notebooks/05_Model_Evaluation.ipynb

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   "cell_type": "markdown",
   "metadata": {
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    "slideshow": {
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   "source": [
    "# 05 Model Evaluation\n",
    "\n",
    "- Model Evaluation\n",
    "- Over-fitting, Under-fitting and Model Selection\n",
    "- Ridge Regression\n",
    "- Grid Search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Evaluation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">How can you be certain the model works in the real world and performs optimally."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/01_out_of_sample.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\") \n",
    "\n",
    "\n",
    "# Import clean data \n",
    "url = 'https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/DA0101EN/module_5_auto.csv'\n",
    "df = pd.read_csv(url)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Save dataset into data directory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df.to_csv('../data/module_5_auto.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Use numeric data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   },
   "outputs": [
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       "      <th>Unnamed: 0</th>\n",
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       "      <th>symboling</th>\n",
       "      <th>normalized-losses</th>\n",
       "      <th>wheel-base</th>\n",
       "      <th>length</th>\n",
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       "      <th>curb-weight</th>\n",
       "      <th>engine-size</th>\n",
       "      <th>...</th>\n",
       "      <th>stroke</th>\n",
       "      <th>compression-ratio</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>price</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
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       "      <td>2.68</td>\n",
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       "      <td>52.4</td>\n",
       "      <td>2823</td>\n",
       "      <td>152</td>\n",
       "      <td>...</td>\n",
       "      <td>3.47</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>16500.0</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>0.919444</td>\n",
       "      <td>54.3</td>\n",
       "      <td>2337</td>\n",
       "      <td>109</td>\n",
       "      <td>...</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
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       "      <td>4</td>\n",
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       "      <td>54.3</td>\n",
       "      <td>2824</td>\n",
       "      <td>136</td>\n",
       "      <td>...</td>\n",
       "      <td>3.40</td>\n",
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       "      <td>0</td>\n",
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       "   Unnamed: 0  Unnamed: 0.1  symboling  normalized-losses  wheel-base  \\\n",
       "0           0             0          3                122        88.6   \n",
       "1           1             1          3                122        88.6   \n",
       "2           2             2          1                122        94.5   \n",
       "3           3             3          2                164        99.8   \n",
       "4           4             4          2                164        99.4   \n",
       "\n",
       "     length     width  height  curb-weight  engine-size  ...  stroke  \\\n",
       "0  0.811148  0.890278    48.8         2548          130  ...    2.68   \n",
       "1  0.811148  0.890278    48.8         2548          130  ...    2.68   \n",
       "2  0.822681  0.909722    52.4         2823          152  ...    3.47   \n",
       "3  0.848630  0.919444    54.3         2337          109  ...    3.40   \n",
       "4  0.848630  0.922222    54.3         2824          136  ...    3.40   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm  city-mpg  highway-mpg    price  \\\n",
       "0                9.0       111.0    5000.0        21           27  13495.0   \n",
       "1                9.0       111.0    5000.0        21           27  16500.0   \n",
       "2                9.0       154.0    5000.0        19           26  16500.0   \n",
       "3               10.0       102.0    5500.0        24           30  13950.0   \n",
       "4                8.0       115.0    5500.0        18           22  17450.0   \n",
       "\n",
       "   city-L/100km  diesel  gas  \n",
       "0     11.190476       0    1  \n",
       "1     11.190476       0    1  \n",
       "2     12.368421       0    1  \n",
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     "metadata": {},
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   ],
   "source": [
    "df = df._get_numeric_data()\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Import plotting libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import display\n",
    "from ipywidgets import widgets, interact, interactive, fixed, interact_manual"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Functions for plotting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    }
   },
   "outputs": [],
   "source": [
    "def DistributionPlot(RedFunction, BlueFunction, RedName, BlueName, Title):\n",
    "    width = 12\n",
    "    height = 10\n",
    "    plt.figure(figsize=(width, height))\n",
    "\n",
    "    ax1 = sns.distplot(RedFunction, hist=False, color=\"r\", label=RedName)\n",
    "    ax2 = sns.distplot(BlueFunction, hist=False, color=\"b\", label=BlueName, ax=ax1)\n",
    "\n",
    "    plt.title(Title)\n",
    "    plt.xlabel('Price (in dollars)')\n",
    "    plt.ylabel('Proportion of Cars')\n",
    "    \n",
    "    title_str = Title.lower().replace(\" \", \"_\") + '_distplot'\n",
    "    filename = f'../figs/05_Model_Evaluation/02_select/{title_str}'\n",
    "    plt.savefig(filename)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "def PollyPlot(xtrain, xtest, y_train, y_test, lr, poly_transform):\n",
    "    # xtrain, y_train: training data \n",
    "    # xtest, y_test: testing data \n",
    "    # lr:  linear regression object \n",
    "    # poly_transform:  polynomial transformation object\n",
    "    \n",
    "    width = 12\n",
    "    height = 10\n",
    "    plt.figure(figsize=(width, height))         \n",
    " \n",
    "    xmax = max([xtrain.values.max(), xtest.values.max()])\n",
    "    xmin = min([xtrain.values.min(), xtest.values.min()])\n",
    "\n",
    "    x = np.arange(xmin, xmax, 0.1)\n",
    "\n",
    "    plt.plot(xtrain, y_train, 'ro', label='Training Data')\n",
    "    plt.plot(xtest, y_test, 'go', label='Test Data')\n",
    "    plt.plot(x, lr.predict(poly_transform.fit_transform(x.reshape(-1, 1))), label='Predicted Function')\n",
    "    plt.ylim([-10000, 60000])\n",
    "    plt.ylabel('Price')\n",
    "    plt.legend()    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Training and Testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Split your data into training and testing data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/02_split_dataset.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/03_training_testing.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/04_train_test_split.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    13495.0\n",
       "1    16500.0\n",
       "2    16500.0\n",
       "3    13950.0\n",
       "4    17450.0\n",
       "Name: price, dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# place the target data price in a separate dataframe y\n",
    "y_data = df['price']\n",
    "y_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
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       "      <th>peak-rpm</th>\n",
       "      <th>city-mpg</th>\n",
       "      <th>highway-mpg</th>\n",
       "      <th>city-L/100km</th>\n",
       "      <th>diesel</th>\n",
       "      <th>gas</th>\n",
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       "      <td>2</td>\n",
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       "      <td>122</td>\n",
       "      <td>94.5</td>\n",
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       "      <td>2.68</td>\n",
       "      <td>3.47</td>\n",
       "      <td>9.0</td>\n",
       "      <td>154.0</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>19</td>\n",
       "      <td>26</td>\n",
       "      <td>12.368421</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>99.8</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>0.919444</td>\n",
       "      <td>54.3</td>\n",
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       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>10.0</td>\n",
       "      <td>102.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>24</td>\n",
       "      <td>30</td>\n",
       "      <td>9.791667</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <th>4</th>\n",
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       "      <td>4</td>\n",
       "      <td>2</td>\n",
       "      <td>164</td>\n",
       "      <td>99.4</td>\n",
       "      <td>0.848630</td>\n",
       "      <td>0.922222</td>\n",
       "      <td>54.3</td>\n",
       "      <td>2824</td>\n",
       "      <td>136</td>\n",
       "      <td>3.19</td>\n",
       "      <td>3.40</td>\n",
       "      <td>8.0</td>\n",
       "      <td>115.0</td>\n",
       "      <td>5500.0</td>\n",
       "      <td>18</td>\n",
       "      <td>22</td>\n",
       "      <td>13.055556</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Unnamed: 0.1  symboling  normalized-losses  wheel-base  \\\n",
       "0           0             0          3                122        88.6   \n",
       "1           1             1          3                122        88.6   \n",
       "2           2             2          1                122        94.5   \n",
       "3           3             3          2                164        99.8   \n",
       "4           4             4          2                164        99.4   \n",
       "\n",
       "     length     width  height  curb-weight  engine-size  bore  stroke  \\\n",
       "0  0.811148  0.890278    48.8         2548          130  3.47    2.68   \n",
       "1  0.811148  0.890278    48.8         2548          130  3.47    2.68   \n",
       "2  0.822681  0.909722    52.4         2823          152  2.68    3.47   \n",
       "3  0.848630  0.919444    54.3         2337          109  3.19    3.40   \n",
       "4  0.848630  0.922222    54.3         2824          136  3.19    3.40   \n",
       "\n",
       "   compression-ratio  horsepower  peak-rpm  city-mpg  highway-mpg  \\\n",
       "0                9.0       111.0    5000.0        21           27   \n",
       "1                9.0       111.0    5000.0        21           27   \n",
       "2                9.0       154.0    5000.0        19           26   \n",
       "3               10.0       102.0    5500.0        24           30   \n",
       "4                8.0       115.0    5500.0        18           22   \n",
       "\n",
       "   city-L/100km  diesel  gas  \n",
       "0     11.190476       0    1  \n",
       "1     11.190476       0    1  \n",
       "2     12.368421       0    1  \n",
       "3      9.791667       0    1  \n",
       "4     13.055556       0    1  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# drop price data in x data\n",
    "x_data=df.drop('price',axis=1)\n",
    "x_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Use the function \"train_test_split\" to split up the data set \n",
    "- 15% of the data samples will be utilized for testing\n",
    "- set the parameter \"random_state\" equal to zero. \n",
    "- The output of the function should be the following: \n",
    " - \"x_train\" , \"x_test\", \"y_train\" and \"y_test\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# split our data into training and testing data\n",
