scripts/python_ML_MultiLinearRegression_StartInvest.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Machine Learning Multivariate Regression Analysis: Startup Investor Data Set\n",
    "\n",
    "The most basic building block in machine learning is regression analysis. This notebook I discuss, with python demonstration, the procedure to carry out a machine learning project using regression analysis. I use Housing Price as an example and data set can be downloaded from [here](https://github.com/PacktPublishing/Hands-on-Python-for-Finance/tree/master/Chapter%207).\n",
    "\n",
    "There are the following steps\n",
    "- $\\textbf{Environment Initiation}$. We first start by importing the packages we need for this project. Then we get data that is already saved in the data folder. Next we set up a model we want to study and we pull the variables from the data we uploaded.\n",
    "- $\\textbf{Machine Learning: Linear Regression}$. Regression analysis plays important role in finance and machine learning. Regression models (both linear and non-linear) are used to predict real values, ex. housing prices, salaries, or stock returns. I am going to discuss the fundamentals of simple regression analysis and we are going to use *sklearn* package to train a regression model in python notebook. Then I discuss the interpretations behind the coefficient and intercept term obtained from regression analysis and how these concepts apply in real life. \n",
    "- $\\textbf{Machine Learning: Training and Testing}$. It is essential to understand the difference of the performance of machine on existing data and the performance of machine on potential future data. To carry out an unbiased and impartial learning process, it is important to separate training data and testing data so that the observations do not repeat and the performance is robust, consistent, and honest.\n",
    "- $\\textbf{Software Development / Product Management}$. Every data science project has two phases. Phase I is about end-to-end research and select the most optimal machine learning procedure. Phase II is about delivering a software product to consumer and clients so that the python codes can be called and there is no need to redo everything that has already been done."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Environment Initiation\n",
    "\n",
    "Let us start by initiating packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('~/OneDrive/Documents/YinsPy/data/startups_Invest.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   R&D Spend  Administration  Marketing Spend       State     Profit\n",
      "0  165349.20       136897.80        471784.10    New York  192261.83\n",
      "1  162597.70       151377.59        443898.53  California  191792.06\n",
      "2  153441.51       101145.55        407934.54     Florida  191050.39\n"
     ]
    }
   ],
   "source": [
    "print(data.head(3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    R&D Spend  Administration  Marketing Spend       State\n",
      "0   165349.20       136897.80        471784.10    New York\n",
      "1   162597.70       151377.59        443898.53  California\n",
      "2   153441.51       101145.55        407934.54     Florida\n",
      "3   144372.41       118671.85        383199.62    New York\n",
      "4   142107.34        91391.77        366168.42     Florida\n",
      "5   131876.90        99814.71        362861.36    New York\n",
      "6   134615.46       147198.87        127716.82  California\n",
      "7   130298.13       145530.06        323876.68     Florida\n",
      "8   120542.52       148718.95        311613.29    New York\n",
      "9   123334.88       108679.17        304981.62  California\n",
      "10  101913.08       110594.11        229160.95     Florida\n",
      "11  100671.96        91790.61        249744.55  California\n",
      "12   93863.75       127320.38        249839.44     Florida\n",
      "13   91992.39       135495.07        252664.93  California\n",
      "14  119943.24       156547.42        256512.92     Florida\n",
      "15  114523.61       122616.84        261776.23    New York\n",
      "16   78013.11       121597.55        264346.06  California\n",
      "17   94657.16       145077.58        282574.31    New York\n",
      "18   91749.16       114175.79        294919.57     Florida\n",
      "19   86419.70       153514.11             0.00    New York\n",
      "20   76253.86       113867.30        298664.47  California\n",
