu630wTHoGdvscmIVOI5J1NJIWkfR77a+w5MHo690PA9OvGpGW0P9zRCS9Fv8TZl4Cr1wfHZMWkRZTSYtI+ix5EB4+F/ocDSfdqSlukVZSSYtIeiyfAzMmQs8D4NQZUFASOpFI1tvpwjEz2+mV1919bXrjiEjWencGdB0Mpz8KHbqGTiOSE8x3cszIzN4DHDCgP1CR/LobsMzdB7VFyG2GDx/u8+fPb8uXFJFdcY+mtd1h63oo6hY6kUi2afK40E6nu919kLsPBmYD4929p7v3AE4CZqY3o4hknYp34B+Hw9q3oqJWQYukVarHpA9394e23XD3h4EjMxNJRLLChuUwdRSsXwJeGzqNSE5KdTOTD83sv4DbkrfPAT7MTCQRib3KVTD1eNhSAWc+AT2GhU4kkpNSHUlPAsqA6cC05NeTMhVKRGJsSwVMHQ0bl8GpD0LvQ0InEslZKY2kk6u4LzOzju6+OcOZRCTOLA+Ke8CI6dD36NBpRHJaSiNpMzvSzN4AFiVvH2hmf85oMhGJl9otUFMVnV41cTYMHBM6kUjOS3W6+1pgDLAGwN1fAUZkKpSIxExdDTxwNkwfB/V12klMpI2kvOOYuy9vcFddmrOISBx5PTx6Ibx7H+x1GuQlQicSaTdSXd293MyOBNzMCoDLSE59i0gOc4fHvgaLboejfwqHfD10IpF2JdWR9FeArwF9gA+Ag4CvZiqUiMTEvP+BV66Dz10Bh34/dBqRdifVkfTe7n7O9neY2VHAv9IfSURi4zNnQH01HHmNjkOLBJDqSPoPKd4nIrngw3nRVHePoXDUf6ugRQLZ1VWwjiDa/rPMzL693UNdAK0eEclFC/8Gj5wPo2+E/S8OnUakXdvVdHch0Cn5vM7b3b8BmJipUCISyNvTopXc/UfBPufs+vkiklE7LWl3fxJ40sxucfelbZRJREJ4/9HoXOjdDoNT7oX8otCJRNq9VI9J32hmn1yDzsxKzezRDGUSkba2pQJmnBldKOO0h6CgY+hEIkLqq7t7uvu6bTfcvcLMemUok4i0taJSGH8X9DpY14QWiZFUR9L1ZtZ/2w0zGwB4ZiKJSJtZswjevjf6euAYKNG/vUXiJNWR9FXA02b2JGDAMcDkjKUSkcxb/x5MHQUYDBwNBSWhE4lIA6leqvIRMzsEODx51zfdfXXmYolIRm36EO4eBbVVcOaTKmiRmNrpdLeZDU1+PgToD3yY/OifvE9Esk3laph6PFSugtMegbL9QycSkSbsaiR9OfBl4H8becyBY9OeSEQya/HtsH4JnPYw7H5o6DQishPmnj3rv4YPH+7z588PHUMku7lDxdvQ/TOhk4hIpMl9d3e1LehpO3vc3ae1NJGItKG6aph1KQz/DvTcVwUtkiV2Nd09Pvm5F9Ee3o8nb38BeAZQSYvEXX0tPHQOvDUV+o2MSlpEssKutgW9EMDMZgLD3H1l8vbuwC0ZTycireP1MPPLUUGP/C3se37oRCLSDKluZtJvW0EnfUy02ltE4sodnvgWLLwFjvgxfPZboROJSDOlupnJY8m9uu9I3j4LmJ2ZSCKSFnXVsOb1qJyPuDp0GhFpgVQ3M/lPMzsVGJG8a4q7T89cLBFplfpayO8Apz4EiUKwJhePikiMpTqSBngJ2Ojus82sxMw6u/vGTAUTkRZ65XpYeCuc/jB06Bo6jYi0QkrHpM3sy8BU4PrkXX2AezMVSkRaaNE/YPZ/RFe1yi8OnUZEWinVhWNfA44CNgC4+9tEp2WJSFy8cz88/CXoOwLGT42muUUkq6Va0lvdvXrbDTPLR5eqFImPZU/AA2dC70Pg1BlQoFG0SC5ItaSfNLMfAMVmdjxwNzAjc7FEpFm69IcBx0f7cRd2Dp1GRNIkpb27zcyAS4DRRHuMPgrc6G288bf27hZpYOMK6NRHq7dFslvL9u4GMLMEsNDdhwI3pDOViLTC2rfgn8fAfhfBMT8PnUZEMmCX093uXge8aWbaYUwkLjYsg6mjol3F9r0gdBoRyZBUz5MuBRaa2fPA5m13uvvJGUklIk3b/BHcfRxUb4Az50D3vUMnEpEMSbWkf5jRFCKSGq+H6eNh04cwcRb0Oih0IhHJoF1dT7oI+AqwF/AacJO717ZFMBFphOXB0f8DloA+R4ZOIyIZtquR9K1ADfAUcAIwDLgs06FEpIHaLbBiLgwcDQPHhE4jIm1kVyU9zN33BzCzm4Dn0x0guXp8PvCBu5+U7p8vkvXqamDGmfDeQ3DhYijdK3QiEWkju1rdXbPtiwxOc18GLMrQzxbJbvV18Mj5sGQGHPsHFbRIO7Orkj7QzDYkPzYCB2z72sw2tPbFzawvcCJwY2t/lkjOcY8ulrH4DjjmF3DQf4ROJCJtbKfT3e6eyPDr/x9wBdDkPoZmNhmYDNC/v07Vlnbk/UfhtRvgsB/Aod8LnUZEAkh17+60M7OTgFXu/uLOnufuU9x9uLsPLysra6N0IjEwaGx0mtVR/xM6iYgEEqykiS59ebKZvQ/cCRxrZrcFzCMSD69OgY9fjr4eMEr7cou0Y8FK2t2/7+593X0gcDbwuLufGyqPSCy8fjPMuhRe/n3oJCISAyFH0iKyvTfvhpmXwIDRMOq60GlEJAZS3RY0o9x9DjAncAyRcN57GB46B3Y/AiZMg/wOoROJSAxoJC0SB6/dBD33h9MehIKOodOISEzEYiQt0u6d+A+o3gQduoZOIiIxopG0SCirX4epo6GyHBKFUNw9dCIRiRmNpEVCWPcuTD0eMKjeCCXaA0BEPk0lLdLWNq6Au0dFF84460noNjh0IhGJKZW0SFuqLI9G0FvWwBmPQ899QycSkRjTMWmRtlS7BRId4NQHYbfhodOISMxpJC3SFmqqonOfu/SD814C07+PRWTX9JtCJNNqt8J9E+CRC6PLT6qgRSRF+m0hkkn1tfDgJFg6C/p9QRfLEJFmUUmLZIrXw6MXwTvT4Qu/g/0uCJ1IRLKMSlokU578Drzxdzjqv+GQb4ROIyJZSAvHRDJlzwlQ0AkOuyp0EhHJUippkXQrfw3K9od+n48+RERaSNPdIum04M/wtwNgyUOhk4hIDlBJi6TLG7fBY1+DweNhwPGh04hIDlBJi6TD2/fCIxdA/2Nh/F2QKAidSERygEpapLXWvw8PngW7fQ4m3Af5RaETiUiO0MIxkdbqOhBG3wSDT4TCTqHTiEgOUUmLtNSqBVC3FXY/DIadGzqNiOQgTXeLtMSaxTB1NDx6MdTXhU4jIjlKJS3SXOvfh6mjogtlTJgOeYnQiUQkR2m6W6Q5Nq2MCrpmM5z1JJQOCZ1IRHKYSlqkOV78LWz+CM54DMoOCJ1GRHKcSlqkOY75OQz7UrTtp4hIhumYtMiu1FTBrEujqe68fBW0iLQZlbTIztRVw4yJ8OoNsHJe6DQi0s5oulukKfV18NB58N5DcPz1MOTU0IlEpJ3RSFqkMe7RFPdbd8GIX8MBk0MnEpF2SCUt0pit62Dls3D41fC574ROIyLtlKa7RRryeigqhS8+BwUdQ6cRkXZMI2mR7c3/Lcw4M1owVtgJzEInEpF2TCUtss2rN8CTl0fbfZq2+hSR8FTSIgCL74wWig06Acbdpv24RSQWVNIiSx6Eh8+DPkfD+KmQKAydSEQEUEmLQFF36DsSTn0ACkpCpxER+YRKWtqvyvLo8x5HwBmzoEOXsHlERBpQSUv7VP4a3Lw3LPhL6CQiIk1SSUv7U/E2TD0e8ktg0NjQaUREmqTNTKR92bAc7h4FXgcTn4Cug0InEhFpkkpa2o/aLdEIuno9nPEE9NgndCIRkZ1SSUv7kV8En7sCuu8NvQ8OnUZEZJdU0pL7qjfB2kWw2+dg/4tCpxERSZkWjkluq90C950Cdx8HlatDpxERaRaNpCV31dXAA2fBssfghL9BSc/QiUREmkUjaclNXg+PXADv3g/H/QmGnRc6kYhIs6mkJTctvBUW/wOO/hkc9NXQaUREWkTT3ZKbhn0JOpTCkFNCJxERaTGNpCW3vHIdbFgWXWpSBS0iWS5YSZtZPzN7wszeMLOFZnZZqCySI176A8z+D3jp96GTiIikRcjp7lrgcnd/ycw6Ay+a2Sx3fyNgJslWC2+FJ74Be50CI34ROo2ISFoEG0m7+0p3fyn59UZgEdAnVB7JYm/dA49eBAOOhxPvhDwttRCR3BCLY9JmNhA4GHgubBLJOl4P838Nux8OE6ZDfofQiURE0ib4kMPMOgH3AN909w2NPD4ZmAzQv3//Nk4nsWd5cNoj0dcFHcNmERFJs6AjaTMrICro2919WmPPcfcp7j7c3YeXlZW1bUCJr49fhAe/CDVVUNQt+hARyTHBRtJmZsBNwCJ3/22oHJKF1rwBU8dAYSfYWgEFxaETiYhkRMiR9FHAecCxZrYg+TEuYB7JBuuWRNeEThTAxNnQaY/QiUREMibYSNrdnwYs1OtLFtr4AUwdFV3Z6qwnoXSv0IlERDIqFqu7RVJSVR59Pv0R6Llf2CwiIm0g+OpukV2qq4ZEIfQ6CC58M5rqFhFpBzSSlnirqYS7j4NnfhLdVkGLSDuikpb4qt0K958GHz4DPfYJnUZEpM1pulviqb4WHjoH3n8URt8Ee58ZOpGISJvTSFriadal8PY9MPJa2P+i0GlERILQSFriqd8XoOsg+Ow3QycREQlGJS3xsu5d6LYnDDs3dBIRkeA03S3x8fyv4JZh0b7cIiKikpaYeOU6eOp7sNepUHZQ6DQiIrGgkpbwFt0Os78Kg0+EE/4OeYnQiUREYkElLWF9/CI8fD70+zycdLc2KxER2Y4WjklYvQ6Gz/8G9r9Yl5wUEWlAI2kJY+Vz0Upuy4tOsyrsHDqRiEjsqKSl7a16Be4ZC49eHDqJiEisqaSlba19E+4ZHY2cT7g1dBoRkVhTSUvb2bAU7h4VfT1xNnQZEDaPiEjMaeGYtJ2nfgA1m+DMOdD9M6HTiIjEnkpa2s7x18G6JdDrwNBJRESygqa7JbOqN8Kcb0P1pug4tApaRCRlKmnJnJoquPdkeOn38NHzodOIiGQdTXdLZtRVwwNnwPInYdzfof+xoROJiGQdlbSkX30dPPwlWPIgjLoO9jkndCIRkayk6W5Jv00rYPkcOOaXcOClodOIiGQtjaQlfdyjz10GwAULobhH2DwiIllOI2lJn3n/DU9+NyprFbSISKuppCU9Xvw/eOZHsGU14KHTiIjkBJW0tN5rN8Gcb8GQ02H0jdGVrUREpNX021Ra5827YOaXYcBoGHc75GmZg4hIuqikpXUsEZ0DPWE65HcInUZEJKdo2CMts3U9dOgKnzkdhpwGZqETiYjkHI2kpflWPg83DoZ37o9uq6BFRDJCJS3Ns/p1mDY2GkX3/mzoNCIiOU0lLamreAemHg/5xTBxNnTuEzqRiEhO0zFpSU3VWpg6Cupq4Oy50G1w6EQiIjlPJS2pKSqFfS+EPU+CHsNCpxERaRdU0rJzW9ZBVTmUDoEjfxQ6jYhIu6Jj0tK0ms0w/US461ioqQqdRkSk3dFIWhpXuwXuPQVWzoOT7oKC4tCJRETaHZW0fFp9LTw4CZbNhrG3RBuWiIhIm9N0t3zaC7+Bd+6FY/8A+54fOo2ISLulkbR82iHfgK6DYOhZoZOIiLRrGknLv716Q7Qnd0GJClpEJAZU0hJ57ucwazK8cl3oJCIikqSSFnj5j/D0D2Cfc+Bz3w2dRkREklTS7d3CW+Hxr8OeE2DMzWD6KyEiEhf6jdye1W6BZ34M/Y+Dk+6EREHoRCIish2t7m7P8ovgrCehqHv0tYiIxIpG0u3RiqdhzrfB66FLfyjsFDqRiIg0QiXd3nz8UrQf95IHo9OtREQktoKWtJmNNbM3zewdM7syZJZ2Yc0iuGcMdOgGE2dHl58UEZHYClbSZpYA/gScAAwDJpmZLlScKevfg6nHgyXgjNnQpV/oRCIisgshR9KHAu+4+xJ3rwbuBCYEzJPbKt4GHCbOiq4NLSIisReypPsAy7e7vSJ53w7MbLKZzTez+eXl5W0WLmfU10WfB46Gi96Bsv3D5hERkZTFfuGYu09x9+HuPrysrCx0nOyydQPceVS0YQnomtAiIlkmZEl/AGx/YLRv8j5Jh5pKuHc8fPwiFPUInUZERFogZEm/AAwxs0FmVgicDdwfME/uqKuG+0+HFU/BCbfBnieFTiQiIi0QbMcxd681s/8EHgUSwF/dfWGoPDnD6+Ghc+D9R+D4G3TJSRGRLBZ0W1B3fwh4KGSG3GNQdiDsfjgccEnoMCIi0grauztXuMOmD6FzHzj8v0KnERGRNIj96m5J0TM/gr/tH21aIiIiOUElnQte+A3M+2/Y6zToMjB0GhERSROVdLZ7dQrM/S585kw4/nowC51IRETSRCWdzZbOhllfgUHjYNzfIS8ROpGIiKSRSjqb9TkajvgRjJ8KicLQaUREJM1U0tnow2ehai3kF8GRP9J2nyIiOUolnW0+nBddcvKxr4ZOIiIiGaaSziblr8K0E6DjbjDy2tBpREQkw1TS2WLtW9EIuqAjTJwNnXYPnUhERDJMJZ0tZk2OdhWbOBu6DgydRkRE2oC2Bc0W426HqtXQY2joJCIi0kY0ko6zLRXw7DVQXxftyd3rwNCJRESkDamk46p6Y7RI7LmfRgvGRESk3dF0dxzVboH7ToGP5kcblfQ+OHQiEREJQCUdN3U1MONMWPY4nPB3GHJK6EQiIhKIprvjZs1CWP44HPdnGHZu6DQiIhKQRtJx0+sguOhtnQctIiIaSceCO8z9Hiz4c3RbBS0iIqik4+G5n8ILv4I1b4ROIiIiMaKSDu2l38G/fgjDvgTH/j50GhERiRGVdEiv3wxPfBP2OhXG3ASm/xwiIvJvaoWQtlTAwDFw4h2QpzV8IiKyI5V0CDVV0efh34ZTH4T8DmHziIhILKmk29qKuXDjIFj5fHQ7LxE2j4iIxJZKui19NB+mnwRFpdB1UOg0IiIScyrptrLmDbhnLBT1iK4JXVIWOpGIiMScSrotbFgOd4+CRCGcMTu67KSIiMguqKTbQsfdYK8JMHEWdNszdBoREckSOu8nkyrLAYeSXjDqL6HTiIhIllFJZ8qWdXDPmOjrc+droxIREWk2lXQm1GyOVnGvfh1OuU8FLSIiLaKSTrfarXDfabDyWTjxThh0QuhEIiKSpVTS6fb092HpTBjzV9j7jNBpREQki6mk0+3QK6H3Z2Gfc0InERGRLKeDpengDgtvhbqaaCW3ClpERNJAJZ0O//oveOQCWHRb6CQiIpJDVNKt9fwv4bmfwQGTYd8LQqcREZEcopJujQV/hqeuhKFfhOP+DGahE4mISA5RSbdU1Rp4+gcweDyMvUWXnBQRkbTT6u6WKu4BZ/8r2os7URA6jYiI5CCNpJtr6Wx48dro6577Qn5R2DwiIpKzVNLN8cEzcO8EWHgL1G4JnUZERHKcSjpVqxbA9HHRtaBPn6kRtIiIZJxKOhVrFsPU0VDYBSbOho69QycSEZF2QCWdipXzotXbE2dDl/6h04iISDuh1d074x6d+7zfBTDkNOjQJXQiERFpRzSSbkrVGrjjCFj6WHRbBS0iIm1MI+nGVG+EaSdA+avaRUxERIJRSTdUUwXTx8Oql+HkadD/2NCJRESknQoy3W1mvzazxWb2qplNN7NuIXJ8Sl01zJgIK+bC2L/BnuNDJxIRkXYs1DHpWcB+7n4A8Bbw/UA5dmR5UNIbjr8e9pkUOo2IiLRzQaa73X3mdjfnARND5PiEO2ypgOLuMOYmHYcWEZFYiMPq7ouAh5t60Mwmm9l8M5tfXl6e/ld3hycvh9uHQ9VaFbSIiMRGxkrazGab2euNfEzY7jlXAbXA7U39HHef4u7D3X14WVlZ+oM+e010wYzB46GoNP0/X0REpIUyNt3t7qN29riZXQCcBBzn7p6pHDs1/7fw7I9h3wvhC9dqFC0iIrES5Ji0mY0FrgA+7+6VITLw5l3RNPdnJsLoG6JFYyIiIjESqpn+CHQGZpnZAjO7rs0T9B8Fw78D426P9uUWERGJmVCru/cK8bo7KO4On/916BQiIiJN0hyviIhITKmkRUREYkolLSIiElMqaRERkZhSSYuIiMSUSlpERCSmVNIiIiIxpZIWERGJKZW0iIhITKmkRUREYkolLSIiElMqaRERkZhSSYuIiMSUSlpERCSmVNIiIiIxpZIWERGJKZW0iIhITKmkRUREYkolLSIiElPm7qEzpMzMyoGlGXyJnsDqDP78kHL5vUFuvz+9t+yVy+9P7y19Vrv72MYeyKqSzjQzm+/uw0PnyIRcfm+Q2+9P7y175fL703trG5ruFhERiSmVtIiISEyppHc0JXSADMrl9wa5/f703rJXLr8/vbc2oGPSIiIiMaWRtIiISEyppEVERGJKJd2Amf3azBab2atmNt3MuoXO1FpmNtbM3jSzd8zsytB50sXM+pnZE2b2hpktNLPLQmdKNzNLmNnLZvZA6CzpZmbdzGxq8v9vi8zsiNCZ0sXMvpX8O/m6md1hZkWhM7WGmf3VzFaZ2evb3dfdzGaZ2dvJz6UhM7ZUE+8tNj2gkv60WcB+7n4A8Bbw/cB5WsXMEsCfgBOAYcAkMxsWNlXa1AKXu/sw4HDgazn03ra5DFgUOkSG/A54xN2HAgeSI+/TzPoA3wCGu/t+QAI4O2yqVrsFaLjZxpXAY+4+BHgseTsb3cKn31tsekAl3YC7z3T32uTNeUDfkHnS4FDgHXdf4u7VwJ3AhMCZ0sLdV7r7S8mvNxL9ku8TNlX6mFlf4ETgxtBZ0s3MugIjgJsA3L3a3deFTZVW+UCxmeUDJcCHgfO0irvPBdY2uHsCcGvy61uBU9o0VJo09t7i1AMq6Z27CHg4dIhW6gMs3+72CnKoyLYxs4HAwcBzYZOk1f8BVwD1oYNkwCCgHLg5OZ1/o5l1DB0qHdz9A+A3wDJgJbDe3WeGTZURvd19ZfLrj4DeIcNkUNAeaJclbWazk8eKGn5M2O45VxFNp94eLqmkwsw6AfcA33T3DaHzpIOZnQSscvcXQ2fJkHzgEOAv7n4wsJnsnS7dQfLY7ASif4jsAXQ0s3PDpsosj87lzbnzeePQA/mhXjgkdx+1s8fN7ALgJOA4z/4TyT8A+m13u2/yvpxgZgVEBX27u08LnSeNjgJONrNxQBHQxcxuc/dc+WW/Aljh7ttmPqaSIyUNjALec/dyADObBhwJ3BY0Vfp9bGa7u/tKM9sdWBU6UDrFpQfa5Uh6Z8xsLNEU48nuXhk6Txq8AAwxs0FmVki0gOX+wJnSwsyM6JjmInf/beg86eTu33f3vu4+kOi/2eM5VNC4+0fAcjPbO3nXccAbASOl0zLgcDMrSf4dPY4cWRTXwP3A+cmvzwfuC5glreLUA9pxrAEzewfoAKxJ3jXP3b8SMFKrJUdj/0e0yvSv7v7TwJHSwsyOBp4CXuPfx21/4O4PhUuVfmY2EviOu58UOks6mdlBRIviCoElwIXuXhE2VXqY2U+As4imSl8GLnH3rWFTtZyZ3QGMJLqE48fAj4B7gbuA/kSXED7T3RsuLou9Jt7b94lJD6ikRUREYkrT3SIiIjGlkhYREYkplbSIiEhMqaRFRERiSiUtIiISUyppkRxnZqeYmZvZ0F0875tmVtKK17nAzP7Y0u8XkU9TSYvkvknA0//f3