    "# using the function train_test_split.\n",
    "from sklearn.model_selection import train_test_split\n",
    "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.15, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 31\n",
      "number of training samples: 170\n"
     ]
    }
   ],
   "source": [
    "print(f\"number of test samples : { x_test.shape[0]}\")\n",
    "print(f\"number of training samples: {x_train.shape[0]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Import LinearRegression from the module linear_model\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Create a Linear Regression object:\n",
    "lre=LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the model using the feature horsepower\n",
    "lre.fit(x_train[['horsepower']], y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 on the test data  = 0.79231\n"
     ]
    }
   ],
   "source": [
    "# Calculate the R^2 on the test data:\n",
    "r_squared = lre.score(x_test[['horsepower']], y_test)\n",
    "print(f\"R^2 on the test data  = {r_squared:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Use the function \"train_test_split\" to split up the data set \n",
    "- 40% of the data samples will be utilized for testing\n",
    "- set the parameter \"random_state\" equal to zero. \n",
    "- The output of the function should be the following: \n",
    " - \"x_train_1\" , \"x_test_1\", \"y_train_1\" and \"y_test_1\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# split our data into training and testing data\n",
    "# using the function train_test_split.\n",
    "from sklearn.model_selection import train_test_split\n",
    "x_train_1, x_test_1, y_train_1, y_test_1 = train_test_split(x_data, y_data, test_size=0.40, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 81\n",
      "number of training samples: 120\n"
     ]
    }
   ],
   "source": [
    "print(f\"number of test samples : { x_test_1.shape[0]}\")\n",
    "print(f\"number of training samples: {x_train_1.shape[0]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Import LinearRegression from the module linear_model\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Create a Linear Regression object:\n",
    "lre1=LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the model using the feature horsepower\n",
    "lre1.fit(x_train_1[['horsepower']], y_train_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 on the test data 1 = 0.71394\n"
     ]
    }
   ],
   "source": [
    "# Calculate the R^2 on the test data:\n",
    "r_squared = lre1.score(x_test_1[['horsepower']], y_test_1)\n",
    "print(f\"R^2 on the test data 1 = {r_squared:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R^2 is much smaller using the test data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Find the R^2 on the test data using 90% of the data for training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "x_train_2, x_test_2, y_train_2, y_test_2 = train_test_split(x_data, y_data, test_size=0.10, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "number of test samples : 21\n",
      "number of training samples: 180\n"
     ]
    }
   ],
   "source": [
    "print(f\"number of test samples : { x_test_2.shape[0]}\")\n",
    "print(f\"number of training samples: {x_train_2.shape[0]}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 on the test data 2 = 0.73407\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lre2 = LinearRegression()\n",
    "lre2.fit(x_train_2[['horsepower']], y_train_2)\n",
    "r_squared = lre2.score(x_test_2[['horsepower']], y_test_2)\n",
    "print(f\"R^2 on the test data 2 = {r_squared:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Cross-validation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/05_generalization_error.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/06_generalization_error_train_test.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/07_train_test.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/08_good_accuracy_poor_precision.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/09_poor_accuracy_good_precision.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Cross-validation Score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perform Cross-validation when you do not have sufficient testing data\n",
    ">All  error estimates are relatively close together,\n",
    "but they are further away from the true generalization performance.\n",
    "- To overcome this problem, we use cross validation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/10_cross_validation.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/11_cross_val_score_1.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/12_cross_val_score_2.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/13_cross_val_score_3.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# import cross_val_score from the module model_selection.\n",
    "from sklearn.model_selection import cross_val_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# input the object, \n",
    "# the feature 'horsepower' in this case, \n",
    "# the target data (y_data). \n",
    "# parameter 'cv' determines the number of folds; 4 in this case.\n",
    "Rcross = cross_val_score(lre, x_data[['horsepower']], y_data, cv=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.7746232 , 0.51716687, 0.74785353, 0.04839605])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The default scoring is R^2; \n",
    "# each element in the array has the average R^2 value in the fold:\n",
    "Rcross"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean of the folds are 0.52201\n",
      "Standard deviation is 0.29118\n"
     ]
    }
   ],
   "source": [
    "# Calculate average and standard deviation of the estimate\n",
    "print(f\"Mean of the folds are {Rcross.mean():.5f}\")\n",
    "print(f\"Standard deviation is {Rcross.std():.5f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['20,254,143', '43,745,493', '12,539,630', '17,561,928']"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use mean squared error as a score \n",
    "# by setting the parameter 'scoring' metric to 'neg_mean_squared_error'.\n",
    "mse_cross = -1 * cross_val_score(lre,x_data[['horsepower']], y_data,cv=4,scoring='neg_mean_squared_error')\n",
    "['{:,.0f}'.format(i) for i in mse_cross.tolist()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Calculate the average R^2 using two folds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    ">Calculate the average R^2 using two folds\n",
    "- find the average R^2 for the second fold utilizing the horsepower as a feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 using two folds : ['0.59016', '0.44320']\n",
      "Average R^2 using two folds = 0.51668\n",
      "Standard deviation is 0.07348\n"
     ]
    }
   ],
   "source": [
    "Rcross2 = cross_val_score(lre, x_data[['horsepower']], y_data, cv=2)\n",
    "Rcross2_str  = ['{:.5f}'.format(i) for i in Rcross2.tolist()]\n",
    "print(f\"R^2 using two folds : {Rcross2_str}\")\n",
    "print(f\"Average R^2 using two folds = {Rcross2.mean():.5f}\")\n",
    "print(f\"Standard deviation is {Rcross2.std():.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Predict using cross_val_predict"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/14_cross_val_predict_1.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/15_cross_val_predict_2.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/16_cross_val_predict_3.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/01_evaluate/17_cross_val_predict_4.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['14,142', '14,142', '20,814', '12,745', '14,762']"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# use the function 'cross_val_predict' to predict the output. \n",
    "# splits up the data into the specified number of folds, \n",
    "# using one fold to get a prediction\n",
    "# while the rest of the folds are used as test data\n",
    "\n",
    "from sklearn.model_selection import cross_val_predict\n",
    "\n",
    "yhat = cross_val_predict(lre,x_data[['horsepower']], y_data,cv=4)\n",
    "['{:,.0f}'.format(i) for i in yhat[0:5].tolist()]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Overfitting, Underfitting and Model Selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How to pick the best polynomial order?\n",
    "- Assume the training points come from a polynomial function plus some noise.\n",
    "- The goal of model selection is to determine the order of the polynomial to provide the best estimate of the function $y$ = $f(x)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Select polynomial order that minimizes the test error\n",
    "- **Any order less is considered under-fitting.**\n",
    "- **Any order more is considered over-fitting.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/01_true_function.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/02_sample_points_true_function_noise.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/03_underfit_linear_model.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/04_underfit_2_poly.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/05_fit_8_poly.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/06_overfit_16_poly.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create Multiple linear regression objects and train the model \n",
    "# using 'horsepower', 'curb-weight', 'engine-size' and 'highway-mpg' as features.\n",
    "lr = LinearRegression()\n",
    "lr.fit(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['10,028', '7,611', '20,199', '8,332', '11,254']"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Prediction using training data:\n",
    "yhat_train = lr.predict(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "['{:,.0f}'.format(i) for i in yhat_train[0:5].tolist()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['5,131', '10,413', '19,890', '21,975', '20,760']"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Prediction using test data\n",
    "yhat_test = lr.predict(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']])\n",
    "['{:,.0f}'.format(i) for i in yhat_test[0:5].tolist()]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Perform some model evaluation using our training and testing data separately.\n",
    "# First we import the seaborn and matplotlibb library for plotting.\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Examine the distribution of the predicted values of the training data.\n",
    "Title = 'Distribution Plot of Predicted Value Using Training Data vs Data Distribution of Training Data'\n",
    "DistributionPlot(y_train, yhat_train, \"Actual Values (Train)\", \"Predicted Values (Train)\", Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot of predicted values using the training data compared to the actual training data.\n",
    "\n",
    ">Model seems to be doing well in learning from the training dataset. \n",
    "\n",
    ">When the model generates new values from the test data, we see the distribution of the predicted values is much different from the actual target values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Title='Distribution  Plot of  Predicted Value Using Test Data vs Data Distribution of Test Data'\n",
    "DistributionPlot(y_test,yhat_test,\"Actual Values (Test)\",\"Predicted Values (Test)\",Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Plot of predicted value using the test data compared to the test data.\n",
    "\n",
    ">Comparing the figures\n",
    ">The distribution of the test data in first figure is much better at fitting the data. \n",
    "\n",
    ">This difference in second figure is apparent where the ranges are from 5000 to 15 000. \n",
    "\n",
    ">This is where the distribution shape is exceptionally different. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# see if polynomial regression also exhibits a drop in the prediction accuracy when analysing the test dataset.\n",