      "21   78389.47       153773.43        299737.29    New York\n",
      "22   73994.56       122782.75        303319.26     Florida\n",
      "23   67532.53       105751.03        304768.73     Florida\n",
      "24   77044.01        99281.34        140574.81    New York\n",
      "25   64664.71       139553.16        137962.62  California\n",
      "26   75328.87       144135.98        134050.07     Florida\n",
      "27   72107.60       127864.55        353183.81    New York\n",
      "28   66051.52       182645.56        118148.20     Florida\n",
      "29   65605.48       153032.06        107138.38    New York\n",
      "30   61994.48       115641.28         91131.24     Florida\n",
      "31   61136.38       152701.92         88218.23    New York\n",
      "32   63408.86       129219.61         46085.25  California\n",
      "33   55493.95       103057.49        214634.81     Florida\n",
      "34   46426.07       157693.92        210797.67  California\n",
      "35   46014.02        85047.44        205517.64    New York\n",
      "36   28663.76       127056.21        201126.82     Florida\n",
      "37   44069.95        51283.14        197029.42  California\n",
      "38   20229.59        65947.93        185265.10    New York\n",
      "39   38558.51        82982.09        174999.30  California\n",
      "40   28754.33       118546.05        172795.67  California\n",
      "41   27892.92        84710.77        164470.71     Florida\n",
      "42   23640.93        96189.63        148001.11  California\n",
      "43   15505.73       127382.30         35534.17    New York\n",
      "44   22177.74       154806.14         28334.72  California\n",
      "45    1000.23       124153.04          1903.93    New York\n",
      "46    1315.46       115816.21        297114.46     Florida\n",
      "47       0.00       135426.92             0.00  California\n",
      "48     542.05        51743.15             0.00    New York\n",
      "49       0.00       116983.80         45173.06  California\n"
     ]
    }
   ],
   "source": [
    "print(data.iloc[:, :-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(50, 4) (50,)\n"
     ]
    }
   ],
   "source": [
    "X = data.iloc[:, :-1]\n",
    "Y = data.iloc[:, 4]\n",
    "print(X.shape, Y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that we have the column 'State' to be strings and there are different levels for this variable. We need to process this data into a format that the python can read. I use *.get_dummies* to achieve this task."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Florida</th>\n",
       "      <th>New York</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Florida  New York\n",
       "0        0         1\n",
       "1        0         0\n",
       "2        1         0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "State = pd.get_dummies(X.iloc[:, 3], drop_first=True)\n",
    "State.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The code above allows us to take all the states and convert them into dummy variables. For example, instance 0 (the first row) says it is not Florida and it is New York which gives us the power of interpretability in our data set.\n",
    "\n",
    "Now what we need is to replace the original 'State' variable with out newly defined dummy variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>R&amp;D Spend</th>\n",
       "      <th>Administration</th>\n",
       "      <th>Marketing Spend</th>\n",
       "      <th>Florida</th>\n",
       "      <th>New York</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>165349.20</td>\n",
       "      <td>136897.80</td>\n",
       "      <td>471784.10</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>162597.70</td>\n",
       "      <td>151377.59</td>\n",
       "      <td>443898.53</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>153441.51</td>\n",
       "      <td>101145.55</td>\n",
       "      <td>407934.54</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   R&D Spend  Administration  Marketing Spend  Florida  New York\n",
       "0  165349.20       136897.80        471784.10        0         1\n",
       "1  162597.70       151377.59        443898.53        0         0\n",
       "2  153441.51       101145.55        407934.54        1         0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.drop('State', axis=1, inplace=True)\n",
    "X.head(3)\n",
    "X = pd.concat([X, State], axis=1)\n",
