Salary Prediction.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Salary Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import warnings\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import libraries\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.model_selection import train_test_split\n",
    "import statsmodels.api as sm\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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",
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       "    }\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>YearsExperience</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.1</td>\n",
       "      <td>39343.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.3</td>\n",
       "      <td>46205.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.5</td>\n",
       "      <td>37731.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.0</td>\n",
       "      <td>43525.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.2</td>\n",
       "      <td>39891.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   YearsExperience   Salary\n",
       "0              1.1  39343.0\n",
       "1              1.3  46205.0\n",
       "2              1.5  37731.0\n",
       "3              2.0  43525.0\n",
       "4              2.2  39891.0"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#import data\n",
    "data = pd.read_csv('Salary_Data.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let us inspect the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We hardly have 30 data points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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>YearsExperience</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>30.000000</td>\n",
       "      <td>30.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.313333</td>\n",
       "      <td>76003.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.837888</td>\n",
       "      <td>27414.429785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.100000</td>\n",
       "      <td>37731.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.200000</td>\n",
       "      <td>56720.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.700000</td>\n",
       "      <td>65237.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.700000</td>\n",
       "      <td>100544.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>10.500000</td>\n",
       "      <td>122391.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       YearsExperience         Salary\n",
       "count        30.000000      30.000000\n",
       "mean          5.313333   76003.000000\n",
       "std           2.837888   27414.429785\n",
       "min           1.100000   37731.000000\n",
       "25%           3.200000   56720.750000\n",
       "50%           4.700000   65237.000000\n",