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Overfitting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Overfitting occurs when the model fits the noise, not the underlying process. \n",
    "\n",
    "> when testing your model using the test-set, your model does not perform as well as it is modelling noise, not the underlying process that generated the relationship. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/07_train_error.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/08_test_error.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/09_select_min_test_error.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/10_ irreducible_ error_random_noise_term.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/11_wrong_poly_sin.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/12_mean_order_0_poly.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/13_linear_order_1_poly.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/14_order_2_poly.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/15_order_3_poly.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/16_order_4_poly_200_hp.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Create a degree 5 polynomial model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# use 55 percent of the data for testing and the rest for training\n",
    "x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=0.45, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=5, include_bias=True, interaction_only=False,\n",
       "                   order='C')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Perform a degree 5 polynomial transformation on the feature 'horse power'.\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "pr = PolynomialFeatures(degree=5)\n",
    "x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "x_test_pr = pr.fit_transform(x_test[['horsepower']])\n",
    "pr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Create a linear regression model \"poly\" and train it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly = LinearRegression()\n",
    "poly.fit(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# See the output of our model using the method \"predict.\" then \n",
    "# assign the values to \"yhat\".\n",
    "\n",
    "yhat = poly.predict(x_test_pr)\n",
    "yhat = [float('{:.1f}'.format(i)) for i in yhat[0:4]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted values: [6728.7, 7308.0, 12213.8, 18893.2]\n",
      "True values     : [ 6295. 10698. 13860. 13499.]\n"
     ]
    }
   ],
   "source": [
    "# Take the first five predicted values and \n",
    "# compare it to the actual targets.\n",
    "\n",
    "print(f\"Predicted values: {yhat}\")\n",
    "print(f\"True values     : {y_test[0:4].values}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Use PollyPlot to display the training data, testing data, and the predicted function.\n",
    "\n",
    "PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train, y_test, poly,pr)\n",
    "plt.gcf()\n",
    "filename = f'../figs/05_Model_Evaluation/02_select/degree5_poly_horse_power.png'\n",
    "plt.savefig(filename)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Polynomial regression model\n",
    "- red dots represent training data\n",
    "- green dots represent test data\n",
    "- blue line represents the model prediction.\n",
    "\n",
    ">The estimated function appears to track the data but around 200 horsepower, the function begins to diverge from the data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 on the training data = 0.55677\n"
     ]
    }
   ],
   "source": [
    "# R^2 of the training data\n",
    "\n",
    "r_squared = poly.score(x_train_pr, y_train)\n",
    "print(f\"R^2 on the training data = {r_squared:.5f}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 on the test data = -29.87134\n"
     ]
    }
   ],
   "source": [
    "#R^2 of the test data\n",
    "\n",
    "r_squared = poly.score(x_test_pr, y_test)\n",
    "print(f\"R^2 on the test data = {r_squared:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### R^2 for the training data is 0.5567 while the R^2 on the test data was -29.87. \n",
    "- The lower the R^2, the worse the model\n",
    "- Negative R^2 is a sign of overfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R^2 Using Test Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/17_max_r_squared_order_3.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/02_select/18_calculate_r_squared_orders.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# How the R^2 changes on the test data for different order polynomials and\n",
    "# plot the results\n",
    "\n",
    "Rsqu_test = []\n",
    "\n",
    "order = [1, 2, 3, 4]\n",
    "for n in order:\n",
    "    pr = PolynomialFeatures(degree=n)\n",
    "    \n",
    "    x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "    \n",
    "    x_test_pr = pr.fit_transform(x_test[['horsepower']])    \n",
    "    \n",
    "    lr.fit(x_train_pr, y_train)\n",
    "    \n",
    "    Rsqu_test.append(lr.score(x_test_pr, y_test))\n",
    "    \n",
    "Rsqu_max = max(Rsqu_test)\n",
    "Rsqu_max_order = Rsqu_test.index(Rsqu_max) + 1\n",
    "\n",
    "Rsqu_max_str = f'Max R^2 = {Rsqu_max:.5f}'\n",
    "Rsqu_max_order_str = f'@ {Rsqu_max_order} order'\n",
    "\n",
    "plt.plot(order, Rsqu_test)\n",
    "plt.xlabel('order')\n",
    "plt.ylabel('R^2')\n",
    "plt.title('R^2 Using Test Data')\n",
    "plt.text(Rsqu_max_order+0.1, Rsqu_max, Rsqu_max_str)\n",
    "plt.text(Rsqu_max_order+0.15, Rsqu_max-0.03, Rsqu_max_order_str)\n",
    "\n",
    "plt.savefig('../figs/05_Model_Evaluation/02_select/r_squared_order_horsepower.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### R^2 gradually increases until an order three polynomial is used. Then the R^2 dramatically decreases at four."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Experiment with different polynomial orders"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# The function f is used to experiment with different polynomial orders\n",
    "def f(order, test_data):\n",
    "    x_train, x_test, y_train, y_test = train_test_split(x_data, y_data, test_size=test_data, random_state=0)\n",
    "    pr = PolynomialFeatures(degree=order)\n",
    "    x_train_pr = pr.fit_transform(x_train[['horsepower']])\n",
    "    x_test_pr = pr.fit_transform(x_test[['horsepower']])\n",
    "    poly = LinearRegression()\n",
    "    poly.fit(x_train_pr,y_train)\n",
    "    PollyPlot(x_train[['horsepower']], x_test[['horsepower']], y_train,y_test, poly, pr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "23771d6eaacb4808a1b47a32481bda4e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntSlider(value=3, description='order', max=6), FloatSlider(value=0.45, description='tes…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Experiment with different polynomial orders and different amounts of data.\n",
    "interact(f, order=(0, 6, 1), test_data=(0.05, 0.95, 0.05));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Create a \"PolynomialFeatures\" object \"pr1\" of degree two"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PolynomialFeatures(degree=2, include_bias=True, interaction_only=False,\n",
       "                   order='C')"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pr1 = PolynomialFeatures(degree=2)\n",
    "pr1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Transform the training and testing samples for the features 'horsepower', 'curb-weight', 'engine-size' and 'highway-mpg'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "x_train_pr1 = pr1.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size' , 'highway-mpg']])\n",
    "x_test_pr1 = pr1.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size' , 'highway-mpg']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train_pr1.shape[1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Create a linear regression model \"poly1\" and train the object "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly1 = LinearRegression()\n",
    "poly1.fit(x_train_pr1, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Use the method \"predict\" to predict an output on the polynomial features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mmLD1D1V4/avxJ7Njg8C+sXOukXOuazB/HaVfm1hW4792LKvO0LL/DquzsXOuvnPu/qDOJsF2J1IvzrlP8RczY/C99c+F5pnZQPzN0T8Emjg/esU2fI9IpLKOt9XAqIh213X+ptZIq4DW4T2BZlYPfxG0Mmj31865McG0ifiv6strHT6QDjmUXqLV+PzT8O3LcM7NCnq5H3LO9cD3YGbhv/qHso/pWM7Hp7fMCl7vV/G9Xc2D1+kjDr5O0ep4EpiN/5q+Ef4r7Wiva8hL+J7fwfjzwOfgu9DjbFuZzOzEYL1PE2hXtO24Ff8a9gmWH17GdkRrwwD8eSLaOXubc+4G51wb/MXh7WbWP057Enk9I88Lu4JvAyLfQ7Up2ctfkXP2bqJfgMTzHb4nM/zc0ZrknEdXAzkR75OGzrlxAM65b51zF+LPHU8BbwQXhxV6nwS9zaM4eHz9Dr9PewbHyzmUPF4i6zkbf5/YOfgL42b4z9hYx9gn+PdIKFAPPY8XqFf0HBAyDLjc/ChEoVS+J80s0ZvcVwOXRDl3zaPs7Y/W9hLHMQcvwkKifab9Lcpn2mMAzrmJzrmh+LhqIz6VqUpToF5FmVkjMzsbn9/4vHPu2yjLnG1mJwUByHZ8j2JoqMX1+Hzw8ro06IWqh/9Qe8354RvzgLpmNjo44d+OT1sIWQ+0tdijl7wE3GRm7YIesj8CLzv/dXeqvAKMNrNhQZt/jQ+GPw9rc7x99CLwE/NDeR0VtPkr59yKZDfUObcO33v3f8FrX8PM2ptZ6GvUV4BfmVkr8yMOxPv25Cl8alCvoAfjJDMLfeBGbvPzwDlmNsLMapofsm6ImbVyPl1mJnCXmdUJApBzEtic5/BfATemZKpMQ3xQthGoZWZ34NMcoinreHscuDe0XWbWzMzGxCjrK2APcGuwffXx+bkz8T3odczsx2Z2dPB1bOi9VF6v4I+XzsH7544KlBHyOD6I6whgZk3MbGzwf18z620+zWcnPje4Qu97MzvG/Pj7D+NTbbbje01r4/OsD5jZufhevZD1QPOInu6GwDbnXIGZdcXfABnPm/gA4H/x9xa4BLYt3nbUD3pLJ+Jzaz8sq13Op0xto+T+aojvbdxqfhi+mENdRmnD0ebHsn4en/u9OMoy5wbnQAvqTsY5+wrz46s3wKeAhYZXXAA0DTv/3UXJz/z1QKgt0byEP4+0NrOG+PskXgy9VokK9vME4I/B69Qef/GVjN9M+AhoZGa/MLOjzKxWcL7OAjCzy82safAZth1/wQB+2+uZTyUrU3CO6I5P26rFwVF9GuKP061m1hyIHFo18jVtyMHOr9BnSrzU0tn43PfR+Pts1gT1DyN2oL4e3zFR0TTAC/DvzezgbxFwC/HTLcM9DvzefOojZtbUDg7/Wtb2r8ffGxMuBxgXfD4NxO+LeP6Jj2MGB5+jGWY2PPiMaGN+eNkMfCywk4qd6yuVAvWq520z24G/Kvxf/I18P4mxbAfgQ/xdz18Af3fOTQ3m3Yf/oN9q5fuhg3/jb9b8Dn9zxq/A9wThv1J8Ct8TshN/c0vIq8HjZjOLlt/7TFD2NPyNRHvwd4anTJB7din+JtBN+CDznCBvDsrYR865Kfgek9fxvaXtOZgzngqX4W++mY+/Ueg1fAoK+J7B9/G5+7PxN+NG5Zx7Ff8V+4v4mz8ncrAnrcQ2O+dW43u//wcfQK/Gn5RD54YfAafie9F+T1gPeRzP4XvMXg4+pEPex6c25OF7svcQIz0kgePtEfxoApOD98uXQTujlbUXf3IfEpSxDP+1/g/Dgo7/AlaY/zr2GvxxUy7OuXfxvTMf41PSvghm7Y25UuyyXsKPGvFG0KYc/I2+4C+AnsXfZLUMvy9DvUJPAH2C13d8nCoWmR9HOg9/3F3rgmEhg3SGm/EXWZvxI4RMCls3F7/vVwb1NAVuwn/dXIC/wTDuWNzO5/C/hQ84XgybFW/bonkqeP2/w6cCvkDJi8my2nUH8GqwHefi72M5NtjuzyK2O5bJQfkrORjQXBNj2c749IXQyBsPOue+DObdi7/43Gpm5ckP/jc+qF6DD0R/DcWv4w34fZKP30fhqSrj8T2VW8zsc0p7DH+e+RyfSrcFKCtVJ5arg8eV+OD6KQ6mO1VY8N4egX9vrMJfXP4Vf3M0+KAzLzhGbgcudj5v+Tv8cTUv2N+dY1Tx82Dd7/GfcUuBU9zBoSTvx5/rvse/7yPv4XkQuMb8GPt34z9LZuI/A5cEjzvibN9+/MhgK5xzoR+6mgbsjHYhGHgHfy7faGaJpkCG17nFOfdd6A/fubLVOReznRHr/xP/ef9mcO6azcEL/bK2/3mgWbC/Pg6m/QafvrQNf6NsWeeWhfjP6fvw7+MV+M8S8Bc5d+AvCDbiL0huSmS70slc+S6ORUQkAcGH/1z80J2p/OZIRESqKfWoi4gkiZmdH3xN3gSf/vO2gnQREakoBeoiIslzNf4r1aX43MdfpLc5IiJyOFPqi4iIiIhIFaQedRERERGRKqiiw/dUe8cee6xr27ZtupshIiIiItXYrFmzNjnnmkWbp0A9hrZt2zJz5sx0N0NEREREqjEzi/mr30p9ERERERGpghSoi4iIiIhUQQrURURERESqIOWoi4iIiAQKCwvJz89nz5496W6KVDN169alVatW1K5dO+F1FKiLiIiIBPLz82nYsCFt27bFzNLdHKkmnHNs3ryZ/Px82rVrl/B6Sn0RERERCezZs4djjjlGQboklZlxzDHHlPubGgXqIiIiImEUpEsqVOS4UqAuIiIiIlIFKVAXEREREamCFKiLiIiIVDETJkzAzFi4cGGZyz777LOsXbu2wnVNnTqVs88+u8S0nTt3cswxx7Bt27YS08877zxeeeWVcpWVbA8//DDPPfccv/zlL8nOzqZLly5kZGSQnZ1NdnY2r732WrnKmz17Nu+9917x84kTJ3L33Xcnu9kVokBdREREpIp56aWXGDBgAOPHjy9z2UMN1KOpX78+w4cPZ+LEicXTtm3bxmeffZbyQDyeoqIinnnmGX70ox/x6KOPkpOTw6RJk2jfvj05OTnk5ORw4YUXlqvMyEB9zJgxvP7661ViiE4F6iIiIiLR3HgjDBmS3L8bbyyz2oKCAqZPn87TTz9dKlB/4IEH6NatG1lZWdx666289tprzJw5kx//+MdkZ2eze/du2rZty6ZNmwCYOXMmQ4YMAWDGjBn069ePHj160K9fPxYtWhS3HePGjStR/4QJExg5ciT16tVLqKw777yTBx98sPh5ZmYmK1asAOD555/nlFNOITs7m6uvvpr9+/ezf/9+rrjiCjIzM+nWrRt//vOfS5X50Ucf0bNnT2rVij/C+OLFixkxYgS9evVi0KBB5OXlATB+/HgyMzPJyspi6NCh7N69mz/84Q+88MILxb3xZsbAgQOZNGlS3Doqg8ZRFxEREalCJk6cyMiRIzn55JNp2rQps2fPpmfPnrz77rtMnDiRr776inr16rFlyxaaNm3K3/72Nx588EF69+4dt9xOnToxbdo0atWqxYcffsj//M//8Prrr8dcfuTIkVx55ZVs3ryZY445hvHjx3P99ddXqKxwCxYs4OWXX2b69OnUrl2ba6+9lhdeeIGuXbuyZs0a5s6dC8DWrVtLrTt9+nR69epVZh0///nPeeqpp2jfvj3Tp0/nuuuuY/Lkydx1111MnTqVFi1asHXrVjIyMrjjjjuYO3cuDz/8cPH6vXv35tNPP+WCCy5IaJtSRYG6iIiISDRhgVtleumll7gx6Hm/5JJLeOmll+jZsycffvghP/nJT6hXrx4ATZs2LVe527Zt4/LLL2fx4sWYGYWFhXGXr1OnDueeey6vvfYaY8eOJScnh+HDh1eorHBTpkxh1qxZ9OnTB4Ddu3fTvHlzzjnnHJYtW8b111/P6NGji+sKt27dOjp37hy3/K1bt/Lll18yduzY4mlFRUUA9O/fn8suu4yLLroobhDevHnzpKcTVYQCdREREZEqYvPmzXz00UfMnTsXM2P//v2YGQ888ADOuYTG4q5VqxYHDhwAKJFn/bvf/Y6hQ4cyYcIEVqxYUZwSE8+4ceO45557cM4xZswYateunXBZ4e0Ib4tzjssvv5z77ruv1Dq5ubm8//77PProo7zyyis888wzJeZnZGSUmTvunOPYY48lJyen1Lwnn3ySr776infeeYesrCzmzJkTtYw9e/aQkZERt57KoBx1ERERkSritdde47LLLmPlypWsWLGC1atX065dOz777DOGDx/OM888w65duwDYsmULAA0bNmTHjh3FZbRt25ZZs2YBlEhH2bZtG8cffzzgb0BNxNChQ1m8eDGPPvoo48aNK1dZbdu2Zfbs2YC/YXP58uUADBs2jNdee40NGzYUb8fKlSvZtGkTBw4cYOzYsdx9993F64br3LkzS5YsidvmJk2a0LJlSyZMmADAgQMHyM3NBWDZsmX07duXu+++myZNmrBmzZpS+w8gLy+PzMzMsnZPyilQFxEREakiXnrpJc4///wS08aOHcuLL77IyJEjOffcc+nduzfZ2dnFN2peccUVXHPNNcU3k/7+97/nhhtuYODAgdSsWbO4nN/85jfcdttt9O/fn/379yfUnho1ajB27Fg2b97MoEGDylXW2LFj2bJlC9nZ2Tz22GOcfPLJAHTp0oV77rmH4cOH0717d84880zWrVvHmjVrGDJkCNnZ2VxxxRVRe9xHjRrFtGnTymz3+PHjefzxx8nKyqJr16688847ANx0001069aNbt26ccYZZ5CZmcnpp59Obm4uPXr0KB7a8eOPP+ass85KaB+lkjnn0t2GKql3795u5syZ6W6GiIiIVKIFCxaUmQMt6XX++efzwAMP0KFDh5SUv3btWq644gomT56c9LKjHV9mNss5F/VOYPWoi4iIiMhh4/7772fdunUpK3/16tUlhpVMp5QG6mY20swWmdkSM7s1ynwzs78E8+eYWc+y1jWzpmb2gZktDh6bhM27LVh+kZmNCJs+zsy+Dep4z8yOTeV2i4iIiEhqdOzYsUQaTrKdeuqpdO/ePWXll0fKAnUzqwk8CowCugDjzKxLxGKjgA7B38+BxxJY91ZginOuAzAleE4w/xKgKzAS+LuZ1TSzWsAjwFDnXHdgDnBdSjZaRERERCRJUtmjfgqwxDm3zDm3DxgPjIlYZgzwnPO+BBqbWcsy1h0D/Cv4/1/AeWHTxzvn9jrnlgNLgnIs+KtvfkyjRkD6B8YUEREREYkjlYH68cDqsOf5wbRElom3bgvn3DqA4LF5vLKcc4XAL4Bv8QF6F+DpaA02s5+b2Uwzm7lx48ZEtlFEREREJCVSGahHG5E/coiZWMsksm5C9ZlZbXyg3gP4AT715bZoBTjnnnDO9XbO9W7WrFkZ1Ykkl3Pw6KNwzz2wb1+6WyMiIiLplspAPR84Iex5K0qnnMRaJt6664P0GILHDWWUlQ3gnFvq/FiUrwD9KrZJIqlRWAhXXQXXXQe/+x2ccgrMnZvuVomISDrUrFmT7OxsMjMzueiii4p/4Kgipk6dytlnnw3AW2+9xf333x9z2a1bt/L3v/+93HXceeedpUZJmTp1KqeddlqJaUVFRbRo0SLuiC3Rykq2Cy+8kGXLlnHqqaeSnZ1N69atadasGdnZ2WRnZ7NixYpylffGG2+wcOHC4uc33nhjQmO9JyKVgfrXQAcza2dmdfA3er4VscxbwGXB6C99gW1BOku8dd8CLg/+vxx4M2z6JWZ2lJm1w9+gOgNYA3Qxs1AX+ZnAgmRvrEhFbd0Ko0bB00/D7bfDm2/CunXQqxc89BCE/fqyiIgcATIyMsjJyWHu3LnUqVOHxx9/vMR85xwHKvDhcO6553LrraUG4StW0UA9mkGDBpGfn18i6P3www/JzMykZcuWSamjIubNm8f+/fs58cQT+eqrr8jJyeEPf/gDF198MTk5OeTk5NC2bdtylRkZqF9//fVRf6ypIlIWqDvnivCjq7yPD4xfcc7NM7NrzOyaYLFJwDL8jZ9PAtfGWzdY537gTDNbjA+67w/WmYfvLZ8PvAf80jm33zm3FrgLmGZmc/A97H9M1WCPTRkAACAASURBVHaLlMfy5dCvH0ybBs8+C3ffDeee63vTzzoLfv1rOOMMKChId0tFRI48N94IQ4Yk9+/GG8vXhoEDB7JkyRJWrFhB586dufbaa+nZsyerV69m8uTJnHbaafTs2ZOLLrqIguDD4r333qNTp04MGDCAN954o7isZ599luuu8wPfrV+/nvPPP5+srCyysrL4/PPPufXWW1m6dCnZ2dnccsstAPzpT3+iT58+dO/end///vfFZd1777107NiRM844g0WLFpVqd40aNbjooot4+eWXi6eNHz+ecePGAfDkk0/Sp08fsrKyGDt2bNRvDYYMGULoxyc3bdpUHEDv37+fW265pbhd//jHPwBYt24dgwYNKv424tNPPy1V5gsvvMCYMZFjm5T27rvvFu/biy++mJ07dwJwyy230KVLF7p3785vf/tbPv30UyZNmsRNN91U3Bvfvn171q1bRzLud0zpOOrOuUnOuZOdc+2dc/cG0x53zj0e/O+cc78M5ndzzs2Mt24wfbNzbphzrkPwuCVs3r3B8h2dc++GTX/cOdfZOdfdOXeOc25zKrdbJBGbN8Npp8F338HkyXD55QfnNWsGb7wBTzwBH38MEZ0pIiJyBCgqKuLdd9+lW7duACxatIjLLruMb775hvr163PPPffw4YcfMnv2bHr37s1DDz3Enj17uOqqq3j77bf59NNP+e6776KW/atf/YrBgweTm5vL7Nmz6dq1K/fffz/t27cnJyeHP/3pT0yePJnFixczY8YMcnJymDVrFtOmTWPWrFmMHz+eb775hjfeeIOvv/46ah3jxo1j/PjxAOzdu5dJkyYxduxYAC644AK+/vprcnNz6dy5M08/HXWcj6iefvppjj76aL7++mu+/vprnnzySZYvX86LL77IiBEjyMnJITc3l+zs7FLrTp8+nV69esUtf8OGDdx///1MmTKF2bNn0717dx555BHWr1/PpEmTmDdvHnPmzOG2225j4MCBnHXWWfz5z38u0Rvfo0cPPv/884S3KZZah1yCiFTIP/8J69fDjBnQp0/p+WY+b338eJ8Cc/31cNRRld9OEZEj1cMPp6fe3bt3FweZAwcO5Gc/+xlr166lTZs29O3bF4Avv/yS+fPn079/fwD27dvHaaedxsKFC2nXrh0dOnQA4NJLL+WJJ54oVcdHH33Ec889B/ic+KOPPprvv/++xDKTJ09m8uTJ9OjRA4CCggIWL17Mjh07OP/886lXrx7gU2qi6dOnDwUFBSxatIgFCxbQt29fmjTxv1M5d+5cbr/9drZu3UpBQQEjRoyIWkY0kydPZs6cObz22msAbNu2jcWLF9OnTx9++tOfUlhYyHnnnRc1UF+3bh1lDRjy+eefM3/+fPr187c07tu3jwEDBtC0aVNq1KjBVVddxejRo4tz/6Np3rw5a9ce+mjgCtRF0uDAAfjHP2DAgOhBerjbboMzz4TnnvOBu4iIVG+hHPVI9evXL/7fOceZZ57JSy+9VGKZnJwc/M/GHDrnHLfddhtXX311iekPP/xwwnVccskljB8/ngULFhSnvQBcccUVTJw4kaysLJ599lmmTp1aat1atWoV5+Lv2bOnRLv++te/Rg3up02bxn/+8x/+67/+i1tuuYXLLrusxPyMjIwSZUXjnGPkyJH8+9//LjVv5syZfPDBB4wfP57HHnuMyZMnRy1jz549ZGRkxK0nESlNfRGR6KZMgSVL4Jpryl522DB/Y+kDD8D+/alvm4iIVH19+/Zl+vTpLFmyBIBdu3aRl5dHp06dWL58OUuXLgUoFciHDBs2jMceewzwOd/bt2+nYcOG7Nixo3iZESNG8MwzzxTnvq9Zs4YNGzYwaNAgJkyYwO7du9mxYwdvv/12zHaOGzeO559/no8++qhEz/uOHTto2bIlhYWFvPDCC1HXbdu2LbNmzQIo7j0Pteuxxx6jsLAQgLy8PHbu3MnKlStp3rw5V111FT/72c+YPXt2qTI7d+5cvM9i6devH5988gnLli0DYOfOncXfJGzfvp2zzz6bP//5z3zzzTcApfZbqE2ZmZlx60mEAnWRNHj8cTj2WLjwwrKXNfO96kuWwOuvp75tIiJS9TVr1oxnn32WcePG0b17d/r27cvChQupW7cuTzzxBKNHj2bAgAG0adMm6vqPPPIIH3/8Md26daNXr17MmzePY445hv79+5OZmcktt9zC8OHD+dGPfsRpp51Gt27duPDCC9mxY0fxDZbZ2dmMHTuWgQMHxmxnly5dqFevHqeffnqJbwTuvvtuTj31VM4880w6deoUdd2bb76Zxx57jH79+rFp06bi6VdeeSVdunShZ8+eZGZmcvXVV1NUVMTUqVPJzs6mR48evP7669xwww2lyhw9enTU3vtwLVq04Omnn+biiy8mKyuLfv36kZeXx7Zt2xg9ejRZWVmcfvrpPPTQQ4C/GPnjH/9YfDPp3r17WbFiRXHK0KEwP7S4ROrdu7cL3Wkskkxr1kCbNvDf/+17yROxfz906QL168OsWT54FxGR5FuwYAGdO3dOdzMkRXbv3s3QoUOZPn06NWvWTEkdr776KvPnzy8xSk5ItOPLzGY553pHK0s96iKV7OmnfeAdkfIXV82a8NvfwjffwAcfpK5tIiIi1VlGRgZ33XUXa9asSVkdzjluuummpJSlHvUY1KMuqVBUBG3bQteu8P775Vt33z448UTo0MEP2SgiIsm3YMECOnXqlLQbMkVCnHMsXLhQPeoiVdU77/jUl1/8ovzr1qnjfwBp6lT48sukN01ERIC6deuyefNm1JEpyeScY/PmzdStW7dc66lHPQb1qEsqjBzpf3V0xQqoVYHBUQsKoHVrGD0aoowaJSIih6iwsJD8/Pwyh/ATKa+6devSqlUrateuXWJ6vB51jaMuUkmWLvXpLnfeWbEgHaBBAzjnHN8zv3+/z10XEZHkqV27Nu3atUt3M0QApb6IVJrnnoMaNeDKKw+tnLPPhi1blP4iIiJS3SlQF6kkU6b4XyE9/vhDK2f4cN8j/847yWmXiIiIVE0K1EUqwc6dMGMGDBly6GUdfTQMHKhAXUREpLpToC5SCb74AgoLkxOog09/mTsXVq5MTnkiIiJS9ShQF6kEn3zib/zs3z855Y0e7R//85/klCciIiJVjwJ1kUowdSr06gUNGyanvJNPhpNOUvqLiIhIdaZAXSTFdu2Cr75KXtoLgJlPf/noI5//LiIiItWPAnWRFEt2fnrI6NGwd68P1kVERKT6UaAukmKffOLHT09WfnrIoEH+B5CU/iIiIlI9KVAXSbFQfnqjRsktt04dGDHCB+rOJbdsERERST8F6iIplIr89HBnnw1r10JOTmrKFxERkfRRoC6SQl9+Cfv2weDBqSl/1Cj/qGEaRUREqh8F6iIpFMpPHzAgNeW3aAGnnKI8dRERkepIgbpICk2dCj17wtFHp66Os86CGTPg++9TV4eIiIhUPgXqIimye7dPfUlVfnrIwIH+ZtKvvkptPSIiIlK5FKiLpEiq89NDTjnFp9d8/nlq6xEREZHKpUBdJEVSnZ8e0qABZGUpUBcREaluFKiLpMjUqdCjBzRunPq6+vXzqS9FRamvS0RERCqHAnWRFCgq8oHzwIGVU1+/flBQAHPnVk59IiIiknoK1EVSYPFi2LPH96hXhn79/KPSX0RERKoPBeoiKZCb6x+zsiqnvjZtoGVLBeoiIiLViQJ1kRTIzYVataBTp8qpzwz694fp0yunPhEREUk9BeoiKTBnDnTuDEcdVXl19usHK1bA2rWVV6eIiIikjgJ1kRTIza28tJeQUJ76F19Ubr0iIiKSGgrURZJs82ZYswa6d6/cenv08D34ylMXERGpHhSoiyRZZd9IGlKnDvTpo0BdRESkulCgLpJkc+b4x8oO1MGnv8ya5YeGFBERkcObAnWRJMvNhRYt/F9l69cPCgt9sC4iIiKHNwXqIkmWm1v5+ekhp53mH5X+IiIicvhToC6SREVFMG9eetJeAJo3h5NOUqAuIiJSHShQF0miRYtg3770Berg018+/xycS18bRERE5NApUBdJotCIL+lKfQEfqG/YAMuWpa8NIiIicugUqIsk0Zw5ULs2dOqUvjaEfvhI6S8iIiKHNwXqIkmUmwtduvgxzdOlSxeoV08jv4iIiBzuFKiLJFFubnrz0wFq1vRtmD07ve0QERGRQ6NAXSRJNm6EdevSm58e0qMH5OTAgQPpbomIiIhUlAJ1kSRJ5y+SRurZE3bs0A2lIiIihzMF6iJJEhrxpSoE6j16+Eelv4iIiBy+FKiLJEluLhx3HDRrlu6WQNeufvSZb75Jd0tERESkohSoiyTJnDlVozcd4KijfLCuHnUREZHDV610N0CkOigshPnzYfjwCqy8a5df+dtv/d/69XD77dC58yG1qWdPePtt/wulZodUlIiIiKSBAnWRJFi4EPbtK2eP+s6dMHo0TJvmo2mAunWhVi2YOhWmT4e2bSvcph494JlnYM0aaNWqwsWIiIhImij1RSQJvv3WP3brVo6V7rgDPvkEfvtbeP11yMuDggL/k6K7dsGZZ8J331W4TT17+kflqYuIiByeFKiLJEFenk8v6dAhwRW++goefhh+8Qu47z644AK/cs2aPtqfNAnWroURI2Dr1gq1qXt33yblqYuIiByeFKiLJEFeHrRp4zNXyrR3L/z0p/CDH8D990df5rTTYMIEWLDAp8fs3FnuNjVoAB07qkddRETkcKVAXSQJ8vLg5JMTXPi++/zNo48/Do0axV5u+HB48UX48ku48ELYv7/c7erRQz3qIiIih6uUBupmNtLMFpnZEjO7Ncp8M7O/BPPnmFnPstY1s6Zm9oGZLQ4em4TNuy1YfpGZjQimNTSznLC/TWb2cCq3W44szsHixQkG6t9+C/feCz/+se8pL8uFF8Ijj8B778Gbb5a7bT17wurVsGlTuVcVERGRNEtZoG5mNYFHgVFAF2CcmXWJWGwU0CH4+znwWALr3gpMcc51AKYEzwnmXwJ0BUYCfzezms65Hc657NAfsBJ4I0WbLUegDRtg+/YEAvWiIp/y0qSJz09P1C9+Ae3bw//7fwdHh0lQ6BdKlf4iIiJy+Ellj/opwBLn3DLn3D5gPDAmYpkxwHPO+xJobGYty1h3DPCv4P9/AeeFTR/vnNvrnFsOLAnKKWZmHYDmwKfJ3FA5suXl+ccyA/VHHoGZM+Gvf4Vjj028gpo14eabYcYMP0pMOShQFxEROXylMlA/Hlgd9jw/mJbIMvHWbeGcWwcQPDYvR33jgJedi94taWY/N7OZZjZz48aNcTZN5KBQoB53xJeiInjgAZ93/sMflr+Syy+H5s1j33waQ9Om/iZXBeoiIiKHn1QG6tF+CzEyQI61TCLrVqS+S4CXYhXgnHvCOdfbOde7WbNmZVQn4uXlQe3aPiCO6ZNPfI7MVVdV7GdCMzLghhvg/fchJ6dcq/bsqRtKRUREDkepDNTzgRPCnrcC1ia4TLx11wfpMQSPGxKpz8yygFrOuVkV2RiRWBYvhpNO8hkqMb38MtSvD2edVfGKrr0WGjb0PfPl0KOHb+OOHRWvWkRERCpfKgP1r4EOZtbOzOrge7PfiljmLeCyYPSXvsC2IJ0l3rpvAZcH/18OvBk2/RIzO8rM2uFvUJ0RVtc44vSmi1RUmUMzFhb6Xx4991yoV6/iFTVuDFdf7YP+ZcsSXq1nT38Pam5uxasWERGRypeyQN05VwRcB7wPLABecc7NM7NrzOyaYLFJwDL8jZ9PAtfGWzdY537gTDNbDJwZPCeY/wowH3gP+KVzLnzg6R+iQF2SbP9+WLKkjEB9yhTYsgUuvvjQK7zxRt91/3//l/AquqFURETk8GQx7qs84vXu3dvNnDkz3c2QKm7FCmjXDp54wqefR/WTn8Abb/gc9aOOOvRKf/Yz/0NIK1f6G0zL4By0bAmjRsE//3no1YuIiEjymNks51zvaPP0y6Qih2DxYv8Ys0d9716YMAHOOy85QTrALbf4cv/614QWN/O96upRFxERObwoUBc5BGWOoT55Mmzblpy0l5BOnWDMGHjsMZ//noDu3WHBgoQXFxERkSpAgbrIIcjLgwYN4LjjYizw8sv+l0jPOCO5FV9+OWzeDFOnJrR49+6wb9/BCwsRERGp+hSoixyC0IgvUYdG370b3nwTLrgA6tRJbsUjRvgrhFdeSWjxbt3847ffJrcZIiIikjoK1EUOQV5enF8knTQJCgrgkkuSX3FGhh/uccKEhPJZOnWCWrUUqIuIiBxOFKiLVNC+fX7Ul5j56S+/DM2awZAhqWnARRf59JePPy5z0Tp1oGNHBeoiIiKHEwXqIhW0bBkcOBAjUC8ogHfegQsv9F3ZqTBypE9/efXVhBbv3h3mzElNU0RERCT5FKiLVFDcEV/eecfnqCdztJdIdev69Jc33kgo/aVbNz/0+vbtqWuSiIiIJI8CdZEKCgXqUXPU33nH/xjRgAGpbcQPf+h/9TSB9JfQDaVz56a2SSIiIpIcCtRFKigvz6egN2kSZeZnn8GgQVCzZmobMWIENGyY0OgvGvlFRETk8KJAXaSCFi+O0Zuen+9zTFLdmw4+/eWccxIa/aV1a2jUSHnqIiIihwsF6iIVFBpDvZTp0/1j//6V05BQ+stHH8VdzMz3qqtHXURE5PCgQF2kAgoKYO3aGIH6Z59B/fqQnV05jQmlvyQw+ksoUHeuEtolIiIih0SBukgFLF7sH2MG6n37pm5Yxkih0V8SSH/p1g22boU1ayqnaSIiIlJxCtRFKiDm0Izbt/sk8MpKewm56KKE0l9CN5QqT11ERKTqU6AuUgGhHvX27SNmfPml/xWkyriRNFyC6S8a+UVEROTwoUBdpALy8uCEE6BevYgZn30GNWr41JfKVLeu/6XSd9+Nm4DeuLFvtwJ1ERGRqk+BukgFxByacfp0fxNpw4aV3iZGjPB3uJbxi0Ya+UVEROTwoEBdpAKWL4d27SImFhb61JfKzk8PGTHCP77/ftzFunWDBQvKvO9URERE0kyBukg57d4N69dHCdRzcmDXrsrPTw9p1Qq6dCkzUO/e3QfpixZVUrtERESkQhSoi5TTihX+sVSgXtk/dBTNiBHw6af+giEG3VAqIiJyeFCgLlJOy5f7x7ZtI2Z89pmfePzxldyiMCNHwt698MknMRfp2NEP8a5AXUREpGpToC5STlF71J3zgXq60l5CBg70I8DESX+pUwc6ddJY6iIiIlWdAnWRclq+3MfCxx0XNnHZMp+4nu5APSMDBg+G996Lu5hGfhEREan6FKiLlNPy5dCmDZiFTfzsM/+Yzvz0kBEj/J2iK1fGXKR7d1i1CrZtq8R2iYiISLkoUBcpp6hDM372mf81oS5d0tKmEhIYpjF0Q2kZQ66LiIhIGilQFymnFStijPjSv7//VdJ069zZ//xonEA9M9M/KlAXERGpuqpAVCFy+Ni+HbZsiRjxZdMm/wtCVSHtBXxOzogRMGUKFBVFXaR1a2jQQIG6iIhIVaZAXaQcQkMzluhR/+IL/5juG0nDjRjhE9C/+irqbDPfq65AXUREpOpSoC5SDlGHZpw920e+PXumo0nRDRvm03DijP6SmelHfnGuEtslIiIiCVOgLlIOUXvUc3OhQweoXz8tbYqqSRM49dQy89Q3b4YNGyqxXSIiIpIwBeoi5bB8uc/tbto0bOKcOZCVlbY2xTRyJMyc6XPoo9ANpSIiIlWbAnWRcgiN+FI8hvqOHbB0qR+YvKoZMcLntXz4YdTZCtRFRESqNgXqIuVQagz10M97VsUe9d69/djuU6ZEnd28ORx7rAJ1ERGRqkqBukiCnPOBeomhGefM8Y9VsUe9Zk0YNAg+/jjq7NDIL/PmVXK7REREJCEK1EUStHkzFBREuZH06KP9wORV0dChPjVn9eqos0NDNGrkFxERkapHgbpIgqIOzThnju9NL05ar2KGDvWPU6dGnZ2Z6dPsY8TxIiIikkYK1EUSFBqasTj15cCBqjviS0i3bn6ImhjpL7qhVEREpOpSoC6SoFJjqK9Y4XNhqmJ+ekiNGjB4cMwe9a5d/aMCdRERkapHgbpIglas8J3TjRoFE3Jz/WNV7lEHn/6yfDmsXFlqVuPG0KqVAnUREZGqSIG6SIKijvhidrBbuqoaMsQ/xkl/UaAuIiJS9ShQF0lQqTHUc3OhQweoXz9tbUpI165+wPQ4gfr8+bB/fyW3S0REROJSoC6SAOd85kjUEV+quho1fK/61KlRx2HMzIS9e/0ojiIiIlJ1KFAXScB338GePWGB+o4dPrKt6vnpIUOHwqpVB++IDaORX0RERKomBeoiCSg1NGMoqj0cetQhbp56584+1V6BuoiISNWiQF0kAaWGZjxcRnwJ6dwZWrSIOkxjvXrQvr0CdRERkapGgbpIAkK/Slrcoz5nDhx9NLRunaYWlZOZ71X/+OOoeepduypQFxERqWoUqIskYPly3yGdkRFMyM31aS9maW1XuQwZAmvWwJIlpWZlZkJenr+pVERERKoGBeoiCSgxNOOBA/Dtt4dPfnrI0KH+MUr6S2amH55x0aLKbZKIiIjEpkBdJAErVoQF6itW+FFfDpf89JCTT4aWLaPeUKqRX0RERKoeBeoiZdi/349sWCI/HQ6/HvU4eeonnwy1ailQFxERqUoUqIuUIT8fiooiRnwxO9gNfTgZOtQPCh+R41KnDnTsqEBdRESkKlGgLlKGVav8Y5s2wYTcXDjpJKhfP21tqrDQeOqffFJqVmamAnUREZGqRIG6SBlCgXrxSIxz5hx++ekhJ53k89RjBOrLl0NBQRraJSIiIqUoUBcpQyhQP+EE/E2kS5cefvnpIWYweLAP1CPy1EOZPPPnp6FdIiIiUooCdZEyrF4NxxwTZLqEothu3dLapkMyZAisXesvOMKEAvV58yq/SSIiIlJaSgN1MxtpZovMbImZ3RplvpnZX4L5c8ysZ1nrmllTM/vAzBYHj03C5t0WLL/IzEaETa9jZk+YWZ6ZLTSzsancbqleVq0KetPh4E2YnTqlrT2HbPBg/xgxnnq7dv4HnZSnLiIiUjWkLFA3s5rAo8AooAswzsy6RCw2CugQ/P0ceCyBdW8FpjjnOgBTgucE8y8BugIjgb8H5QD8L7DBOXdyUF7pBF2RGFatCstPX7TIj2PYvn1a23RIOnb0P7MakadesyZ06aJAXUREpKpIZY/6KcAS59wy59w+YDwwJmKZMcBzzvsSaGxmLctYdwzwr+D/fwHnhU0f75zb65xbDiwJygH4KXAfgHPugHNuU7I3Vqqv1asjAvUTT4TatdPapkNiBoMGxcxTV6AuIiJSNaQyUD8eWB32PD+Ylsgy8dZt4ZxbBxA8No9Xlpk1Dp7fbWazzexVM2sRrcFm9nMzm2lmMzdu3JjINko1t307bN0aFqgvXOh7pA93gwf7K5AVK0pMzsz06etbtqSnWSIiInJQKgN1izLNJbhMIusmWl8toBUw3TnXE/gCeDBaAc65J5xzvZ1zvZs1a1ZGdXIkWB1c+p1wAv4nSpcsObzz00NCeeoR6S+6oVRERKTqSGWgng+cEPa8FbA2wWXirbs+SI8heNxQRlmbgV3AhGD6q0BPRBJQYgz1lSth797q0aPepYsfyiZGoK70FxERkfRLZaD+NdDBzNqZWR38jZ5vRSzzFnBZMPpLX2BbkM4Sb923gMuD/y8H3gybfomZHWVm7fA3qM5wzjngbWBIsNwwQCNFS0JCPeqtW+PTXqB6BOo1ahzMUw9z/PFw9NEK1EVERKqCWqkq2DlXZGbXAe8DNYFnnHPzzOyaYP7jwCTgLPyNn7uAn8RbNyj6fuAVM/sZsAq4KFhnnpm9gg/Ci4BfOuf2B+v8Fvi3mT0MbAzVI1KWVav8aCgtWwKvBkMzVodAHXz6y4QJ/mokGH/STDeUioiIVBUpC9QBnHOT8MF4+LTHw/53wC8TXTeYvhnfKx5tnXuBe6NMXwkMKk/bRcAH6scf74N1Fi2Cpk3h2GPT3azkCM9Tv/TS4smZmfDqq35AGIt254eIiIhUCv0yqUgcpcZQ79ix+kSv3bpB48al0l+6dvWjvnz3XZraJSIiIoACdZG4SoyhXl2GZgypWdPnqUf8QqluKBUREakaFKiLxHDgQFj69vbtvou5OgzNGG7wYD/k5NqDAzIpUBcREakaFKiLxLB+PRQWBj3qi6rZjaQhUcZTb9YMmjdXoC4iIpJuCtRFYqi2QzOGy86GRo2ijqeuQF1ERCS9FKiLxFDix44WLfI53e3bp7VNSVezJgwYEDVQnzfPp/+IiIhIeihQF4khFKifcAI+UD/xRKhTJ61tSonBg/03BuvXF0/KzISdO/2PsYqIiEh6KFAXiWHVKmjQwI9gWDw0Y3UUylOfNq14km4oFRERST8F6iIxhIZmtAP7IS+v+gbqPXtC/fol0l+6dvWPCtRFRETSR4G6SAzFP3a0ahXs3Vv9hmYMqV0b+vcvEag3auS3XYG6iIhI+ihQF4lh1aqw/HSovj3q4NNf5s6FTZuKJ2nkFxERkfRSoC4SxZ49sGFDNR9DPVyMPPWFC/1Y8iIiIlL5FKiLRJGf7x+Lx1Bv3Nj/ElB11acPZGSUSH/p1g327fPp+SIiIlL5FKiLRFFqDPVOncAsrW1KqTp1oF+/EoF69+7+cc6cNLVJRETkCKdAXSSKUmOoV+e0l5DBg31U/v33gL82qV0bcnPT3C4REZEjlAJ1kShWr/aPrRpth7Vrj5xA3Tn49FPAd7J36aJAXUREJF0UqItEsWoVHHccHLUySNCurkMzhjvlFDjqqFLpLwrURURE0kOBukgUxWOoHwkjvoTUrQt9+5YI1LOyYN062Lgxje0SERE5QilQF4mik1cfPwAAIABJREFUxBjqNWpA+/bpblLlGDwYvvkGtm0DfKAOuqFUREQkHRSoi0RwzueoFw/N2K6dTwk5EgweDAcOwPTpwMGRX5T+IiIiUvkUqItE+P572LkzYmjGI0Xfvn6olyD9pXlzn6uvHnUREZHKp0BdJELxGOqtDsDixXDyyeltUGWqV8/fVDp1avGkrCz1qIuIiKSDAnWRCMVjqGdsgt27oUOH9Daosg0eDLNmwY4dgE9/mT8fCgvT3C4REZEjjAJ1kQihMdRbFy71/xwpN5KGDB4M+/fD558Dvkd9376DA+CIiIhI5VCgLhJh1Sr/Yz/NNi3wE460QL1fP6hVqzhPPTTyi9JfREREKpcCdZEI+fl+aMYay5dCzZrBXaVHkAYNoHfv4kC9Y0d/4aJAXUREpHIpUBeJkJ8PrVoBS5dC27Z+FJQjzZAhMGMGFBRQuzZ06aJAXUREpLIpUBeJUCJQP9LSXkKGDYOiIpg2DfDpLxqiUUREpHIpUBcJ41xYoL5kyZEbqPfv73/kacoUwI/88t13sGFDmtslIiJyBFGgLhJm40Y/wkmrJjth69YjN1DPyPA3lQaBum4oFRERqXwK1EXC5Of7x1Y11vp/TjopfY1Jt2HDfGS+cSPdu/tJSn8RERGpPArURcIUB+r7lvl/jtQedfCBOsDHH9OsGbRsqR51ERGRyqRAXSRMcaC+fb7/58QT09eYdOvdGxo1KpH+okBdRESk8ihQFwmTn+9/66f5+m/hBz+AevXS3aT0qVXL/0ppWKC+YIHP4RcREZHUU6AuEiY/H44/HmosO4JHfAk3bJgfpnLlSrp3h8JCWLgw3Y0SERE5MihQFwmjMdQjhPLUp0zRyC8iIiKVTIG6SJj8fGjVsgjWrlWgDtC1K7RoAVOm0LEj1K0L33yT7kaJiIgcGRSoiwSKf+yo/lY/4UgemjHEDE4/HT76iFo1HdnZMGtWuhslIiJyZFCgLhL4/nvYvRta1VznJ6hH3Rs2zP8s6fz59OoFs2fDgQPpbpSIiEj1p0BdJFA8NGPhcv+PAnUvLE+9Vy8oKIC8vPQ2SURE5EigQF0kUByoFyyExo2hadP0NqiqaNvWjyc/ZQq9e/tJM2emtUUiIiJHBAXqIoHiQH1zrvLTIw0bBlOn0rlDERkZylMXERGpDArURQL5+VCjBhyXP1NpL5GGDYPt26mVM1M3lIqIiFQSBeoigfx8aNnSUWulxlAv5fTT/WOQpz57Nuzfn94miYiIVHcK1EUC+flwQrO9PgJVoF5Ss2aQlQUffECvXrBzp24oFRERSTUF6iKB/Hxo1VBjqMc0ciRMn07vTgWA0l9ERERSTYG6SCA/H1rVXu+fqEe9tFGjoKiITvkfkpGhkV9ERERSTYG6CLB9O+zYAa2KVkLdutCyZbqbVPX06weNGlFr8iR69FCPuoiISKopUBcBVq/2j612LfJjhtfQW6OU2rXhjDPg3Xfp1dPphlIREZEUUzQiQvgY6nOUnx7PyJGQn0/vlmvYtQsWLUp3g0RERKovBeoihAXqa2coPz2eUaMA6LXlA0DpLyIiIqmkQF0EH6ibOVruXa5APZ5WrSAzk06zX6RePd1QKiIikkoK1EXwgXqLJoXUoVCBellGjqTmZ5/Qo3uRetRFRERSSIG6CMHQjI22+yfKUY9v1CgoLKTXsav45hvdUCoiIpIqCtRFCAL1OhugZk1o0ybdzanaBgyABg3ovesTdu2ChQvT3SAREZHqSYG6CEGg7lZD69Z+GEKJrU4dGDaMXgteAHRDqYiISKqkNFA3s5FmtsjMlpjZrVHmm5n9JZg/x8x6lrWumTU1sw/MbHHw2CRs3m3B8ovMbETY9KnBtJzgr3kqt1sOLwUF/H/27jw+qur+//jrk4QdZN/DvqgoAkJVxF3ZZFWrEBQRWpHW3davS9ufXWyrtlZrXVqsC1oVcUFwBxG1FaxGWZSwBgIJIJuArAlJzu+PM9AAyWSAzNyZyfv5eNzHzdx7bvKZNuonZz7nc9i2DdL3LFd9eqQGDOD49bOpVbNYC0pFRESiJGqJupmlAo8BA4EuQIaZdTlk2ECgU+gYDzwRwbN3ArOcc52AWaHXhO6PBE4CBgCPh77Pflc657qHjo0V/X4lca1d68/p2xdBu3bBBpMoBg4klWJ6NF2vGXUREZEoieaM+mnACufcSudcATAZGHbImGHAc877DKhnZs3LeXYYMCn09SRgeInrk51z+c65VcCK0PcRCetAD/UdWUrUI9WmDZx4IqcVzeWrr6CgIOiAREREkk80E/WWQG6J13mha5GMCfdsU+fceoDQeX8ZS3k/75lQ2cuvzMxKC9jMxptZppllbtq0qbz3J0niQKJOnhL1IzFgAGeue4W9e+Grr4IORkREJPlEM1EvLRl2EY6J5Nkj+XlXOue6AmeHjtGlfQPn3ETnXC/nXK/GjRuX8+MkWexP1FuyVon6kRg4kD6FHwPw6acBxyIiIpKEopmo5wGtSrxOB9ZFOCbcsxtC5TGEzvvrzct8xjm3NnTeAbyISmKkhLw8aFRrD9XJV6J+JM45h2a1d9G+ziYl6iIiIlEQzUT9C6CTmbUzs6r4hZ7TDxkzHbg61P3lDGB7qJwl3LPTgTGhr8cA00pcH2lm1cysHX6B6udmlmZmjQDMrAowGPgmGm9YElNeHqTX3AI1a4I+SYlctWp+Vn3fR3z6qcOV95mXiIiIHJGoJerOuULgBuB9YDEwxTm3yMwmmNmE0LB3gJX4hZ9PAj8N92zomfuAvma2HOgbek3o/hQgC3gPuN45VwRUA943s4XAfGBt6GeJAD5Rb5W6zs+ml758QcpyySX02fsBGzca2dlBByMiIpJc0qL5zZ1z7+CT8ZLX/l7iawdcH+mzoetbgAvLeOb3wO8PubYL6HmksUvlkZcHvd0qlb0cjYsvpk/aA1Do69Q7dgw6IBERkeShnUmlUtu7FzZvhvQdS5SoH426delyQTPqpnzPp/9R7YuIiEhFUqIuldqBzY4KsqFt20BjSVQplw6nd/GnzJmdH3QoIiIiSUWJulRq6qFeAYYNow9zWJRdna1bgw5GREQkeShRl0otN7RFlhL1Y9CsGX26+Ax97tyAYxEREUki5SbqZlbLzFJCX3c2s6GhNociCU+bHVWM00Z1JJVCPn17W9ChiIiIJI1IZtQ/AaqbWUtgFjAWeDaaQYnESl4e1K+2i1r1q0HdukGHk7BqXTGIHszj0/d3Bh2KiIhI0ogkUTfn3G7gUuBvzrlLgC7RDUskNvLyIL3KRs2mH6tOnejTYAmfr2rEvn1BByMiIpIcIkrUzaw3cCXwduhaVPuvi8RKXh6kuzVK1CtAn/OqsKe4OvM+1IpSERGRihBJon4zcBcwNbSzaHtgdnTDEomNvDxH+p4VStQrQJ/xJwHw6TPLAo5EREQkOYSdGTezVGCIc27o/mvOuZXATdEOTCTaCgpgwwYjndVK1CtAi34n0yY1l08/LuTWoIMRERFJAmFn1J1zRUDPGMUiElPr1vmzWjNWEDP6dNzAp9+2x32/I+hoREREEl4kpS/zzGy6mY02s0v3H1GPTCTKtNlRxeszsC7f0pxVT6s6TkRE5FhFkqg3ALYAFwBDQsfgaAYlEgsHJept2wYaS7I4+5oOAHz0zKqAIxEREUl85XZvcc6NjUUgIrF2IFFvWgjVqwcbTJI4+ZQUmtX6nhlfN2Pc5s3QqFHQIYmIiCSsSHYmrW5m15vZ42b29P4jFsGJRFNeHtRJ3cVxHRoHHUrSMIN+5xcy011E0ZTXgg5HREQkoUVS+vI80AzoD3wMpANaKSYJLy8P0lPWqT69gvUfWZ/vaMhXEzODDkVERCShRZKod3TO/QrY5ZybBAwCukY3LJHoy8stJn1fjhL1CnZRXwNgxoImsHp1wNGIiIgkrkgS9f0bgm8zs5OBukDbqEUkEiN5a4pJJ1cLSStYkybQ46R83qc/vPRS0OGIiIgkrEgS9YlmVh/4JTAdyAIeiGpUIlFWWAjrN6bSilzNqEdB/yHVmGtn8v1zbwQdioiISMIqN1F3zv3TObfVOfeJc669c66Jc+7vsQhOJFq+/RaKi0091KOkXz8odGnMXtwUFi4MOhwREZGEVGaibma3mdmPSrl+o5ndEt2wRKLrQGvGlPXQqlWwwSShM8+EWjUdM6w/vPhi0OGIiIgkpHAz6uPwHV8ONTF0TyRhHUjUmxVCWrnbCcgRqlYNzjvfmFFjmE/Ui4uDDklERCThhEvUnXOuoJSL+YBFLySR6MvN9ef09lWDDSSJ9esHK3a3ZGVuGnz6adDhiIiIJJywNepm1jSSayKJJi8Patpu6nXSZkfR0r+/P8+oMhheeCHYYERERBJQuET9T8DbZnaumdUJHecBbwJ/jkl0IlGSt7qQdJeLtddC0mjp3Blat4YZTUfDlCmQnx90SCIiIgmlzETdOfcc8Cvgt0AOsAr4DXBPaOMjkYSVt7JAHV+izMyXv8z6rjv7tu6AqVODDklERCShhC19cc6965w71znX0DnXKPT1u7EKTiRa8vLUmjEW+veH73dX4fPmw+HJJ4MOR0REJKFEsuGRSFIpKoJ1W6oqUY+BCy+ElBR4/4Sb4cMPYfnyoEMSERFJGErUpdLZuBEKi1NJT9sAzZoFHU5Sq18fzjgDpm04HVJT4Z//DDokERGRhBFuw6ObQ+c+sQtHJPoO9FBvus8XUktUXXEFLMyqwuLzfgLPPAMFh3V9FRERkVKEm1EfGzr/LRaBiMTKgUS9TWqwgVQSl1/u/x56udnNsGkTTJsWdEgiIiIJIVyivtjMcoDjzWxhieNrM1sYo/hEKtyBRP34WsEGUkm0aAHnnAMvf9kB17oNTJwYdEgiIiIJIVx7xgzgDGAFMKTEMTh0FklIeSv2UpV8Gp2ozY5iZeRIWLLEWDj4bvjgA8jODjokERGRuFdee8ZvnXPdgPVAndCxzjm3OhbBiURD3vLdpJOHtWsbcCSVx2WX+bWkL6dk+DYwWlQqIiJSrnK7vpjZucBy4DHgcWCZmZ0T7cBEoiVvdZFaM8ZY48a+VePkt+vgBg2Gp5/WolIREZFyRNKe8S9Av9BmR+cA/YGHohuWSPTkbaiiRD0AI0bAqlWQef7tvkfmm28GHZKIiEhciyRRr+KcW7r/hXNuGVAleiGJRI9zkLe1FulVN/km3xIzl1wCVarA5DVnQno6/P3vQYckIiIS1yJJ1DPN7CkzOy90PAl8Ge3ARKJh82YoKK5Cq8Z71EM9xurXhwEDYMqrKRRfe51fVJqVFXRYIiIicSuSRP0nwCLgJuBmIAuYEM2gRKLlQGvGlsHGUVmNGOH/P5jT43qoXh0efjjokEREROJWuYm6cy7fOfcX59ylzrlLnHMPOefyYxGcSEXLy3UApHeoFnAkldPQoT4/f3lGfbjqKnj+ef8xh4iIiBwmkhl1kaSRt3gHAOkn1Q04ksqpTh0YNAimTIHCG26BvXvhH/8IOiwREZG4pERdKpW8xTtIYx9NujYNOpRKa/Ro3/Rl2oqToF8/eOwxtWoUEREphRJ1qVRyswtoyVpSOqg1Y1AGD4b27eGhh4Bbb4X16+Hll4MOS0REJO5EsuFRZzN70sxmmNmH+49YBCdS0fLWme+h3rZt0KFUWqmpcNNN8Omn8Hn9/nDiiT5rdy7o0EREROJKJDPqrwBfAb8Ebi9xiCScvM01SK+2GWrVCjqUSm3cODjuOHjoYYNbboF58+Df/w46LBERkbgSSaJe6Jx7wjn3uXPuy/1H1CMTqWDOQd7OuqTX3xV0KJVenTpw7bXwyiuQe/7V0LBhqBZGRERE9oskUX/TzH5qZs3NrMH+I+qRiVSwrVthT3F10psXBR2KADfe6P94+tuT1WHCBJg2DbKzgw5LREQkbkSSqI/Bl7rMwe9I+iWQGc2gRKIhb7VP0NPbpgUciQC0aQOXXQYTJ8LOa26AtDT461+DDktERCRuRLLhUbtSjvaxCE6kIuUt8BvrpHeuGXAkst9tt8H27fDse83gyivhn/+ETZuCDktERCQuRNL1pYqZ3WRmr4aOG8ysSiyCE6lIeV9vAyD9FFVuxYszzvDHww9D0c/v8BsgaVZdREQEiKz05QmgJ/B46OgZuiaSUPKW7yGFIpqd2iLoUKSEW2/1penTl50Al14Kjz4K338fdFgiIiKBiyRR/4Fzboxz7sPQMRb4QbQDE6loeWuKac560tq3DjoUKeHSS6FjR7jrLij4+d2+FuYJzQWIiIhEkqgXmVmH/S/MrD2gthmScPI2ViG96kaoWjXoUKSEtDRf+rJ0Kfzt01OhXz/fqnHPnqBDExERCVQkifrtwGwz+8jMPgY+BH4W3bBEKl7ettqkH6eSing0aBBcfDH85jfw7XX3wIYN8OyzQYclIiISqEi6vswCOgE3hY7jnXOzox2YSEXL29uI9MYFQYchZXjoIb+W9M7pvaF3b3jgASgsDDosERGRwJSZqJvZBaHzpcAgoCPQARgUuiaSML7flM8OV4f09KAjkbJ07uzbNU6aZHx2yf2QkwOTJwcdloiISGDCzaifGzoPKeUYHMk3N7MBZrbUzFaY2Z2l3DczeyR0f6GZnVres6GdUWea2fLQuX6Je3eFxi81s/6l/LzpZvZNJLFLcsn7Yj0A6R2rBxyJhPOLX0Dz5nDjlLMoPqkr/PGPUFwcdFgiIiKBKDNRd87dE/ryt865sSUP4HflfWMzSwUeAwYCXYAMM+tyyLCB+LKaTsB4Qm0fy3n2TmCWc64TMCv0mtD9kcBJwADg8dD32R/PpcDO8uKW5JQ332921OrkugFHIuHUqQN/+hNkZhrPnDkRsrJg+vSgwxIREQlEJItJXyvl2qsRPHcasMI5t9I5VwBMBoYdMmYY8JzzPgPqmVnzcp4dBkwKfT0JGF7i+mTnXL5zbhWwIvR9MLPawG3AvRHELUkob8kOANJPbRJwJFKeUaOgTx/4v9dOZ3Xrs+Hee8G5oMMSERGJuXA16ieY2WVAXTO7tMRxDRBJ/UBLILfE67zQtUjGhHu2qXNuPUDovD/zCvfM74AHgd3hAjaz8WaWaWaZm7SNeVLJW7kPo5jm3ZsGHYqUwwyeeQYKC40fprzG3i+/gffeCzosERGRmAs3o348vha9HgfXp58KXBvB97ZSrh06LVbWmEiejejnmVl3oKNzbmo5z+Ocm+ic6+Wc69W4cePyhksCyVuXQtPUzVStHsmHSBK0Tp3guecgM6cxN9d+Cn73O82qi4hIpROuRn0a8GPgwUNq1G9yzs2J4HvnAa1KvE4H1kU4JtyzG0LlMYTOG8v5Xr2BnmaWA/wH6GxmH0UQvySR3C01Sa+1Negw5AgMGwZ33gkTd17JM3OPhw8/DDokERGRmAo7veicKwL6HuX3/gLoZGbtzKwqfqHnoavCpgNXh7q/nAFsD5WzhHt2OjAm9PUYYFqJ6yPNrJqZtcMvUP3cOfeEc66Fc64tcBawzDl33lG+J0lQebvqkd5AO10mmt/9Di48v4if8jjz/u+loMMRERGJqUjqAOaY2aNmdraZnbr/KO8h51whcAPwPrAYmOKcW2RmE8xsQmjYO8BK/MLPJ4Gfhns29Mx9QF8zW47/I+K+0DOLgClAFvAecH3oDw2p7HbsIK+oOenN9euQaNLS4KWXU2lUr5DLvrqbLW/NDTokERGRmDFXTt2nmZW2C6lzzl0QnZDiQ69evVxmZmbQYUgF2PnZN9TpfTL3ZSzgjhe7BR2OHIX/fryXc8+Dk+rkMmtNJ+rVCzoiERGRimFmXzrnepV2r9wZdefc+aUcSZ2kS3JZ+9UGANJPqB1wJHK0Tj+3Oq+PfYuvd7RhwFk7+f77oCMSERGJvnITdTOra2Z/2d+20MweNDPtGiMJI++bbQCkd2sYcCRyLC7+a39eqT2OL7OqM2gQ7NT2ZSIikuQiqVF/GtgBXBE6vgeeiWZQIhUpb4VfRJp+kv6+TGh16jDsjhN40WUwZ45j6FDYHXZnBBERkcQWSaLewTl3T2iX0JXOud8A7aMdmEhFyVvj12G0TC+t1b4klBtv5PK6M3n+1If56CMYOlQz6yIikrwiSdT3mNlZ+1+YWR9Afe4kYeRtqkqjqtupHsl+uhLf6taFm25iVOZtTPp9HrNnQ79+sFUt8kVEJAlFkqj/BHjMzHLMbDXwKHBddMMSqSDOkbe9DunH7Qg6Eqkot9wCtWszeuHtvPoqfPklnH8+bNgQdGAiIiIVK5KuL/Odc92AU4CuzrkezrmF0Q9NpAJs2eJ7qDcpCDoSqSgNGsD118PLL3NJl6W89RYsXw7nnANr1gQdnIiISMWJpOtLQzN7BPgImG1mfzUztc+QxLBqFXmkk95a9elJ5bbboHp1+MMf6NsXZszwM+pnnQXZ2UEHJyIiUjEiKX2ZDGwCLgN+GPr65WgGJVJR9i5dzWYak96xRtChSEVq0gQmTIAXXoCVK+nTB2bPhl27fBnMqlVBBygiInLsIknUGzjnfuecWxU67gW0L6AkhLULtwBqzZiUfv5zSEuDP/4RgB49YNYs3wXm/PMhJyfY8ERERI5VJIn6bDMbaWYpoeMK4O1oByZSEfKW+N596Z00o550WrSAH/0IJk06UJzevTt88AFs3+6TddWsi4hIIoskUb8OeBEoCB2TgdvMbIeZaSNviWt5OfsAaNUq4EAkOu64w5/vv//ApVNP9cn61q1w3nmQmxtMaCIiIscqkq4vdZxzKc65tNCRErpWxzl3XCyCFDlaeetSAWjZMuBAJDpat4YxY+Cpp+Dbbw9c7tkTZs6ELVtg8GBtiiQiIokpkhl1zGyomf05dAyOdlAiFaK4mLyttahffTe1agUdjETNHXfAvn3w178edPkHP4BXXoFvvoHRo6G4OKD4REREjlIk7RnvA24GskLHzaFrIvFt3TryipuT3lAb6Sa1jh3hssvg8cd9cXoJ/frBgw/CG2/APfcEFJ+IiMhRimRG/WKgr3Puaefc08CA0DWR+LZqFbm0omVzTaUmvTvugO+/h3/847BbN98M48bBvffCy2osKyIiCSSi0hcObseoPneSGEKJeuv2VYKORKKtZ0+46CJ46CHYu/egW2Z+sv3MM2HsWPjqq4BiFBEROUKRJOp/BOaZ2bNmNgn4EvhDdMMSOXZ7luWykaa07qIC9Urhjjv8gtLnnz/sVrVq8Prr0KgRDB9+WIWMiIhIXAqbqJuZAf8BzgBeDx29nXOTYxCbyDHJy/LdQ1u104x6pXDhhX5m/U9/gqKiw243beoXl65dC7ffHkB8IiIiRyhsou6cc8Abzrn1zrnpzrlpzrlvwz0jEi9yV+QDvoOfVAJmflZ9+XKYOrXUIaefDj/7GTz5pO+1LiIiEs8iKX35zMx+EPVIRCrYmrX+11ubHVUil17qu8Dcfz84V+qQ3/wGOneGa69Vf3UREYlvkSTq5+OT9WwzW2hmX5vZwmgHJnJMCgrI/a42AOnpAccisZOa6utaMjNh9uxSh9SoAU8/DatXw113xTg+ERGRIxBJoj4QaA9cAAwBBofOIvErN5c1tKLpcbupVi3oYCSmrr7aF6Tff3+ZQ/r0gZtugkcfhU8+iWFsIiIiR6DMRN3MqpvZLcDt+N7pa51zq/cfMYtQ5GisWsUaWtO6RWHQkUisVa/us/AZM2DRojKH/f730L6977G+e3cM4xMREYlQuBn1SUAv4Gv8rPqDMYlIpCKEeqi3apsadCQShPHjfcL+17+WOaRWLXjqKcjO9o1iRERE4k24RL2Lc+4q59w/gB8CZ8coJpFj5laGZtQ71wg6FAlCo0YwerTvqb55c5nDzjsPLrsMHnwQNm2KXXgiIiKRCJeo79v/hXNO9QOSULYt28guatO6baSb70rSuflmv0vpxIlhh917L+zaBX/8Y4ziEhERiVC4LKabmX0fOnYAp+z/2sy+j1WAIkdjzTK/jbxaM1ZiJ50EffvCY49BQUGZw044AcaO9cPWrIlhfCIiIuUoM1F3zqU6544LHXWcc2klvj4ulkGKHKk1uQZos6NK79ZbYd06ePXVsMPuucfvl/TrX8cmLBERkUioLkCSz65d5G6vA2hGvdLr3x+OPx4eeqjMDZDA/57ccANMmgRZWTGMT0REJAwl6pJ8cnJYQ2uqpBbRtGnQwUigUlJ8rXpmJsydG3boXXdB7drwy1/GKDYREZFyKFGX5BNqzZjedB8p+g2Xq6+GevXg4YfDDmvY0G9qOnUq/Pe/MYpNREQkDKUxknz2b3bURr/egm+YPn48vPYarA6/V9stt0CTJvCrX8UoNhERkTCUyUjyWbWKNdaG1h2rBB2JxIvrr/erRR97LOyw2rXhtttg5kz4+usYxSYiIlIGJeqSdIpWrmata0GrVhZ0KBIvWreGYcPg6ad9b/Uwrr0WatYst1JGREQk6pSoS9JZv2wHRaSpNaMc7Cc/gS1bfAlMGA0awJgx8MILsHFjjGITEREphRJ1SS7Okbu6GFBrRjnEBRdAx47wxBPlDr35ZsjPj2ioiIhI1ChRl+SydStrdjcEtNmRHCIlBSZMgE8/LbcA/fjjYdAgePzxcitlREREokaJuiSXUMcX0Iy6lOKaa6BaNfj738sdeuutvvTlpZeiH5aIiEhplKhLcsnOJpdWHFe7iLp1gw5G4k7DhnDFFfD887BzZ9ihF1wAXbuWu6mpiIhI1ChRl+SSnc0aWms2Xco2YQLs2AEvvhh2mJnvq/711/DhhzGKTUREpAQl6pJcsrPJTWtH67apQUci8ap3bzjlFF/+Us5U+ahRfgOkhx6KUWwiIiIlKFGX5BKaUddCUimTmZ9VnzcPPv887NDq1X1Xx7ffhuXLYxSfiIhIiBJ1SSq7V6xjc2F9lb5IeFdd5bchjWBR6fjxvmHMs8+Pr4qgAAAgAElEQVRGPywREZGSlKhL8sjPJy/Pf6kZdQmrTh248kqYPBm++y7s0BYtoH9/mDQJiopiFJ+IiAhK1CWZ5OSwBj+Vrhl1KddPfuKbpD//fLlDx46FtWvhgw9iEJeIiEiIEnVJHqHWjKAZdYlAt27Qqxc8/XS5i0qHDoUGDeCZZ2IUm4iICErUJZmEFpICtGwZcCySGMaNg4UL/cLSMKpV8x1gpk4tt1JGRESkwihRl+SRnc2atPY0a+aoVi3oYCQhZGT41i5PP13u0LFjoaBAO5WKiEjsKFGX5LFyJbnVO9G6tQUdiSSKevXg0kvhhRd8vXoYPXr4ahmVv4iISKwoUZfkoV1J5WiMGwfbtsEbb4QdZuZn1b/80u9WKiIiEm1K1CU5FBfjsleSu7exFpLKkTn/fGjTJqLylyuvhCpVNKsuIiKxoURdksP69XyXX5PdhdU0oy5HJiXFT5V/8AGsXh12aKNGMGQI/OtfsG9fjOITEZFKS4m6JIcSHV+UqMsRu+Yaf540qdyhY8fCpk3w9tvRDUlERESJuiSHlStZTRsA2rYNNhRJQG3awIUX+pqW4uKwQwcMgKZNI9onSURE5JgoUZfkkJ1NjrUDlKjLURo7FnJy4KOPwg5LS4PLL4d33oEdO2ISmYiIVFJRTdTNbICZLTWzFWZ2Zyn3zcweCd1faGanlvesmTUws5lmtjx0rl/i3l2h8UvNrH+J6++Z2QIzW2Rmfzez1Gi+bwlAdjY5tbtSqxY0bBh0MJKQLrkE6taNaFHpiBG+m+Obb8YgLhERqbSilqiHkuHHgIFAFyDDzLocMmwg0Cl0jAeeiODZO4FZzrlOwKzQa0L3RwInAQOAx0sk5Fc457oBJwONgcsr/A1LsLKzyal2PG3b+jZ6IkesRg2//ehrr/l2jWGceabf/fbll2MUm4iIVErRnFE/DVjhnFvpnCsAJgPDDhkzDHjOeZ8B9cyseTnPDgP2r/iaBAwvcX2ycy7fObcKWBH6Pjjnvg+NSQOqAq6C36sELTubHNdaZS9ybMaO9VPlr74adlhKii9/ee+9cnN6ERGRoxbNRL0lkFvidV7oWiRjwj3b1Dm3HiB0bhLJzzOz94GNwA6g1P8Km9l4M8s0s8xNmzaV9/4kXmzfDlu2kLOrsRJ1OTa9esHxx0e0UnTECCgogGnTYhCXiIhUStFM1EsrQDh0JrusMZE8e0Q/zznXH2gOVAMuKO0bOOcmOud6Oed6NW7cuJwfJ3Fj5Uq2UZfte6srUZdjYwajR8Mnn/iFpWGcfrpvFjNlSmxCExGRyieaiXoeULKjdTqwLsIx4Z7dECqPIXTeGOnPc87tBaZzeAmOJLLsbHJoC6jji1SAK6/05xdeCDvMDK64AmbMgO++i0FcIiJS6UQzUf8C6GRm7cysKn6h5/RDxkwHrg51fzkD2B4qZwn37HRgTOjrMcC0EtdHmlk1M2uHX6D6uZnVLpHYpwEXA0ui8YYlIErUpSK1bQtnn+3LX1z4D/JGjIDCQpg6NTahiYhI5RK1RN05VwjcALwPLAamOOcWmdkEM5sQGvYOsBK/8PNJ4Kfhng09cx/Q18yWA31DrwndnwJkAe8B1zvnioBawHQzWwgswM/A/z1a71sCkJ1NTq2TASXqUkFGj4alSyEzM+ywU0+F9u3V/UVERKLDXDkzRpVVr169XGY5/5GWOHHhhdya9WOe3JHBjh1qzygVYNs2aNYMxo+HRx4JO/Tuu+GBB2D9etDSFhEROVJm9qVzrldp97QzqSS+lSvJSeuoHupScerVgyFDYPJk2Lcv7NARI6CoCF5/PUaxiYhIpaFEXRJbQQGsWUPOvnSVvUjFGj0aNm2C998PO+yUU3xHR5W/iIhIRVOiLolt9WooLiZnRwMl6lKxBgyAhg3hX/8KO2x/95ePP4aNG8MOFREROSJK1CWxZWezjbps211NibpUrKpVYeRIv6PR9u1hh156KRQXw1tvxSg2ERGpFJSoS2LLzmY1bQB1fJEoGD0a9u6F114LO6xbN7/50RtvxCguERGpFJSoS2LLzianSmfAJ0oiFeq006BTJ99TPQwzGD7cb360c2eMYhMRkaSnRF0S28qV5DQ4FdCMukSBGVx1lS9Az8sLO3T4cMjPL3ftqYiISMSUqEtiy84mp2YXataERo2CDkaSUkaG36G0nLYuZ53l156q/EVERCqKEnVJXMXFPlFPaace6hI9nTpBz57w0kthh6Wl+dbrb71Vbut1ERGRiChRl8S1bh3s2UNOfnOVvUh0ZWTAl1/C8uVhhw0f7jc1/fjjGMUlIiJJTYm6JK5lywDI2VZPibpE14gR/iObcmbV+/aFGjVU/iIiIhVDibokrmXLfA/1nVWUqEt0pafD2Wf7RN25MofVrOn3SXrjjbDDREREIqJEXRLXsmWsrupbMypRl6jLyIAlS2DhwrDDhg+HtWt9pYyIiMixUKIuiWv5clY3PwNQoi4x8MMf+hWj5ZS/DBoEqakqfxERkWOnRF0S17Jl5NTrDihRlxho1MgXoU+eHLaupWFDOOccmDo1hrGJiEhSUqIuiWnfPr/ZUdXO6qEusZORAatXw9y5YYddcglkZR1Y7ywiInJUlKhLYsrJgcJCcopaqYe6xM7w4VC9ernlL8OG+fP06TGISUREkpYSdUlMoX7WOTsbquxFYqdOHRg8GKZMgcLCMoe1bg3duvnNj0RERI6WEnVJTPt7qG+sqURdYisjAzZuhNmzww4bPBj+8x/YujVGcYmISNJRoi6JadkyttdtzdZtKUrUJbYGDvQz6+WUvwweDEVF8N57MYpLRESSjhJ1SUzLlrG61VmAOr5IjNWo4VeLvv465OeXOey006BxY3jzzRjGJiIiSUWJuiSm5cvJadgTgDZtAo5FKp+MDNi+Hd59t8whKSm+p/q774YtZxcRESmTEnVJPHv2wJo15NTsAmhGXQJw4YW+J2gE5S/btsGcOTGKS0REkooSdUk8K1YAkGNtqVHDlxeIxFSVKnD55b6uZefOMof16+eHqvxFRESOhhJ1STyhji8rdzWjXTv1UJeAZGT4T3fCNEuvUwfOO09tGkVE5OgoUZfEE+qhvmJjHTp2DDgWqbz69IH09HLLX4YMgSVLDnwQJCIiEjEl6pJ4li3DNW3GypxUJeoSnJQUGDkS3n8fvvuuzGGDBvmzZtVFRORIKVGXxLNsGevb9mbPHujQIehgpFLLyIB9++C118oc0r49dOmiRF1ERI6cEnVJPMuWsaLRGQCaUZdg9egBnTtHVP7y8ce+o6OIiEiklKhLYtm2DTZtIrtmV0Az6hIwMz+r/tFHsG5dmcMGD/a91GfMiF1oIiKS+JSoS2LZv5DUdSA1FVq3DjgekYwMcA6mTClzSO/e0KCByl9EROTIKFGXxBJqzZi9qylt2/oe1SKBOv54XwITpvwlNRUuvhjeeQeKimIYm4iIJDQl6pJYli0DM1ZsqKOyF4kfGRnw+eeQnV3mkMGDYfNm+O9/YxiXiIgkNCXqkliWL8e1acuK7BQtJJX4MWKEP0+eXOaQ/v0hLU27lIqISOSUqEtiWbaM79r1ZPt2LSSVONK6NZx1Frz4oq9XL0W9enD22apTFxGRyClRl8ThHCxbRnaj0wG1ZpQ4M2oUZGXB11+XOWTIEPjmG8jJiV1YIiKSuJSoS+LYsAF27GBFDbVmlDh0+eW+tuXFF8scMniwP2tWXUREIqFEXRJHqDVjtmsP+B0fReJGo0bQt6+vUy8uLnVIp05+fyQl6iIiEgkl6pI4Qq0ZV+xqRsuWUKNGwPGIHGrUKFi9GubOLXPIkCEwezbs2BHDuEREJCEpUZfEsWwZVK1K9re1VZ8u8WnYMP8XZDnlLwUF8MEHMYxLREQSkhJ1SRzLlkGHDqzINtWnS3yqUweGDvW7lO7bV+qQPn2gbl2Vv4iISPmUqEviWLyYnZ16sGGDOr5IHMvI8DsbzZpV6u0qVWDgQHj77TJL2UVERAAl6pIo8vNhxQqym54JqOOLxLEBA3zT9HLKXzZsgMzMGMYlIiIJR4m6JIbly6GoiOxapwCaUZc4Vq0a/PCHMHUq7N5d6pCBAyElReUvIiISnhJ1SQyLFgGQjZ9K14y6xLWMDNi5s8xMvEEDX6v+5psxjktERBKKEnVJDFlZkJLCih1NaNTIL8YTiVvnngvNm8NLL5U5ZPBgmD8f8vJiGJeIiCQUJeqSGLKyoEMHsnPSNJsu8S81FUaOhHfega1bSx0yZIg/q/xFRETKokRdEkNWFnTpwooVKnuRBDFqlG+Y/vrrpd4+4QS/u64SdRERKYsSdYl/+/bBsmXkd+5Kbq4WkkqC6NnT/7KW0f3FzM+qz5pV5ppTERGp5JSoS/xbvhwKC8lp/AOKizWjLgnCzM+qz54N69eXOmTwYNi7t8yW6yIiUskpUZf4l5UFQHa1LoBm1CWBZGSAc/Dyy6XePuccv5mpyl9ERKQ0StQl/mVlgRkrCloDmlGXBHLCCdCjR5nlL1WrQv/+PlF3LsaxiYhI3FOiLvEvKwvatSM7tyq1a0OTJkEHJHIERo2CL77wJVylGDwY1q2DefNiHJeIiMQ9JeoS/xYtOqjji1nQAYkcgZEj/S/t5Mml3r74Yn9b5S8iInIoJeoS3woLYelS6NKF7GzVp0sCSk+Hs8+GF14otb6lcWM44wztUioiIodToi7xLTsb9u2j6ISTWLVK9emSoEaN8n9wzp9f6u3BgyEzs8zmMCIiUklFNVE3swFmttTMVpjZnaXcNzN7JHR/oZmdWt6zZtbAzGaa2fLQuX6Je3eFxi81s/6hazXN7G0zW2Jmi8zsvmi+Z6lgoY4vOfW6U1AAxx8fcDwiR+OHP4S0tDIXle7fpfTtt2MYk4iIxL2oJepmlgo8BgwEugAZZtblkGEDgU6hYzzwRATP3gnMcs51AmaFXhO6PxI4CRgAPB76PgB/ds6dAPQA+pjZwIp/xxIVoUR9cWEnwDfREEk4DRvCgAG+Tr24+LDbJ58MrVurTl1ERA4WzRn104AVzrmVzrkCYDIw7JAxw4DnnPcZUM/Mmpfz7DBgUujrScDwEtcnO+fynXOrgBXAac653c652QCh7/UVkB6NNyxRsGgRtGnDktU1ACXqksAyMiAvD/7zn8Numfnyl5kz/QZIIiIiEN1EvSWQW+J1XuhaJGPCPdvUObceIHTe36yv3J9nZvWAIfiZ+MOY2XgzyzSzzE2bNoV9cxIjWVnQpQuLF/u2jA0aBB2QyFEaOhRq1gxb/rJ7t9/IVEREBKKbqJfWRO/QlgdljYnk2SP6eWaWBrwEPOKcW1naN3DOTXTO9XLO9WrcuHE5P06irqgIliyBLl1YsgROPDHogESOQe3aMGwYvPIKFBQcdvu886BWLXV/ERGR/4lmop4HtCrxOh1YF+GYcM9uCJXHEDpvjPDnTQSWO+cePuJ3IsFYtQry83En+hl1lb1Iwhs1Cr77Dt5997Bb1av7XUqnTy+1jF1ERCqhaCbqXwCdzKydmVXFL/ScfsiY6cDVoe4vZwDbQ+Us4Z6dDowJfT0GmFbi+kgzq2Zm7fALVD8HMLN7gbrALdF4oxIlixYBsKlFN7Zu1Yy6JIH+/X0N13PPlXp7+HBYuxa+/DLGcYmISFyKWqLunCsEbgDeBxYDU5xzi8xsgplNCA17B1iJX/j5JPDTcM+GnrkP6Gtmy4G+odeE7k8BsoD3gOudc0Vmlg78At895iszm29mP47W+5YKtL/ji/NT6ZpRl4RXpYqfVX/zTdiy5bDbgwZBaipMnRpAbCIiEnfMlbJTnkCvXr1cZmZm0GFUbqNHw0cf8Y9f5jJhAqxe7VvYiSS0+fOhRw949FG4/vrDbl90Eaxbd+DvVBERSXJm9qVzrldp97QzqcSvUMeXJUt8s4x0NdWUZNC9O5xyCkyaVOrt4cNh8WK/kamIiFRuStQlPhUX+2yly/8Wkqbot1WSxZgx8MUX/nf8EMNCO0ZMm3bYLRERqWSU+kh8ysmBPXsOzKirPl2SypVX+mL0UmbVW7WCnj3hjTcCiEtEROKKEnWJT6EC3V3tu7J6tTq+SJJp2hQGDIDnn/f7BRxi+HCYOxfWrw8gNhERiRtK1CU+hRL1ZWldAM2oSxIaM8avGv3ww8NuDR/uz9MPbWgrIiKVihJ1iU8LFkDLlixeexygGXVJQkOGQL16pZa/nHQSdOyo8hcRkcpOibrEp3nzoEcPlizxi0g7dgw6IJEKVr06jBwJr78O339/0C0zP6s+a9Zht0REpBJRoi7xZ/du35uuRw8WL4YOHaBataCDEomCMWP8oulXXz3s1vDhsG8fvPtuAHGJiEhcUKIu8efrr317xtCMuurTJWmdfjp07lxq+csZZ0CTJtqlVESkMlOiLvFn/nwACk/uzrJlqk+XJGYGY8fCJ5/A8uUH3UpNhaFD4Z13ID8/oPhERCRQStQl/sybB3XrkkNbCgo0oy5JbswYn5X/85+H3brsMtixA2bMCCAuEREJnBJ1iT/z50P37ixeYoBm1CXJNW/uO8A8+ywUFBx068ILoX59mDIlmNBERCRYStQlvhQVwcKFB+rTQTPqUglcey1s3AhvvnnQ5SpV4NJLYdo02Ls3oNhERCQwStQlvixb5rtgdO/O4sXQrJlvNS2S1Pr3h/R0ePLJw25dcYUvf3n//QDiEhGRQClRl/gyb54/q+OLVCapqTBunC9Gz8k56Nb550PDhip/ERGpjJSoS3yZPx+qVsWdcCKLF6s+XSqRceP8+ZlnDrq8v/xl+nT/YZOIiFQeStQlvsybByefzMatVdi2TTPqUom0aeNLYJ5+2q/VKOHyy2HnTnjvvYBiExGRQChRl/jh3IGOL/sXkmpGXSqVa6+FvLzDMnKVv4iIVE5K1CV+rF0LmzdDjx5kZflLmlGXSmXwYL8d6SGLStPSfE/1N99U+YuISGWiRF3iR2hHUnr0YOFC3+0lPT3YkERiqmpVuOYaeOstWL/+oFtXXAG7dsG77wYTmoiIxJ4SdYkf8+b5LdVPOYX586FbN/9SpFL58Y99jfohi0rPPRcaN1b5i4hIZaJEXeLH/PnQsSNFNevw9dfQvXvQAYkEoFMnX5Q+ceJBi0pLlr/s3h1gfCIiEjNK1CV+zJsH3buTne0/4u/WLeiARAJyww2wevVhO5VefrlP0t9+O6C4REQkppSoS3zYtg1WrYIePViwwF/SjLpUWkOHQqtW8Le/HXT53HOheXP4178CiktERGJKibrEhxLZ+fz5/mP+Ll2CDUkkMGlp8JOfwIcfwqJFBy6npsJVV8E778CmTQHGJyIiMaFEXeJDiY4v8+f7/unVqgUbkkigrr3W/0Pw6KMHXb76aigshBdfDCguERGJGSXqEh/mzYOmTaFZMxYsUH26CI0aQUYGPPecLw0LOflkOPVUf1lERJKbEnWJD/PnQ48ebN7s9z1SfboIcOONfvXoIa0ar74avvoKvvkmoLhERCQmlKhL8PLzfR1u9+4HStU1oy6Cnzo/80x47DEoLj5wOSPDl7FrVl1EJLkpUZfgZWX5ottQfTooURc54MYbITv7oC1JmzSBgQN995fCwgBjExGRqFKiLsH74gt/PvVUFiyAFi38Dowigt/lqHnzw1o1jhkD69fDrFkBxSUiIlGnRF2CN3euXzjXoQPz56s+XeQgVarAhAnw/vuwdOmBy4MHQ/36MGlSgLGJiEhUKVGX4M2ZA717k19gLF6ssheRw1x3nU/YH3nkwKVq1WDkSJg6Fb7/PsDYREQkapSoS7C2bIFly+DMMw+UqitRFzlE06YwejQ8/TRs3Hjg8tVXw9698MorAcYmIiJRo0RdgvXZZ/7cu3fJzUlF5FC33+47JJWoVT/9dOjcGZ59NriwREQkepSoS7DmzvX7ovfqxfz5UKMGdOwYdFAiceiEE2DYMN+qcedOAMzgRz+C//xHPdVFRJKREnUJ1pw5fgq9Vi0WLIBTTvF5u4iU4o47YOtWePLJA5fGjfP16o8/HmBcIiISFUrUJTiFhfD559C7N875zUlVny4SxhlnwLnnwoMPQkEB4BsmjRgBzz+vRaUiIslGiboE55tvYNcu6N2b3FzYtk316SLluuMOWLsWXnzxwKXrr/fVMM8/H2BcIiJS4ZSoS3DmzPHn3r21I6lIpAYM8DViDzwAxcUAnHYa9Orly1+cCzg+ERGpMErUJThz50KzZtC2LfPn+4VxXbsGHZRInDOD//s/WLwY3nrrwOWf/hSysuDjjwOMTUREKpQSdQnO3LnQuzeYsWABdOgAdeoEHZRIAhgxAtq2hfvvP3Bp5Eho0MA3hRERkeSgRF2CsXEjZGf7RB346ivVp4tELC0NfvYzXz72ySeAb206bpzfqXTduoDjExGRCqFEXYIxd64/9+7N+vWQk+MbWohIhMaN86Vjv/rVgcL0CRN82frEiQHHJiIiFUKJugRj7lyoUgV69jyQs595ZrAhiSSUmjXhF7/wM+qzZgG+fGzAAJ+o79sXcHwiInLMlKhLMObOhR49oEYN5s6FqlXh1FODDkokwVx7LbRqBb/85YFZ9RtugPXr4eWXA45NRESOmRJ1ib19++CLLw7Up8+d65P0atUCjksk0VSrBv/v/8F//wtvvw34GfWuXeEPfzjQvVFERBKUEnWJvQULYM8e6N2bggLIzDyQs4vIkRozxte8/OpXUFxMSoqviFm82C8sFRGRxKVEXWKvRFH6/PmQn6/6dJGjVqUK3HMPzJ9/IDP/4Q+hc2e4915tgCQiksiUqEvszZ0LLVtCq1YlNycVkaM1ahSccIIvgykqIjUV7r7b5+7vvBN0cCIicrSUqEvszZlzUH16q1Y+bxeRo5SaCr/9rd+adPJkwOfubdtqVl1EJJEpUZfYWrsWVq8+KFHXbLpIBbjsMujWzZfB7NtHlSpwxx3w2Wcwe3bQwYmIyNFQoi6x9cEH/nzhhaxdC7m5StRFKkRKCvz+937H38cfB+Caa6BFCz+rLiIiiUeJusTWjBnQpAl07aqNjkQq2sUXQ79+8Otfw+bNVK8Ot9/uZ9T3rwcREZHEoURdYqe42M+o9+0LKSnMmQPVq0P37kEHJpIkzOChh2DHDr+wFL8nUuPGB+2JJCIiCUKJusTOwoWwcaNP1PH16T17+l1JRaSCdOkCP/0p/OMfsHAhtWr5CfbZs2HatKCDExGRIxHVRN3MBpjZUjNbYWZ3lnLfzOyR0P2FZnZqec+aWQMzm2lmy0Pn+iXu3RUav9TM+pe4/nszyzWzndF8v1KOmTP9uW9f8vPhq69Uny4SFb/+NdSrB7fcAs4xfjycfDL87Gewd2/QwYmISKSilqibWSrwGDAQ6AJkmFmXQ4YNBDqFjvHAExE8eycwyznXCZgVek3o/kjgJGAA8Hjo+wC8CZwWhbcpR2LGDDjpJGjRgq++goIC1aeLREWDBr5d4+zZ8MYbpKXBww/DypX+LCIiiSGaM+qnASuccyudcwXAZGDYIWOGAc857zOgnpk1L+fZYcCk0NeTgOElrk92zuU751YBK0LfB+fcZ8659dF5mxKRPXvg3//2C9343+akmlEXiZLrrvN/GP/857B3LxdeCMOG+cYw6/VvQxGRhBDNRL0lkFvidV7oWiRjwj3bdH/SHTo3OYKfF5aZjTezTDPL3LRp05E8KuX5z38gP/9AffqcOX4zlmbNgg1LJGmVMo3+5z/7T7Luvjvg2EREJCLRTNStlGuH9hwoa0wkzx7NzwvLOTfROdfLOdercePGR/KolGfGDL9q9JxzcE4bHYnExEUX+Wn03/0OVq2iY0e49VZ49ln44ouggxMRkfKkRfF75wGtSrxOB9ZFOKZqmGc3mFlz59z6UJnMxiP4eRKUmTOhTx+oVYvcNbBunerTRWLikUd8Ccz48TBjBr/4hfHss3Dzzf6DrhT1/kpMe/ZAVhZ8/bWvZdq583/Hrl1w3HHQvLk/WrSAli2ha1e12RJJMNFM1L8AOplZO2AtfqHnqEPGTAduMLPJwOnA9lACvinMs9OBMcB9ofO0EtdfNLO/AC3wC1Q/j9abkyOwYQMsWAB//CPwv+3MzzorwJhEKovWreGBB3zLxmeeoc64cdx/v9+19OGH4bbbgg5QIrJyJbz1ll/r8/XXsHy535tiv9RUqF3bHzVrwvbtsGnTwc3za9TwEybnneePH/xAibtInItaou6cKzSzG4D3gVTgaefcIjObELr/d+Ad4GL8ws/dwNhwz4a+9X3AFDP7EbAGuDz0zCIzmwJkAYXA9c65IgAzewCf6Nc0szzgn865X0frvcshPvjAn0P16e+/7zcnPeWUAGMSqUyuuw4mT/ZZ+YABXH11C6ZOhbvuggsvhG7dgg5QDlNU5D/yeOstePttWLzYX2/b1u8SN2KE/5do167+j7Fq1fyGVyXt2+cnStavh5wc//0++sjvfgVQpw5cdZX//dAvgUhcMqet6krVq1cvl5mZGXQYyWHMGP8fmo0bKSaFpk1hwAB4/vmgAxOpRJYv94ld//4wdSqbtxhdu0LDhr5evUaNoAMUAPLy4Omn4amnYM0aqFIFzj0XBg+GQYOgY8dj/xlbtsAnn8DUqTBlil/of8YZMGECXHGFfhlEYszMvnTO9SrtnqoTJbqc8/XpF10EKSnMmwebN/tcQURiqFMnv6h02jSYMoVGjfyi0kWL4M7DtqOTmCouhjffhCFDoE0buOce6NwZXnrJJ9UzZ/pFBRWRpIP/6+ySS+C55/yCob/8Bb77ztdDtW3rd7UtLKyYnyUix0SJukTXokX+Y9dQ//T33/eXQy9FJJZuucXXJd94I2zeTP/+cNNNfr3p/n82JYYKC/1HiyefDEOHQmYm3HEHrFjhk/ORI315SjQ1aOBbAS1ZAh9+6P9AmDDBl+8azicAACAASURBVMK8887BNe4iEnNK1CW6Zs705xL16T16+Bp1EYmxtDRfUrFtm19c6hz33eebwlxzjV97KDGQn+9nrTt3hquv9gtBX3jBl7r84Q/QoUPsYzKD88/3JTGvv+4b7g8a5D8N/frr2McjIoASdYm2GTPghBOgVSu+/95vdKTZdJEAde0Kv/0tvPIKTJxIjRrw4ou+8uGyy2Dv3qADTGJFRfDMM76EZcIEaNzYlyItWACjRvl69KCZ+bKYRYv8Ry0LFkDPnnD//T5+EYkpJeoSPTt2+A4DoYL0jz7yn/SqPl0kYP/3f/4fxJtvhvnzOeUUX67873/DlVcqH6twzvkyku7dYdw439d8xgz47DNf8hKPzeyrVvUlUkuW+BjvvNO3dFy5MujIRCqVOPy3gySNN9/003OXXw74spdatXwbXxEJUEqKz8wbNvRdPnbsYMQIeOghX/Vw880qTa4wX33le2AOGuQ3KZoyxSfoffse3k4xHjVq5D99ee45WLjQ164/9ZR+QURiRIm6RM/LL0N6OvTuDfhE/fzztb+GSFxo0sR3FcnO9mUYznHLLfDzn8Njj8F99wUdYILbvt2v1P3BD3yN99/+5ncSvfzyxEjQSzKD0aP9++jVC378Y8jI8DugikhUKVGX6Ni+Hd57z/9HKSWF7GyfD6jsRSSOnHMO/OY3vkj9qacAX4p85ZVw992+faMcIef8rPmJJ8Kjj/pFuytWwA03JP4sRevWMGuWX/A6ZYrfXnr16qCjEklqStQlOqZN810DrrgC+F/rNyXqInHmrrt8Z48bb4SFC0lJ8fvt9O3ry6n/9CdVOUQsOxsGDvS7hjZvDp9/7mfS69YNOrKKk5Lif2feegtWrfIz7B9/HHRUIklLibpEx5Qpfvbl9NMBv26qXbuK269DRCpIair861++n/aQIbB+PVWr+r+1r7jCrzudMMHvRi9lyM+He+/1/dDnzPHdUj7/3Cexyerii+G///U17Bdd5Oul9BedSIVToi4Vb+tWn5lfcQWYsW+f30ejX7/EK80UqRSaNvUzpFu2+K3qd+480Lbx7rth4kS/FnL79qADjUOzZ/sFlr/6lf9DZ8kS/+lEamrQkUXf8cf7hbEDBvjSnltv9busikiFUaIuFe+NN/z024gRAMyd6zs1quxFJI716OE/CZs/3++IWVhISgr8/ve+FGb2bN+x6Ztvgg40Tmzc6DcruuACX+b3zjv+f78WLYKOLLbq1vUfv9x6K/z1r36RaX5+0FGJJA0l6lLxXn4Z2rf3m2Tg69NTU/1/z0Qkjl18sS9hePtt37EkVMowdqz/5/jbb+HUU/3kcaXdGKm42H/EcMIJMHky/OIXfnOggQODjiw4KSnwl7/An//s/1gZOFAfv4hUECXqUrG2bIEPPjhQ9uIcvPYanH12cq2nEklaEybA7bfDE0/45Cvkggt8VcfIkb4cu1u3SriGcMEC3+nkuuvglFP863vvhRo1go4sPvzsZ/D8837nrHPPhfXrg45IJOEpUZeK9frrflvDULeXefNg6VK/O7aIJIj77vOtVX/+c1/3EtKokd/3ZsYMX9123nm+0mH+/OBCjYmdO/3/Fj17wvLlMGmSrwU68cSgI4s/V13lP5FZscLvoZGdHXREIglNibpUrClTfGuX7t0BvxitShW47LKA4xKRyKWk+GS0Xz/40Y/g738/6Hbfvr5WfX+Xvh49/NCZM5Ow8ccbb/iE/MEHfb/KpUt9bbpWxpetXz/46CP/B87ZZ/uNnkTkqChRl4qzaZNv7zJiBJhRVOQ3Phw40Hd+E5EEUqOGXyQ4eDD85Cfw8MMH3a5Z0+97k5sLf/yj37SyXz//N/r99/sJ1YS2ejUMHQqXXAL168Onn/radP3LLDK9evlkvbjYl8Ek/ccuItGhRF0qzmuv+X8ph8pe/v1vWLdOZS8iCat6df/P9aWX+q4e999/2JB69eDOOyEnx29uWq2af92pk59pv/deyMyEwsLYh39UCgrggQegSxe/C+ef/gRffglnnhl0ZInn5JP9fwhq1IDzz/d910XkiJhLus8pK0avXr1cZmZm0GEkljPP9D3Us7LAjPHjfenLxo1+9k1EElRhoS/3eOkluOcef4Qp/Vi92i9XefVVv/8PQO3a/l8R55zj2zz26BGHC8xnzvQ90Jcu9bPpf/ub37hNjs3q1X418saNvn79nHOCjkgkrpjZl865UndIU6JeBiXqR+j/t3fn0VFX9//Hn2/CFtn3TUCUyKosKtq61q2AVmoPWNuv+3bc+bq2fKlWvv3+6npqXap+q/WgxZ+4IJa6W6i4VAsIAQkQZC1L2CoCgRhIcr9/vD/jDDEJITCZmeT1OOeemXzmMzN3uJq8537e931nz4Zhw7yO7s03s3s3dO7s1d4mTUp150TkgJWWwlVXwcSJvoL06aehWbN9Pq2gAD78MN4S67D37u3lHmNtyBBfsFrrVq+GW2/1bxdHHOG/x845JwUdqcPWrfMdTFevhqlTtbGGSAIF6jWgQH0/XXyx57OuXQstW/LXv/qE1JtverAuInVACF4RZvx4T2uYOtUD2/3w73/79/q5c+Nt5cr44z167B28Dx0KXboc5M8RU1joi0RjKT2/+pUH7E2bJukN67lNm3whw+LFXnhg1KhU90gkLShQrwEF6vthwwb/63rddT4ThU+4vf++z6Y1apTi/onIwfXee15QPQR44YUD/ja+dauXck0M3pcujVeQ6dzZKyMmBu/dux9A4ZWSEk+ov+ce//01erQH7EpzSb6tW2H4cM/7nzTJ/zsSqeeqCtQb1nZnpA566ikvqnzjjYBPUv3lL3DZZQrSReqks8/2QOsnP/GqMOPH+2x0kyY1erk2bTyFOXH34h07fD+hxOD9nXc8AwegXTvPeY89b+BArypZpRBg2jRf7bpkiSfLv/aa1/uW2tGmjc/inHuuVxooKvKtb0WkQppRr4Rm1KupuBh69vTprjffBHyC7aKLfLH/SSeluH8ikjy7dsH113vN9T59fDfTH/wgaW9XVORlIOfO9UoyH37o+w+B57affrqnlo8YAR06JDyxrMwD9N/+1vNu+vTxdJfzzlM99FTZtctLX773Hjz+ONxwQ6p7JJIySn2pAQXq1TRpkuenv/uuz7LhfygXLvS8033OcIlI5nvnHQ+0Vqzwb+kPPQSdOtXKW69Z45uETp8eT7cz87Xt544s5fwmbzPgz7+EvDw4/HCfTb/8cmioC8opV1zs5XynTfOSmHfckeoeiaSEAvUaUKBeDSH4X8PCwm9LMq5f7xPst95aYcllEamriop8xvr++70azPjxcPXVtVqDsazM99V5Y3Ihb07ezqw1XQHo32QZY84pYszd/RgwSAF6Wtmzxyd7XnqpWqU/ReqiqgJ1zXdKzX32mV9/vummb3+xPvKI/7G89toU901Eald2NvzmN7BgARx3nM+Odu/uGyUllnVJltJSGrz3DkN/O5q7H27DP9d0Y/1xo3j8mgW0P/4I/nvqUQwc3JD+/T0WzMtLfpekGho18nzJyy6DCRPgzjvjq4hFRDPqldGMejVceKFf8l67Fpo3Z/t2/7s8fLhPjohIPfb55/Dww/7LoKzMF57+/OeeSH6wZtkLCz3n5a23fI3MunWerH7ppXDlldCv37enFhT4utFXXvHc9hD84TFjPPtiwICD0yWpobIyuPlm+MMffN3DY48pd1LqDaW+1IAC9X1YuxYOOwzGjvWyZnha6h13+FqtYyv8z01E6p1163yx4P/+r5fmy8ryKivDh/sGOH36QOvW+36d0lLPgV+0yBfBzJjhK9b37PFtT888E/7jP3yBaOPGVb7Uhg3xoH3mzHjQfsEFHrgraE+REOAXv4AHH/SxfPbZfY6lSF2gQL0GFKjvwy23eJ7LsmVw+OHs3u3rtHJyfGGXiMhe9uyBTz/1q3DvvuulW2JatvTFLT17QseOsHu3LzSMtYICyM/3+zEDBnj99hEjvMxiDQO6WND+8svxmfb+/eNBe//+B/i5Zf+EAPfe62sczjoLpkyBFi1S3SuRpFKgXgMK1Kvw5Zf+R/KSS+CZZwB4/nm/2qydSEWkWjZt8hnxlSt9W/lY27LF67E3aeI7hDZp4kXTBwzwqLl/f+jb14P7g2zDBo8LE9NjBgzw/ZDOOw+GDNE6x1ozcSJcdRUMGuSpTbVURUgkFRSo14AC9Sqcf77XQVu2DDp3JgT/XVpW5jWO9YdMRDJdQUE8aP/oIw/au3b18rPnnuvl4jXRm2RvveWXNTp39isxOTmp7pFIUqjqixw8H3wAr78O48b5L0/8KvYXX8DttytIF5G6oUsX32x55kzYuNEneL//fZg8GUaNgrZtPePmrrv81+I336S6x3XQyJGeS7l9u//jf/JJqnskUus0o14JzahXoKzMV4lu2eL5otnZAJxxhu/GvXKl1v2ISN22ezd8/LEXm5k+3RfPl5X5774hQ+CEE7wdf7yvt9fkxUHw5Zd+KWPVKq8Kc/XVqe6RyEGl1JcaUKBegYkTfUe/F17wMmt4BbZjj9WmciJSP23b5vnsH3/sW0vMnu17P4Gn0R99dLz16+fZG507K4Dfb1u3ws9+5pdwr78efv97r8EuUgcoUK8BBerl7Nzpf2F69PDKDWaE4CWRc3N9oqMWNyAUEUlLJSVePXLWLJg/3/d/WrDAszdimjeH3r295eTs3Tp2VBBfqdJST7t88EE45RRfQNCxY6p7JXLAqgrUtZeyVM8DD/jqqldf/favyAsveG7mU08pSBcRAWjYEAYP9hYTghe0yc/3LI5Yy82FqVM9/oxp0SIetB955N5BfLt2tf950kpWlv8tGjzYN7Q69lj485/h1FNT3TORpNGMeiU0o55g9Wq/Znveeb6SCr8K2bev52B++qk2kBMRqYk9e/yK5LJl8QB+6VK/Xb3a899j2rb14H3gQK+0NWiQp9TUy4mSuXPhpz+F5ct9k6QJE7RISjKWUl9qQIF6ZPdun63Iy/Prt4cdBsANN/hM+pw5voBKREQOruJiX6SfGMDn5/uv4q++ip+Xk+MLWL/3PW8DB/rMfp1XWAi33gpPPw1Dh/pl3r59U90rkf2m1BepuXHjfIXUSy99G6TPmQNPPgk33aQgXUQkWZo08bizfOwZAqxb5znwubm+gPXddz0LBDx95pRT4MwzvSrXwIF1NO+9eXP44x+9jONVV3mwfu+9PpNUL76pSH2gGfVKaEYdr5d+/vleTPixxwDPpTz+eP8jsWRJPb3kKiKSZkLwFJpPP/UNmqZP91l48PWWw4f7Rk0//GFSNnVNvYICz1t/+2046ih49FE47bRU90qkWpT6UgP1PlBfscJnJ3JyvO5YkyYAPPGET1a8+CJceGGK+ygiIpVas8YD9r/9zePXr77yioannuqbNv3kJ77bap0Rgq/Ove02/9YyejQ89BD07JnqnolUSYF6DdTrQL242LfcW77cF+z06gX4JdaTTvJcyPffr6OXUkVE6qCSEp9tf+MN+OtfYfFi/x1+4okez44eDd26pbqXB0lRkQfo997rwftNN8HYsXXoA0pdo0C9Bup1oH7jjb772+uv+7QLflVx2DB/eNYs315bREQy05IlXob8lVfgiy/82Pe/D2PGeNB+6KGp7d9BsWaNr7N68UUv7fjzn8Ptt3vSvkgaqSpQV1E9iQsB7r7bg/Tbbvs2SC8qgh//2C+bTpumIF1EJNP17Qt33eUVZJYsgd/8xouo3HILdO/uQfvDD3usm7G6d4dJk7z25bXX+reSo47yxadTpsCuXanuocg+aUa9EvVuRj0EuPNOv1x4xRW+kj4rixB81+aXX4bXXvOAXURE6qalS31fu1de8XRH8AICsZn2jE73/ve/vWTZ44/Dxo3QrBn86Ef+4UaMgOzsVPdQ6imlvtRAvQrUy8o8h++JJzzt5ZFHvt3BaMIEuOceuO8+31NCRETqhy+/jAft8+b5sWHD4kF7VLE385SUwMyZ/sGmTIEtW+CQQ+C44+LF6E84wcvliNQCBeo1UG8C9dJSuOYaePZZuOMOuP9+MCMEePBBD84vuQQmTtTiURGR+mrZsnjQPneuHzvuON+wesQI31MjI3eojgXt06b5att58/wYQI8ecPjhXlChVy//ZtK1q9e3jLUWLXxHVLO9W0mJbxi4Z0+8lf+5omMheA34rKz47SGH+Pu0aOG145s1y9B/bKmMAvUaqBeB+tdf+yYRU6bAr3/tzYzdu+G66zx2HzPGN9GIqjOKiEg9t2KFB+2vvuqbLQF06OA12s86C04+2WPaTJzcCbuKKJv9OSX/mEXJ/DxKV/4LVq+m6cZVNGIPafGRzKB9e+jUyWf9O3XyxWM9e/o/fOxLRYsWqe6pVJMC9Rqo84H6e+95LvqGDfDAA74NM75gdPRo+Pvf4Ve/8tQXfXEXEZGKbNrkf07eecd3R92yxY936eLlfE88EQYP9jWcbdvWbt9C8PmoDRs8Jb2itmULbN8OO3bEb8vKKn/Npo1LyW5cSptDimmXXUS7JoW0y95Jl+aFdG+1je4tt9Gj5TZ6tt9Ju1YlWONGXry+cWO/TWwVHTPzK90lJX67Z49XdNixI962b4fNm/f+IAUFfl6iDh1gwACvcjNwoN8fMADatEnuP7zsNwXqNVBnA/XCQk9xeeop6N8fnn8ejjkGgPx8v4y5ahX86U9w0UWp7aqIiGSOsjJYuND3yPvkE7/917/ij3fp4gH7kUd6QZZDD/XbWDZJixZ+9baymfiSEv8TFotVN23aO1YtH5Bv2uSZJeVlZcUnotu39x22Y+8f60Ni9klZmW8vUlwM33zjxWK2bvW1qbFWUOCPJWrTxj/rkUdCnz4eIw8alKSrDSF48L5qVbwtXQp5eT4ohYXxc7t23Tt4HzTI7+vSecooUK+BOheoh+DTHtdfDytX+gz6//wPNG3Kzp2+L8RDD/kvqalTfSZERETkQKxf7yUgFy70eu1ffOGpM9u2VXx+w4aehp2V5X+2ysq8xSaWK9OwoQffnTt7AF5Riz3Wtu3Bv1Icgs/Or1njX05WrvTFuPn5Hi+vXRs/t2VLOPpoj49jbeBAT0VPihC8U7GgfeFCv79oUfzbRcOGPnk3ZEi8DR7snZWkU6BeA3UmUC8r88j73nvh8889d23iRDjlFEKAyZN9gn3dOrj4Yq/uUqe2lBYRkbSzY4cHr2vXejCfmNkRSz9p0MCbmWeFxGa8Yy02K96pk89ep3OaZmGhx8fz58fbggXxie4GDSAnx2PjxNa5cxI7VVrq35pyc30Rbaxt3Bg/54gj9g7ehwxJcqfqJwXqNZDxgXpRkUfh99/vX+l79/YSLhdfzG5rwuuvexXGf/wDhg6Fxx7zDS5EREQk+crKfOY9FrTn5vr9Vavi53Tu/N3gvXdvv+KQNAUFewfu8+Z5QJ/YqaFD9w7ee/XKzNXDaUKBeg1kZKC+fTu8+abvTPT227Bzp19TGzcORo8mf1kWTz8Nzz3nl+h69PAFo1dckeT/6UVERKRatm71gD03N97y8uJVI5s189SZWODer5/nwHfokMRYedu27868L1rks/Lgif6DB3sOT58+8eT8Hj0UYFSDAvUayIhA/euvYc4cmDULPvoIZszwlTOdOsH557Nt+E+ZyalMn2HMmOGX3Ro29AWjV1/tZbT0/4+IiEh6Ky6GxYvjsXIsgN++PX5Oq1Z7L16N3c/J8bz/g+6bbzywKB+8J3aqSRO/BBDrUJ8+3qHu3X11caNGSehY5klZoG5mw4FHgCzgmRDCfeUet+jxkcAu4LIQwtyqnmtmbYGXgMOAVcAFIYSt0WPjgCuBUuDmEMK70fFjgIlANvAWMDbs44OnTaBeVuYJfCtWxNuyZb7jRH4+ALvIZm2vU1h81AUs6nI6iwp7sDCvAQsW+NOzs31x6NlneyUXpZeJiIhkthA8TSa2YDV2u3Tp3tV2AFq3hm7dvHXt+t37Xbp4nn929gHOyofg5XYSOxS7Xb7cVwXHmPllgFhnyncqtvigdWtf1JrOixAOUEoCdTPLApYCZwFrgdnAz0IIixLOGQnchAfqxwOPhBCOr+q5ZvYA8FUI4T4z+yXQJoTwCzPrD7wIDAO6An8DjgwhlJrZLGAs8BkeqD8aQni7qv6nJFB/+mkvRLt5s+embN7sdZ8Si7o2aMCElg/xYcMzWG9dKdjVim079/5G2qOHXwobNgzOOMN3QlbVJRERkfph1y6Pi/PzvfrMunXe1q/32w0b4lkriRo18rg41lq1it+Pla5s3NhvE+/HbmNl4GMtVg6+tBRKd5dSsnkrx7RezqltFsQ7k9i5zZsr/kBmHqwndi7WwezseIcqa40axUsIVdX69YMzz0zu4FT48SoP1Bsm8X2HActCCCuiTkwGRgGLEs4ZBTwfzW5/ZmatzawLPlte2XNHAadFz38O+AD4RXR8cgihGFhpZsuAYWa2CmgZQvg0eq3ngR8DVQbqKbF8uV826tAB+vb17d1i3zaPOMK3Mu7Rg41jG/HNfBjYFc7qEv/y2bevN21GJiIiUn8dcojXrD/qqIofLy31ie9YjLxhg2fTVtTWrfPbHTs8BSdxUnz/ZAHtufXW9px65/EVn1Jc7ItZ16/36jPbtlXesVWr/LaoKF7ovrjYZ/Vr6oorUhKoVyWZgXo3YE3Cz2vxWfN9ndNtH8/tFEIoAAghFJhZx4TX+qyC19oT3S9//DvM7BrgmujHQjPLr+zDJdXixSl52yq0B7akuhOyTxqnzKBxygwap8ygccoM347T737nLS09+6y32tezsgeSGahXlOVU/mtOZedU57nVfb9qv1YI4Y/AH/fxPvWOmc2p7JKMpA+NU2bQOGUGjVNm0DhlBo1TzSUzM38t0D3h50OB9dU8p6rnbozSY4huN1XjtQ7dRz9ERERERNJKMgP12UCOmfUys8bAhcC0cudMAy4xdwKwLUprqeq504BLo/uXAn9JOH6hmTUxs15ADjArer0dZnZCVGXmkoTniIiIiIikpaSlvoQQSszsRuBdfAXBsyGEPDO7Nnr8KbwCy0hgGV6e8fKqnhu99H3Ay2Z2JfAvYEz0nDwzexlfcFoC3BBCiK1pvo54eca3SceFpOlN6UCZQeOUGTROmUHjlBk0TplB41RD2vBIRERERCQN1d3q8SIiIiIiGUyBuoiIiIhIGlKgLpUys+Fmlm9my6JdYCXJzOxZM9tkZgsTjrU1s/fN7Mvotk3CY+Oi8ck3sx8mHD/GzL6IHns0WkhNtNj6pej4P83ssNr8fHWFmXU3s7+b2WIzyzOzsdFxjVUaMbOmZjbLzOZH4zQhOq5xSjNmlmVm88zsjehnjVEaMrNV0b9xrpnNiY5prJJIgbpUyMyygD8AI4D+wM/MrH9qe1UvTASGlzv2S2B6CCEHmB79TDQeFwIDouc8EY0bwJP45l05UYu95pXA1hBCb+Bh4P6kfZK6rQS4LYTQDzgBuCEaD41VeikGTg8hDAIGA8PNK4xpnNLPWCBxtz+NUfr6QQhhcEJddI1VEilQl8oMA5aFEFaEEHYDk4FRKe5TnRdC+BD4qtzhUcBz0f3ngB8nHJ8cQigOIazEqycNM99foGUI4dPgq8WfL/ec2Gu9CpwRm8mQ6gshFIQQ5kb3d+ABRjc0VmkluMLox0ZRC2ic0oqZHQqcAzyTcFhjlDk0VkmkQF0q0w1Yk/Dz2uiY1L5O0X4ARLcdo+OVjVG36H7543s9J4RQAmwD2iWt5/VAdGl2CPBPNFZpJ0qpyMU3x3s/hKBxSj+/B+4EyhKOaYzSUwDeM7PPzeya6JjGKomSVkddMl5F32BVyzO9VDZGVY2dxvUgMrPmwBTgP0MI26uY+NFYpUi0n8ZgM2sNTDWzgVWcrnGqZWZ2LrAphPC5mZ1WnadUcExjVHtODCGsN7OOwPtmtqSKczVWB4Fm1KUya4HuCT8fCqxPUV/qu43RpUKi203R8crGaG10v/zxvZ5jZg2BVnw31Uaqwcwa4UH6CyGE16LDGqs0FUL4GvgAz4XVOKWPE4HzzGwVnmJ5uplNQmOUlkII66PbTcBUPE1WY5VECtSlMrOBHDPrZWaN8QUh01Lcp/pqGnBpdP9S4C8Jxy+MVsn3whfkzIouPe4wsxOi3L5Lyj0n9lqjgRlBu57tt+jf9U/A4hDC7xIe0lilETPrEM2kY2bZwJnAEjROaSOEMC6EcGgI4TD878yMEMJFaIzSjpk1M7MWsfvA2cBCNFbJFUJQU6uwASOBpcByYHyq+1MfGvAiUADswWcWrsTz86YDX0a3bRPOHx+NTz4wIuH4sfgv0OXA48R3IW4KvIIv6pkFHJ7qz5yJDTgJvxy7AMiN2kiNVXo14GhgXjROC4G7o+MapzRswGnAGxqj9GzA4cD8qOXF4gKNVXJb7B9GRERERETSiFJfRERERETSkAJ1EREREZE0pEBdRERERCQNKVAXEREREUlDCtRFRERERNKQAnURkQxiZqVmlmtmC83sFTM7pJLz3orVED/A9xtiZs9E988zs18ewGvdY2a37+OciWY2Orr/gZkdW9P3S3jNc81swoG+johIbVOgLiKSWYpCCINDCAOB3cC1iQ+aaxBCGBl8N84D9V/AYwAhhGkhhPsOwmsmhZllVfLQm/julxV+qRERSVcK1EVEMtdHQG8zO8zMFpvZE8BcoLuZrTKz9gBmdomZLTCz+Wb25+hYBzObYmazo3Zi+RePdiE8OoQwP/r5MjN7PLo/0cweNbN/mNmK2Cx4Ba8x3szyzexvQJ+E44PN7LOoX1PNrE1VH9TMnjSzOWaWlzg7Hn3Ou83sY2CMmd1sZoui150MEHzDkA+Ac6v9LysikgYaproDIiKy/8ysITACeCc61Ae4PIRwffR47LwB+O6AJ4YQUCVWkwAAAnlJREFUtphZ2+j8R4CHQwgfm1kP4F2gX7m3ie0eWJku+C6tffGtv18t18dj8G3hh+B/b+YCn0cPPw/cFEKYaWb/Dfwa+M8q3mt8COGraNZ8upkdHUJYED32TQjhpOg91wO9QgjF5VJ/5gAnAy9X8R4iImlFgbqISGbJNrPc6P5HwJ+ArsDqEMJnFZx/OvBqCGELQAjhq+j4mUD/WEAPtDSzFiGEHQnP7QJsrqIvr4cQyoBFZtapgsdPBqaGEHYBmNm06LYV0DqEMDM67zl82/CqXGBm1+B/t7oA/YFYoP5SwnkLgBfM7HXg9YTjm/B/JxGRjKFAXUQksxSFEAYnHoiC7Z2VnG9AqOB4A+B7IYSiqt4LaFrF48Xl3qciFb33fjGzXsDtwHEhhK1mNrFcvxI/+znAKcB5wF1mNiCEUBKdX9VnFRFJO8pRFxGp26bjs9HtABJSX94DboydZGaDK3juYqD3Abz3h8D5ZpYd5bv/CCCEsA3YamYnR+ddDMys5DUAWuLB+LZo5n5ERSeZWQOgewjh78CdQGugefTwkVSdxiMiknY0oy4iUoeFEPLM7P8BM82sFJgHXAbcDPzBzBbgfws+pFwFmRDCEjNrVUFKTHXfe66ZvQTkAqvxVJ2YS4GnokosK4DLq3id+WY2D8iLzv2kklOzgElRao3hOfixyjc/AMbt72cQEUkl88XwIiIi32VmtwA7QgjPpLovNRXNwv//EMIZqe6LiMj+UOqLiIhU5Un2zkXPRD2A21LdCRGR/aUZdRERERGRNKQZdRERERGRNKRAXUREREQkDSlQFxERERFJQwrURURERETSkAJ1EREREZE09H/XJ0xQvtgh0wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "yhat_test1=poly1.predict(x_train_pr1)\n",
    "Title='Distribution Plot of Predicted Value Using Test Data vs Data Distribution of Test Data with 4 features '\n",
    "DistributionPlot(y_test, yhat_test1, \"Actual Values (Test)\", \"Predicted Values (Test)\", Title)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Use the distribution plot to determine the two regions were the predicted prices are less accurate than the actual prices."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    ">The predicted value is lower than actual value for cars where the price around 10,000\n",
    "\n",
    "> the predicted price is larger than the price cost from 30,000 to 40,000 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Ridge regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Ridge regression controls the large magnitude of the polynomial coefficients by introducing the parameter alpha.\n",
    "- Alpha\n",
    " - a parameter to select before fitting or training the model\n",
    "- Ridge regression is used to prevent over-fitting.\n",
    "- Consider how the estimated function is approximating the true function.\n",