h2zRhGFURh+j4jYiJBOUExKC0GwsbDRXkRIExuLCFaK6B/IDxBBbMRKsFFEBLGwENKIYGGRlDaWIqiNlsJncW90CGLEGBxm36fZu7M7l9nqMMzynf76O1dpZRCSRsKQliaszzU/CSzT6xJ7R/WNPq9+PcnlJFdoc6ZXk6z2730d7LOY5F5fn0nyuhdjvEgy1WIF6b+bydnd0gw5S+tsfpvkU5LjtPrSeeBYVX1LMldVn5NcA05V1cct9nwJnKiqSnKRNj7x+k7+CGlWGdLStC0Bt/r6QX+/ANzZ6Mv9i1GOB4GHvVRhD/DuH12rpE0MaWmikswBp4GjSYo2u71opSt/YjgzeO9gfRu4WVVP+1zxle1fraRf8Zm0NF2LwP2qOlxV81V1iHbXuwZcSrIbfoQ5wBdg3+D8D0mOJNkFnBsc38/PutMLSNoxhrQ0XUvAk03HHgMHaHWK60nWgPP9s7vA840/jtH6nZ8Br4D3gz1WgEdJ3gBbPb+WtA22YEmSNFLeSUuSNFKGtCRJI2VIS5I0Uoa0JEkjZUhLkjRShrQkSSNlSEuSNFLfAbpCTG0R/IOlAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "If non-linearity is apparent, consider adding a polynomial term\n",
            "\n",
            "=======================================================================================\n",
            "Assumption 2: The error terms are normally distributed\n",
            "\n",
            "Using the Anderson-Darling test for normal distribution\n",
            "p-value from the test - below 0.05 generally means non-normal: 0.10533308696598737\n",
            "Residuals are normally distributed\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/distributions.py:2619: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
            "  warnings.warn(msg, FutureWarning)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Assumption satisfied\n",
            "\n",
            "=======================================================================================\n",
            "Assumption 3: Little to no multicollinearity among predictors\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/seaborn/matrix.py:198: RuntimeWarning: All-NaN slice encountered\n",
            "  vmin = np.nanmin(calc_data)\n",
            "/usr/local/lib/python3.7/dist-packages/seaborn/matrix.py:203: RuntimeWarning: All-NaN slice encountered\n",
            "  vmax = np.nanmax(calc_data)\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x576 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Variance Inflation Factors (VIF)\n",
            "> 10: An indication that multicollinearity may be present\n",
            "> 100: Certain multicollinearity among the variables\n",
            "-------------------------------------\n",
            "\n",
            "=======================================================================================\n",
            "Assumption 4: No Autocorrelation\n",