       "75%           7.700000  100544.750000\n",
       "max          10.500000  122391.000000"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Min years of experience is 1.1 with a salary of 27414.4 and max years of experience is 10.5 with a salary of 122391."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Let us visualise the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0xc86c5c0>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 180x180 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.pairplot(y_vars = 'Salary', x_vars = 'YearsExperience' ,data = data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Salary looks linear related to years of experience."
   ]
  },
  {
   "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>YearsExperience</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>YearsExperience</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.978242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Salary</th>\n",
       "      <td>0.978242</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 YearsExperience    Salary\n",
       "YearsExperience         1.000000  0.978242\n",
       "Salary                  0.978242  1.000000"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checking the correlation of the data\n",
    "data.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "0.97 is highly correlated."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Data preparation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data['YearsExperience']\n",
    "y = data['Salary']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train,X_test,y_train, y_test = train_test_split(X,y, train_size = 0.7, test_size = 0.3, random_state = 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(21,)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(9,)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model Building:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_sm = sm.add_constant(X_train)\n",
    "model = sm.OLS(y_train, X_train_sm).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                 Salary   R-squared:                       0.949\n",
      "Model:                            OLS   Adj. R-squared:                  0.946\n",
      "Method:                 Least Squares   F-statistic:                     352.9\n",
      "Date:                Tue, 22 Oct 2019   Prob (F-statistic):           9.91e-14\n",
      "Time:                        19:38:18   Log-Likelihood:                -211.80\n",
      "No. Observations:                  21   AIC:                             427.6\n",
      "Df Residuals:                      19   BIC:                             429.7\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "===================================================================================\n",