    "- real data has outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/01_true_function_samples_order_4.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/02_true_function_samples_model_order_4.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/03_true_function_samples_model_order_10.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/04_alpha.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/05_alpha_coefs.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/06_alpha_0.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/07_alpha_001.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/08_alpha_01.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/09_alpha_1.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/10_alpha_10.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/11_predict_ridge.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Perform a degree two polynomial transformation on our data.\n",
    "pr=PolynomialFeatures(degree=2)\n",
    "x_train_pr=pr.fit_transform(x_train[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])\n",
    "x_test_pr=pr.fit_transform(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg','normalized-losses','symboling']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Import Ridge from the module linear model.\n",
    "from sklearn.linear_model import Ridge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Create a Ridge regression object\n",
    "# setting the regularization parameter to 0.1\n",
    "RigeModel=Ridge(alpha=0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "      normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the model using the method fit.\n",
    "RigeModel.fit(x_train_pr, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Obtain a prediction:\n",
    "yhat = RigeModel.predict(x_test_pr)\n",
    "yhat = [float('{:.1f}'.format(i)) for i in yhat[0:4]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "predicted: [6567.8, 9598.0, 20836.2, 19347.7]\n",
      "test set : [ 6295. 10698. 13860. 13499.]\n"
     ]
    }
   ],
   "source": [
    "# Compare the first five predicted samples to the test set\n",
    "print(f'predicted: {yhat[0:4]}')\n",
    "print(f'test set : { y_test[0:4].values}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to Select the Value of alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/12_select_alpha_1.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/13_select_alpha_2.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/14_select_alpha_3_calc_r_squared.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/15_select_alpha_4_max_r_squared.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/03_ridge/16_train_val_alpha_r_squared.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Select the value of alpha that minimizes the test error\n",
    "Rsqu_test = []\n",
    "Rsqu_train = []\n",
    "dummy1 = []\n",
    "alphas = 10 * np.array(range(0,1000))\n",
    "for a in alphas:\n",
    "    RigeModel = Ridge(alpha=a) \n",
    "    RigeModel.fit(x_train_pr, y_train)\n",
    "    Rsqu_test.append(RigeModel.score(x_test_pr, y_test))\n",
    "    Rsqu_train.append(RigeModel.score(x_train_pr, y_train))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot out the value of R^2 for different Alphas\n",
    "width = 12\n",
    "height = 10\n",
    "plt.figure(figsize=(width, height))\n",
    "\n",
    "plt.plot(alphas,Rsqu_test, label='validation data  ')\n",
    "plt.plot(alphas,Rsqu_train, 'r', label='training Data ')\n",
    "plt.xlabel('alpha')\n",
    "plt.ylabel('R^2')\n",
    "plt.legend()\n",
    "\n",
    "plt.savefig('../figs/05_Model_Evaluation/03_ridge/r_squared_alpha.png')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "- The blue line represents the R^2 of the test data\n",
    "- The red line represents the R^2 of the training data. \n",
    "- The x-axis represents the different values of alpha\n",
    "\n",
    ">As alpha increases the R^2 decreases; therefore as alpha increases the model performs worse on the test data. \n",
    "\n",
    ">The blue line represents the R^2 on the validation data, as the value for alpha increases the R^2 decreases."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Perform Ridge regression \n",
    "- Calculate the R^2 using the polynomial features\n",
    "- Use the training data to train the model and test data to test the model. \n",
    "- The parameter alpha should be set to 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 for the ridge model  = 0.54186\n"
     ]
    }
   ],
   "source": [
    "RigeModel = Ridge(alpha=10) \n",
    "RigeModel.fit(x_train_pr, y_train)\n",
    "r_squared = RigeModel.score(x_test_pr, y_test)\n",
    "print(f\"R^2 for the ridge model  = {r_squared:.5f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Grid Search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "-"
    }
   },
   "source": [
    "### The term alpha is a hyperparameter\n",
    ">sklearn has the class GridSearchCV to make the process of finding the best hyperparameter simpler."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/01_hyperparameter_1.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/02_hyperparameter_2.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/03_hyperparameter_3.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/04_train_valid_test_1.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/05_train_valid_test_2.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/06_train_valid_test_3.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/07_train_valid_test_4.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/08_alpha_normalize.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/09_alpha_values.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/10_gridsearch_1.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/11_gridsearch_2.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/12_gridsearch_3.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# import GridSearchCV from the module model_selection.\n",
    "from sklearn.model_selection import GridSearchCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000, 100000]}]"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a dictionary of parameter values\n",
    "parameters1= [{'alpha': [0.001,0.1,1, 10, 100, 1000, 10000, 100000, 100000]}]\n",
    "parameters1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "      normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a ridge egression object:\n",
    "RR=Ridge()\n",
    "RR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Create a ridge grid search object\n",
    "Grid1 = GridSearchCV(RR, parameters1,cv=4, iid='deprecated')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=4, error_score='raise-deprecating',\n",
       "             estimator=Ridge(alpha=1.0, copy_X=True, fit_intercept=True,\n",
       "                             max_iter=None, normalize=False, random_state=None,\n",
       "                             solver='auto', tol=0.001),\n",
       "             iid='deprecated', n_jobs=None,\n",
       "             param_grid=[{'alpha': [0.001, 0.1, 1, 10, 100, 1000, 10000, 100000,\n",
       "                                    100000]}],\n",
       "             pre_dispatch='2*n_jobs', refit=True, return_train_score=False,\n",
       "             scoring=None, verbose=0)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Fit the model\n",
    "Grid1.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=10000, copy_X=True, fit_intercept=True, max_iter=None,\n",
       "      normalize=False, random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The object finds the best parameter values on the validation data.\n",
    "# Obtain the estimator with the best parameters and \n",
    "# assign it to the variable BestRR \n",
    "\n",
    "BestRR=Grid1.best_estimator_\n",
    "BestRR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'alpha': 0.001} R^2 on test data: 0.66549\n",
      "{'alpha': 0.1} R^2 on test data: 0.66549\n",
      "{'alpha': 1} R^2 on test data: 0.66549\n",
      "{'alpha': 10} R^2 on test data: 0.66555\n",
      "{'alpha': 100} R^2 on test data: 0.66603\n",
      "{'alpha': 1000} R^2 on test data: 0.66897\n",
      "{'alpha': 10000} R^2 on test data: 0.67335\n",
      "{'alpha': 100000} R^2 on test data: 0.65782\n",
      "{'alpha': 100000} R^2 on test data: 0.65782\n"
     ]
    }
   ],
   "source": [
    "scores1 = Grid1.cv_results_\n",
    "for param, mean_test in zip(scores1['params'], scores1['mean_test_score']):\n",
    "    print(f'{param} R^2 on test data: {mean_test:.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 for grid search for the alpha parameter  = 0.84116\n"
     ]
    }
   ],
   "source": [
    "# Test our model on the test data\n",
    "r_squared = BestRR.score(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_test)\n",
    "print(f\"R^2 for grid search for the alpha parameter  = {r_squared:.5f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Perform a grid search for the alpha and the normalization parameters\n",
    "- find the best values of the parameters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/13_alpha_normalize_values.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/14_alpha_normalize_gridsearch_1.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/15_alpha_normalize_gridsearch_2.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/16_alpha_normalize_gridsearch_3.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "<p align=\"center\"> \n",
    "<img src=\"../images/05_Model_Evaluation/04_grid/17_alpha_normalize_gridsearch_4.png\", width=800, height=600>|\n",
    "</p>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Ridge(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=None, normalize=True,\n",
       "      random_state=None, solver='auto', tol=0.001)"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "parameters2= [{'alpha': [0.001,0.1,1, 10, 100, 1000,10000,100000,100000],'normalize':[True,False]} ]\n",
    "Grid2 = GridSearchCV(Ridge(), parameters2, cv=4, iid='deprecated')\n",
    "Grid2.fit(x_data[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']],y_data)\n",
    "BestRR2 = Grid2.best_estimator_\n",
    "BestRR2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'alpha': 0.001, 'normalize': True} R^2 on test data: 0.66606\n",
      "{'alpha': 0.001, 'normalize': False} R^2 on test data: 0.66549\n",
      "{'alpha': 0.1, 'normalize': True} R^2 on test data: 0.69418\n",
      "{'alpha': 0.1, 'normalize': False} R^2 on test data: 0.66549\n",
      "{'alpha': 1, 'normalize': True} R^2 on test data: 0.69049\n",
      "{'alpha': 1, 'normalize': False} R^2 on test data: 0.66549\n",
      "{'alpha': 10, 'normalize': True} R^2 on test data: 0.32138\n",
      "{'alpha': 10, 'normalize': False} R^2 on test data: 0.66555\n",
      "{'alpha': 100, 'normalize': True} R^2 on test data: 0.01706\n",
      "{'alpha': 100, 'normalize': False} R^2 on test data: 0.66603\n",
      "{'alpha': 1000, 'normalize': True} R^2 on test data: -0.03020\n",
      "{'alpha': 1000, 'normalize': False} R^2 on test data: 0.66897\n",
      "{'alpha': 10000, 'normalize': True} R^2 on test data: -0.03517\n",
      "{'alpha': 10000, 'normalize': False} R^2 on test data: 0.67335\n",
      "{'alpha': 100000, 'normalize': True} R^2 on test data: -0.03567\n",
      "{'alpha': 100000, 'normalize': False} R^2 on test data: 0.65782\n",
      "{'alpha': 100000, 'normalize': True} R^2 on test data: -0.03567\n",
      "{'alpha': 100000, 'normalize': False} R^2 on test data: 0.65782\n"
     ]
    }
   ],
   "source": [
    "scores2 = Grid2.cv_results_\n",
    "for param, mean_test in zip(scores2['params'], scores2['mean_test_score']):\n",
    "    print(f'{param} R^2 on test data: {mean_test:.5f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R^2 for grid search for the alpha and the normalization parameters = 0.84086\n"
     ]
    }
   ],
   "source": [
    "# Test our model on the test data\n",
    "r_squared = BestRR2.score(x_test[['horsepower', 'curb-weight', 'engine-size', 'highway-mpg']], y_test)\n",
    "print(f\"R^2 for grid search for the alpha and the normalization parameters = {r_squared:.5f}\")"
   ]
  }
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