    "X.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From above code, we have a data set that we want. All the information is preserved and we have all the input to be in format that machine can interpret. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Machine Learning: Linear Regression\n",
    "\n",
    "Now we have dependent variable $Y$ and independent variable $X$. We want to start machine learning. This means we want to train a machine to learn from $X$ and to predict $Y$. In this case, the machine will form some rules $f()$ that we can use. It is written in $f()$ form because it is essentially a map that let us draw inference about $Y$ from $X$. Hence, in mathematical form\n",
    "$$\\hat{Y} := f(X)$$\n",
    "and this $\\hat{Y}$ is estimated value of $Y$.\n",
    "\n",
    "Notice that in our case the machine is chosen to be linear regression and we can carry out standard linear regression analysis based on the machine we train. \n",
    "\n",
    "Also note that this is a machine learning project. We need to separate training set and testing set. This purpose is we want to be impartial and honest about the performance of the linear model on this data set. We separate data into training and testing randomly so that we can construct an environment as if there is new data set arriving for future reference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(35, 5) (35,)\n",
      "(15, 5) (15,)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.3, random_state=0)\n",
    "print(X_train.shape, y_train.shape)\n",
    "print(X_test.shape, y_test.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "lm = LinearRegression()\n",
    "lm.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7.90840255e-01 3.01968165e-02 3.10148566e-02 4.63028992e+02\n",
      " 3.04799573e+02] 42403.87087052793\n"
     ]
    }
   ],
   "source": [
    "print(lm.coef_, lm.intercept_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can make the following interpretation:\n",
    "- The sets of coefficients $[7.91, 3.02, 3.10, 4.63, 3.04]$ tells us, respectively, when each of the unit of each of the variables changes what is the change on dependent variable, e.g. investment profits.\n",
    "- The intercept $\\$42$k is the constant term at a cirmcumstan where all the variables to be zero. This in real world would not mean much but we can still guess that perhaps that is the bar for this industry or business activities. Once you are in the game the investment profit is going to be, based on data, at least $\\$42$k on average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Machine Learning: Training Evaluation\n",
    "\n",
    "We have our model trained. How well does it do on existing data? Let us introduce a metric called Root Mean Square Error (RMSE). It is a metric that measure on average how far away it is from real House Price and predicted House Price. The mathematical form is\n",
    "$$RMSE := \\frac{1}{n} \\sum (\\hat{Y} - Y)^2$$\n",
    "and $\\hat{Y}$ is the estimated House Price while $Y$ is the real House Price and $n$ is the sample size used for this particular experiment (in this case it is training sample size and later on we are going to use testing sample size)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Set RMSE is 9466.997852929857\n"
     ]
    }
   ],
   "source": [
    "y_train_pred = lm.predict(X_train)\n",
    "RMSE_train = (((y_train_pred - y_train)**2).mean())**(0.5)\n",
    "print('Training Set RMSE is', RMSE_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "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": [
    "plt.scatter(y_train, y_train_pred)\n",
    "plt.xlabel('Real Y')\n",
    "plt.ylabel('Estimated Y')\n",
    "plt.title('Training Set: (' + str(X_train.shape[0]) + ' samples); \\nPerformance: RMSE = ' + str(RMSE_train))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the RMSE is about $\\$9$k and this means that this machine makes guesses based on linear regression model and the predictions are on average +/- $\\$9$k away from real values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Machine Learning: Prediction\n",
    "\n",
    "Once we have a trained model from above codes we can move forward to the next step which is prediction. If we have future observations that we like to look at, we can simply pull out the House Size in sq. ft. and use our model to predict what these houses ought to be priced at."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Testing Set RMSE is 7867.8551335413895\n"