      "                      coef    std err          t      P>|t|      [0.025      0.975]\n",
      "-----------------------------------------------------------------------------------\n",
      "const             2.52e+04   2875.387      8.765      0.000    1.92e+04    3.12e+04\n",
      "YearsExperience  9731.2038    517.993     18.786      0.000    8647.033    1.08e+04\n",
      "==============================================================================\n",
      "Omnibus:                        1.843   Durbin-Watson:                   1.749\n",
      "Prob(Omnibus):                  0.398   Jarque-Bera (JB):                1.106\n",
      "Skew:                           0.219   Prob(JB):                        0.575\n",
      "Kurtosis:                       1.964   Cond. No.                         12.3\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "print(model.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R2, p value looks fine."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So our linear regression equation is :\n",
    "#### Salary = 25200 + YearsExperience x9731.2038"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "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": [
    "# Let us show the line fitting:\n",
    "plt.scatter(X_train,y_train)\n",
    "plt.plot(X_train, 25200 + X_train * 9731.2038,'r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Residual analysis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_train_pred = model.predict(X_train_sm)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17     76778.268129\n",
       "22    102079.398108\n",
       "11     64127.703139\n",
       "4      46611.536230\n",
       "29    127380.528088\n",
       "dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_pred.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "residual = (y_train - y_train_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17    6309.731871\n",
       "22    -777.398108\n",
       "11   -8333.703139\n",
       "4    -6720.536230\n",
       "29   -5508.528088\n",
       "dtype: float64"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "residual.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xcd57cc0>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Uleqq7h5HalV+BXvLa/nR2aN5a0Nxt8bua4YPjmRGRgIrd5VzanIM44Z5f967k+N5dRcdzyuw6R6ICmjHGpr5ZEcpGYmDGN/BL8v+ZOaERBKiI/j7xmLqm1qcTkf1Y1pAVED7OK+UxuZWLjslqd+dOPcmzBXC1VOTOVLXxHs6zIlykBYQFbBKaupYV1jJ9DFxJOpzMb4lZehAZmTEk7uvip2HjjidjuqntICogGSM4Z0tJQwIdzF7wjCn0wlIsyYOY9jgCP62oVhH7FWO0AKiAtK2g0coqKhl9sRhDAgPzsEST1aYK4Rrs1Koa2rh7Y16g6HqfVpAVMBpamnl/a0lDBscwZmpQ51OJ6AlxQzgO5nDyCs5Qm6hPnxK9S4tICrgrMqvoOp4E5edMgJXiJ4478y56fGkJwziH1sOUlJT53Q6qh/RAqICSm1DMyt3lTNheDTpif3zjvOuChHhmqxkBoS5+Ova/TTopb2ql2gBUQHl051lNDa3MmfScKdT6VOiI8P4wbQUDh9r5C09H6J6iRYQFTCqjjeyuqCSqaOGMEwv2+2yMfGDuDhzGF8X1/D57gqn01H9gE8FRETmishOEckXkfke3o8QkTfs+2tEJLXNe/fb9p0iMqezmCKSZmPstjHD2y3rahExIpLlzwqrwPVxXikCzJqY6HQqfdYF4xKYPDKGZdsO6f0hqsd1WkBExAU8AVwCZALXiUhmu263AlXGmHRgIbDAzpsJZAOTgLnAkyLi6iTmAmChMSYDqLKxT+QSDdwNrPFvdVWgKqmpY9OBas4eG0fswPDOZ1AeiQhXT00mKSaSResOUHqk3umUVBDzZQ9kGpBvjNlrjGkEFgHz2vWZB7xsp5cAs8Q97sQ8YJExpsEYUwDk23geY9p5ZtoY2JhXtFnOw8DvAP1WBJkPt5USERbCBeMSnE6lzwsPDeGGs0YT7grhpS8LqT7e6HRKKkj5UkBGAgfavC6ybR77GGOagRogroN5vbXHAdU2xreWJSKnAynGmHc6SlZEbheRXBHJLS/XZ0j3BXsrjrGz9CgXjEtkYLgOEN0dYgeGc9M5qdQ3tfDSl4Ucb9Q71VX386WAeLoQv/0lHt76dEu7iITgPjT2PzvI093ZmGeMMVnGmKyEBP1rNtAZY1i29RCDI0M5Z2yc0+kElRGxA7jhrNEcrm3k5S8LdeRe1e18KSBFQEqb18nAQW99RCQUiAEqO5jXW3sFEGtjtG2PBiYDn4pIIXAWkKMn0vu+7SVHOFBVx+yJwwhz6UWB3W1swiCyz0yhuLqOl7SIqG7myzd2HZBhr44Kx31SPKddnxzgJjt9NbDcuC9EzwGy7VVaaUAGsNZbTDvPChsDG3OpMabGGBNvjEk1xqQCq4HLjTG5fq63CgCtxvDJjjLiosI5fdQQp9MJWpNGxJB95iiKqo7z0peF1DVqEVHdo9MCYs9H3AUsA7YDi40x20TkIRG53HZ7HogTkXzgXmC+nXcbsBjIAz4A7jTGtHiLaWPdB9xrY8XZ2CoI5R08QklNPTMnJOqQJT1s8kh3ESmuquPZz/dSU9fkdEoqCEgw37GalZVlcnN1J6W3+fIo1VZjeHx5Ps2trdwza5wWkF6SX3aMv6zZx8AwFzefkxrwz1nRR9o6Q0TWG2M6PUWgB52VI/IOHuHQkXouGq97H70pPXEQt80YQ3Or4c8r97CjRG82VP7TAqJ6XasxLN9RRvygcE5NjnU6nX5nZOwA7rhwLHFR4by6eh+f7iyjNYiPRKieowVE9boTex967sM5sQPDuf38sZySHMOHeaW8tKqQI3peRHWRFhDVq3TvI3CEh4bwg6wUrpgykn2VtfzX8t1s10Naqgu0gKhe1XbvI0R078NpIsK0tKHceVE6MQPCeHX1PpZuKqappdXp1FQfoAVE9Rrd+whcidGR/NsFYzkvPZ41BZU8vjyfA5XHnU5LBTgtIKrX7Cj55sor3fsIPKGuEC49JYlbzk2lsaWVp1bu4YOtJbo3orzSAqJ6hTGGT3eVM2RgmO59BLiMxGjumZXBGaOH8NnuCh5fns9+3RtRHmgBUb2ioKKWoqo6ZmQk6JVXfUBkmIvvT03mlnPceyNPr9zD+7o3otrRAqJ6xcpd5URFhHLGaB3zqi/JGObeG8lKHcrnujei2tEConrcweo6dpcd47yxcTribh8UGebiytNH/vPcyNMr9/Dx9lJaWvXmw/5Ov82qx63cVU5EaAjTx+jzPvqyE+dGpqTEsnxHGc9+vlefdtjPaQFRPerwsQa2FtcwPS2OyDCX0+mokxQZ5uKarBSuzUqh9Eg9j6/IJ7/smNNpKYdoAVE96vPdFbhChHPSde8jmExJieXOC9MZFBHKi6sKWLmrnGAe2Vt5pgVE9Zgj9U2s31/F1FFDGBwZ5nQ6qpvFR0dwx4XpTB4Zw7Jth3hrYzHNrXqVVn8S2nkXpfzzZf5hWlsNMzLinU5F9ZDw0BCyz0whITqC5TvKqDreyA3TR+vhyn5C90BUj6hvamFNwWEmj4whblCE0+moHiQizJ44jKunJlNYUcsLqwo43tjsdFqqF2gBUT1iw/4qGppbde+jH5k6egg/nD6akpp6nvu8gGMNWkSCnRYQ1e1ajeGrPYcZNXQgyUMGOp2O6kUTkwbzo7NHc7i2gRe+KKCuscXplFQP0gKiut2uQ0c5XNvIOWP1yqv+KCMxmhvPSqX8WAMvfVlAQ7MWkWClBUR1u1V7KhgcGcqkETFOp6Ickp44iOwzUyiuruO11fv1rvUgpQVEdaudh46yp7yWs8bE6aCJ/dykETFceXoy+eXHWLqpWO8TCUI+FRARmSsiO0UkX0Tme3g/QkTesO+vEZHUNu/db9t3isiczmKKSJqNsdvGDLftPxWRr0Vkk4h8ISKZJ7Piqme89GUBoSHCtNShTqeiAsAZo4dw4fgEcvdV8UV+hdPpqG7WaQERERfwBHAJkAlc5+GX961AlTEmHVgILLDzZgLZwCRgLvCkiLg6ibkAWGiMyQCqbGyA140xpxhjpgC/A/6fn+usekhVbSNvbShmSkosAyP0FiPlNnviMCaPjOGDrYfYcUifuR5MfNkDmQbkG2P2GmMagUXAvHZ95gEv2+klwCwREdu+yBjTYIwpAPJtPI8x7TwzbQxszCsAjDFtt7woQPeHA8xf1+2nobmVc9L10l31jRARrjkjmaSYSBbnHqCyVgdgDBa+FJCRwIE2r4tsm8c+xphmoAaI62Beb+1xQLWN8S/LEpE7RWQP7j2Quz0lKyK3i0iuiOSWl5f7sHqqOzS1tPLqV/s4Nz2O4YMjnU5HBZgwVwjXTx8NwOtr9+mDqYKELwXE05nQ9n/9e+vTXe3uCWOeMMaMBe4Dfu0pWWPMM8aYLGNMVkJCgqcuqgcs23aIkpp6bjknzelUVIAaGhXONWekcLC6nne/LnE6HdUNfCkgRUBKm9fJwEFvfUQkFIgBKjuY11t7BRBrY3hbFrgPeV3hQ+6ql7zwRQGj4wYyc0Ki06moADYxaTAz0uNZW1DJ9hI9H9LX+VJA1gEZ9uqocNwnxXPa9ckBbrLTVwPLjfuavRwg216llQZkAGu9xbTzrLAxsDGXAohIRpvlXQbs7tqqqp6y+UA1G/ZXc9PZqYTopbuqExdnDiMpJpK/bSjiaH2T0+mok9BpAbHnI+4ClgHbgcXGmG0i8pCIXG67PQ/EiUg+cC8w3867DVgM5AEfAHcaY1q8xbSx7gPutbHibGyAu0Rkm4hssss4UbCUw15cVcCgiFCuyUp2OhXVB4S6Qrg2K4XG5lbe2qD3h/RlPl1raYx5D3ivXdtv20zXA9d4mfdR4FFfYtr2vbiv0mrffo8vuareVXbEfTz7h9NHE63P/FA+GjY4kksmD+cfW0pYv6+KLL1vqE/SO9HVSfnL6n00txpuPifV6VRUHzN9TBxp8VG8t7WEI3V6KKsv0gKi/Fbf1MJra/Yzc3wiqfFRTqej+pgQEb5/+khaWg1LNx/UQ1l9kBYQ5bd/bD7I4dpGfnyeXrqr/BM3KILZE4exveQIXxfXOJ2O6iItIMovxhheXFXI+GHROmy7OinnpsczMnYA724pob5Jh37vS7SAKL+sKagkr+QIN5+binsEGqX8EyLCvCkjONbQzEfbS51OR3WBFhDllxdXFRA7MIwrprQf1UaprkseMpDpY4ayes9hiqvrnE5H+UgLiOqyA5XH+SivlOumjWJAuMvpdFSQuHjicAZGhJKzqZhWPaHeJ2gBUV32yleFiAg3njXa6VRUEBkQ7uKSycM5UFXH5gPVTqejfKAFRHVJbUMzi9YdYO7k4YyIHeB0OirITEmJZWTsAD7MK6WxWUfsDXRaQFSXvLWhiKP1zfz43FSnU1FBKESES09Joqauic/z9XEMgU4LiPJZa6vhxS8LOTU5hqmjhjidjgpSafFRTB4xmM92lXOopt7pdFQHtIAon63cXc7e8lp+fG6aXrqretTcyUm0Gvj9sp1Op6I6oAVE+ezFVYUkRkdw6SlJTqeigtzQqHDOGRvH3zYU8XWR3qEeqLSAKJ/klx3js13l3HDWaMJDdbNRPe+i8YnERYXz8Dt5Ok5WgNLfBMonL31ZQLgrhOunj3I6FdVPRIa5+MXF41hbWMmybYecTkd5oAVEdarmeBN/W1/M5VNGED8owul0VD+SfWYK44YN4j/f30FTi17WG2i0gKhOvZG7n7qmFm7RS3dVLwt1hfCrORMoPHycN3OLnE5HtaMFRHWouaWVl7/cx7S0oUwaEeN0OqofmjUxkamjYnnsk106Wm+A0QKiOvTx9lKKq+v0xkHlGBHhV3MnUHqkgVe+KnQ6HdWGFhDVoRe+KCR5yAAuzhzudCqqHztrTBznj0vgyU/3cKReH38bKLSAKK+2FtewtrCSm85OxRWiNw4qZ/1qzniqjzfx3Gd7nU5FWT4VEBGZKyI7RSRfROZ7eD9CRN6w768RkdQ2791v23eKyJzOYopImo2x28YMt+33ikieiGwRkU9ERIeC7WEvripkYLiLa89McToVpZg8MobLTkniuS8KqDjW4HQ6Ch8KiIi4gCeAS4BM4DoRyWzX7VagyhiTDiwEFth5M4FsYBIwF3hSRFydxFwALDTGZABVNjbARiDLGHMqsAT4nX+rrHxRfrSBf2w+yFVTk4kZEOZ0OkoBcO93xtHQ3Mrjy/OdTkXh2x7INCDfGLPXGNMILALmteszD3jZTi8BZol7sKR5wCJjTIMxpgDIt/E8xrTzzLQxsDGvADDGrDDGHLftq4Hkrq+u8tXra/bT2NLKzXryXAWQsQmDuHpqMq+v2U9R1fHOZ1A9ypcCMhI40OZ1kW3z2McY0wzUAHEdzOutPQ6otjG8LQvceyXv+5C78kN9Uwuvrt7HBeMSGJswyOl0lPqWe2ZngMCfPt7tdCr9ni8FxNPZ0/YD03jr013t3yxI5AYgC/i9h76IyO0ikisiueXl+jwBf+RsOkjFsQZumzHG6VSU+hcjYgdw41mjeWtDEbtLjzqdTr/mSwEpAtqeRU0GDnrrIyKhQAxQ2cG83torgFgb41+WJSKzgQeAy40xHs+iGWOeMcZkGWOyEhISfFg91ZYxhue+2MuE4dGcmx7ndDpKeXTHhWMZEObijx/ucjqVfs2XArIOyLBXR4XjPime065PDnCTnb4aWG7cw2fmANn2Kq00IANY6y2mnWeFjYGNuRRARE4HnsZdPMr8W13Vmc92V7Cr9Bg/mTFGn/mhAlbcoAh+MmMMH2w7pM9Pd1CnBcSej7gLWAZsBxYbY7aJyEMicrnt9jwQJyL5wL3AfDvvNmAxkAd8ANxpjGnxFtPGug+418aKs7HBfchqEPCmiGwSkfZFTHWD5z7fS2J0BJefNsLpVJTq0E9mpDFkYJg+dMpBoZ13AWPMe8B77dp+22a6HrjGy7yPAo/6EtO278V9lVb79tm+5Kr8t73kCJ/vruCXc8brMz9UwIuODOPOi9J55N3trMqv4Nz0eKdT6nf0t4T6p+c+L2BAmIsf6jM/VB9xw1mjGRETye8+2KEPnXKAFhAFQNmRenI2F3NtVjKxA8OdTkcpn0SGufj57HFsLqrRh045QAuIAuAGO3whAAATtUlEQVTlrwppbjX8+Lw0p1NRqku+P3UkYxOi+MOHu2jWh071Ki0giuONzfxl9X6+kzmM0XFRTqejVJeEukL49++MJ7/sGG9tLHY6nX5FC4