            "\n",
            "Performing Durbin-Watson Test\n",
            "Values of 1.5 < d < 2.5 generally show that there is no autocorrelation in the data\n",
            "0 to 2< is positive autocorrelation\n",
            ">2 to 4 is negative autocorrelation\n",
            "-------------------------------------\n",
            "Durbin-Watson: 2.3778591970316163\n",
            "Little to no autocorrelation \n",
            "\n",
            "Assumption satisfied\n",
            "\n",
            "=======================================================================================\n",
            "Assumption 5: Homoscedasticity of Error Terms\n",
            "Residuals should have relative constant variance\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 864x432 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "If heteroscedasticity is apparent, confidence intervals and predictions will be affected\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Assumptions cleared with the log transformed dependent variable."
      ],
      "metadata": {
        "id": "tiFR8t-L_-Hf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Adding the intercept constant for the statsmodels API\n",
        "X_train_for_statsmodels_api = sm.add_constant(feature_df, prepend=False)\n",
        "\n",
        "# Fitting the model and viewing the model summary\n",
        "mod = sm.OLS(logLabel_df, X_train_for_statsmodels_api)\n",
        "res = mod.fit()\n",
        "print(res.summary())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QTnVryUDYJlF",
        "outputId": "cbdb6e85-8e7d-41d1-bee6-577ffd83863b"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "                            OLS Regression Results                            \n",
            "==============================================================================\n",
            "Dep. Variable:        average_realGDP   R-squared:                       0.379\n",
            "Model:                            OLS   Adj. R-squared:                  0.365\n",
            "Method:                 Least Squares   F-statistic:                     26.82\n",
            "Date:                Tue, 03 May 2022   Prob (F-statistic):           5.33e-06\n",
            "Time:                        18:50:21   Log-Likelihood:                -72.741\n",
            "No. Observations:                  46   AIC:                             149.5\n",