     ]
    }
   ],
   "source": [
    "y_pred = lm.predict(X_test)\n",
    "RMSE_test = (((y_pred - y_test)**2).mean())**(0.5)\n",
    "print('Testing Set RMSE is', RMSE_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "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": [
    "plt.scatter(y_train, y_train_pred)\n",
    "plt.xlabel('Real Y')\n",
    "plt.ylabel('Estimated Y')\n",
    "plt.title('Testing Set: (' + str(X_test.shape[0]) + ' samples); \\nPerformance: RMSE = ' + str(RMSE_test))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Software Development / Product Management\n",
    "\n",
    "From about analysis, we have established a list of steps we execute to carry out a simple linear regression analysis. Each step is clear written and can be examined for reference. \n",
    "\n",
    "Now it is time to pack everything together into a function so that the above analysis can be summarized into a word and can be pulled for future usage without having to code everything again. Once this software is developed we can get the product shipped to employers or clients and we will be starting negotiation as well as software maintainance (which is crucial for product management)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define function\n",
    "def ML_MultiLinearRegression(X, Y, test_set_size):\n",
    "    # Environment Initiation\n",
    "    import numpy as np\n",
    "    import pandas as pd\n",
    "    from scipy import stats\n",
    "    import statsmodels.api as sm\n",
    "    import matplotlib.pyplot as plt\n",
    "\n",
    "    # ML: Setup\n",
    "    from sklearn.model_selection import train_test_split\n",
    "    X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.3, random_state=0)\n",
    "    \n",
    "    # ML: Multivariate Linear Regression\n",
    "    from sklearn.linear_model import LinearRegression\n",
    "    lm = LinearRegression()\n",
    "    lm.fit(X_train, y_train)\n",
    "    \n",
    "    # ML: Training Performance\n",
    "    y_train_pred = lm.predict(X_train)\n",
    "    RMSE_train = (((y_train_pred - y_train)**2).mean())**(0.5)\n",
    "    plt.scatter(y_train, y_train_pred)\n",
    "    plt.xlabel('Real Y')\n",
    "    plt.ylabel('Estimated Y')\n",
    "    plt.title('Training Set: (' + str(X_train.shape[0]) + ' samples); \\nPerformance: RMSE = ' + str(RMSE_train))\n",
    "    plt.show()\n",
    "    \n",
    "    # ML: Testing Performance\n",
    "    y_pred = lm.predict(X_test)\n",
    "    RMSE_test = (((y_pred - y_test)**2).mean())**(0.5)\n",
    "    plt.scatter(y_train, y_train_pred)\n",
    "    plt.xlabel('Real Y')\n",
    "    plt.ylabel('Estimated Y')\n",
    "    plt.title('Testing Set: (' + str(X_test.shape[0]) + ' samples); \\nPerformance: RMSE = ' + str(RMSE_test))\n",
    "    plt.show()\n",
    "    \n",
    "    # Output\n",
    "    return {\n",
    "        'Data': {\n",
    "            'X_train': X_train,\n",
    "            'X_test': X_test,\n",
    "            'y_train': y_train,\n",
    "            'y_test': y_test\n",
    "        },\n",
    "        'Linear Regression Results': [lm.coef_, lm.intercept_],\n",
    "        'y_train_pred': y_train_pred,\n",
    "        'y_test_pred': y_test,\n",
    "        'Training RMSE': RMSE_train,\n",
    "        'Testing RMSE': RMSE_test\n",
    "    }\n",
    "# End of function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above lines of code finish up the function and let me run it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Set Performance:  7867.8551335413895\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Set Performance:  7866.112393258023\n"
     ]
    }
   ],
   "source": [
    "# Data\n",
    "data = pd.read_csv('~/OneDrive/Documents/YinsPy/data/startups_Invest.csv')\n",
    "X = data.iloc[:, :-1]\n",
    "Y = data.iloc[:, 4]\n",
    "\n",
    "# Data Cleanup\n",
    "State = pd.get_dummies(X.iloc[:, 3], drop_first=True)\n",
    "State.head(3)\n",
    "X.drop('State', axis=1, inplace=True)\n",
    "X.head(3)\n",
    "X = pd.concat([X, State], axis=1)\n",
    "X.head(3)\n",
    "\n",
    "# Run\n",
    "testresult = ML_MultiLinearRegression(X, Y, 0.5)\n",
    "print('Test Set Performance: ', testresult['Testing RMSE'])\n",
    "testresult = ML_MultiLinearRegression(X + X**0.5, Y, 0.5)\n",
    "print('Test Set Performance: ', testresult['Testing RMSE'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}