            "Df Residuals:                      44   BIC:                             153.1\n",
            "Df Model:                           1                                         \n",
            "Covariance Type:            nonrobust                                         \n",
            "==================================================================================\n",
            "                     coef    std err          t      P>|t|      [0.025      0.975]\n",
            "----------------------------------------------------------------------------------\n",
            "average_invest     0.0015      0.000      5.179      0.000       0.001       0.002\n",
            "const              8.8566      0.217     40.863      0.000       8.420       9.293\n",
            "==============================================================================\n",
            "Omnibus:                        0.263   Durbin-Watson:                   2.398\n",
            "Prob(Omnibus):                  0.877   Jarque-Bera (JB):                0.437\n",
            "Skew:                           0.133   Prob(JB):                        0.804\n",
            "Kurtosis:                       2.604   Cond. No.                         935.\n",
            "==============================================================================\n",
            "\n",
            "Warnings:\n",
            "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:117: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
            "  x = pd.concat(x[::order], 1)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "When looking at the results of this analysis, our model produced a model fit of 37.9%, which can be seen by our R-Squared metric. Look to our average_invest coefficient, our model indicates that for a one unit increase in avg_invest will result, on average, in a slope coefficient (0.0015) increase in log(average_realGDP)."
      ],
      "metadata": {
        "id": "J01axdgpSuVy"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Formal Report\n",
        "\n",
        "Submitted formal report alongside this colab document in Canvas.\n",
        "\n",
        "Here's another link: https://docs.google.com/document/d/1OM9-MybXu_v9n67cAsEWHjMRsmpMcLiFYjRJUxJqOH4/edit?usp=sharing\n"
      ],
      "metadata": {
        "id": "EIwaxO-JBPfy"
      }
    }
  ]
}