hiyfoiauqa9MZB1WfNnTycU5NjeOzj3frQqV6kBaSfa2pp5emVe5k6KpYzRg9xOh2l/CIi/GrOBIqr63htzX6n0+k3tID0c29vLKa4uo6fzczQGwdVn3ZeRjznpsfxxIp8jjU0dz6DOmlaQPqxllbDk5/uYdKIwVw4Xod9UX3fL+dMoLK2kec+14dO9QYtIP3Yu1+XUFBRy10XpevehwoKU1JimTtpOM99XsBhfehUj9MC0k+1thqeWJ5PeuIg5kzS552r4PHvc8ZxvLGZJz/d43QqQU8LSD/18fZSdpYe5c6LxhKizztXQSQ9MZqrpibz6up9FFfXOZ1OUNMC0g8ZY3h8RT6jhg7ke6fqoIkq+Pz84nFg4LGPdbj3nqQFpB/6fHcFW4pq+LcLxxLq0k1ABZ+RsQO44azRLFlfxC596FSP0d8e/dDjy/MZPjiS70/19LRgpYLDXTPTGRQRysPv5OlAiz1EC0g/s2bvYdYWVvI/LhhDRKjL6XSU6jFDo8K5Z/Y4Pt9dwac79fHWPUELSD9ijOEPH+4kITqC7DN1yHYV/G48azRp8VE8/G4eTTrQYrfTAtKPrNxVzrrCKu6emc6AcN37UMEvPDSEBy6dyN7yWl5bvc/pdIKOFpB+4sTeR/KQAfxA9z5UPzJrYiLnpcez8OPdVB9vdDqdoKIFpJ/4YOshthYf4eezx+njalW/IiL8+rsTOVrfxJ8+3u10OkFFf5P0A00trfz+w52MTYjiytP1yivV/0wYPpjsaaN4dfU+8suOOZ1O0NAC0g8sWrufveW1zL9kIi6961z1U/dePI6BYS4efVcv6+0uWkCC3JH6JhZ+vJvpaUOZPTHR6XSUckz8oAjunpXBip3lfJhX6nQ6QcGnAiIic0Vkp4jki8h8D+9HiMgb9v01IpLa5r37bftOEZnTWUwRSbMxdtuY4bb9fBHZICLNInL1yax0f/LUp3uorG3k15dl6oi7qt+7+dxUxg+L5n/nbKNWnxly0jotICLiAp4ALgEygetEJLNdt1uBKmNMOrAQWGDnzQSygUnAXOBJEXF1EnMBsNAYkwFU2dgA+4Gbgdf9W9X+p6jqOM9/UcCVp4/klOQYp9NRynFhrhAevXIyB2vq+a9P9IT6yfJlD2QakG+M2WuMaQQWAfPa9ZkHvGynlwCzxP3n7jxgkTGmwRhTAOTbeB5j2nlm2hjYmFcAGGMKjTFbAL0byEcPv5NHiAi/nDPe6VSUChhZqUO5NiuZ578oYMehI06n06f5UkBGAgfavC6ybR77GGOagRogroN5vbXHAdU2hrdlKR+s3FXOsm2l/GxWOiNiBzidjlIBZf4lExk8IIz7lmyhWe9Q95svBcTTgfP2lzB469Nd7T4TkdtFJFdEcsvL++f4Nw3NLTyYs420+ChuPS/N6XSUCjhDo8J58PJJbC6q4YVVBU6n02f5UkCKgJQ2r5OBg976iEgoEANUdjCvt/YKINbG8LasDhljnjHGZBljshIS+udzvp/9bC8FFbU8ePkkHTBRKS++d2oSsycO448f7qKgotbpdPokXwrIOiDDXh0VjvukeE67PjnATXb6amC5cV9onQNk26u00oAMYK23mHaeFTYGNuZS/1ev/8kvO8Z/fZLPpacM54Jx/bOAKuULEeHRKycTHhrCr5ZspqVV7w3pqk4LiD0fcRewDNgOLDbGbBORh0TkctvteSBORPKBe4H5dt5twGIgD/gAuNMY0+Itpo11H3CvjRVnYyMiZ4pIEXAN8LSInOivrNZWw/y/bWFAuIsHL5/kdDpKBbxhgyP535dPYl1hFU9/ps9Q76rQzruAMeY94L12bb9tM12P+xe7p3kfBR71JaZt34v7Kq327etwH9JSXvxlzT5y91Xxh2tOIzE60ul0lOoTrjx9JJ9sL2PhR7s4PyOBySP1kndf6Z3oQaKwopb/fH8HMzLiuUqfNKiUz04cyhoaFc7P39hEXWOL0yn1GVpAgkBTSyv3vLGJ0BBhwVWn6h3nSnVR7MBw/njNFPaUH+O3S7c6nU6foQUkCPz3J7vZfKCa//v9U/WeD6X8dF5GPD+7KJ031xexOPdA5zMoLSB93Zq9h3l8RT5Xn5HMZacmOZ2OUn3aPbPHcc7YOH7z9la2l+hd6p3RAtKHlR2p566/biQ1LkqvulKqG7hChMeyTydmQBi3vZLL4WMNTqcU0LSA9FFNLa3c8doGjtU389SNZzAowqcL6pRSnUiIjuDZH2VRfrSBf/vLBhqbdagTb7SA9FGPvJNH7r4qFlx9KuOGRTudjlJB5bSUWH5/zWmsLazkgb9/rQ+g8kL/bO2Dnv+igJe/2sdtM9K4/LQRTqejVFC6/LQRdmSH3SQOjuCXcyY4nVLA0QLSx3ywtYRH3s1j7qTh3H/JRKfTUSqo/WJ2BuVHG3hixR6GRkXo4KTtaAHpQ77ac5h7Fm1iSkosf8qeQog+31ypHiUiPHLFZKpqG3n4nTwGhru4btoop9MKGHoOpI9YW1DJj19ax6ihA3nuR1lEhukou0r1BleI8KfsKVw0PoH73/qaV78qdDqlgKEFpA/ILazklhfXkhQbyWu3TSduUITTKSnVr0SGuXjqxjOYPTGR3yzdxnOf73U6pYCgBSTAfZxXyg3PryFxcCR/ve0sHSRRKYdEhLp48odncOkpw3nk3e08mLOt3w8Br+dAAtiitft54O2tTB4xmBduPlP3PJRyWHhoCP993VSGD97OC6sKKK6uY+EPpvTb+7B0DyQANTa38pu3tzL/ra85Lz2e1287S4uHUgHCFSL89nuZ/Mf3MvlkeymXP/4Fu0qPOp2WI7SABJji6jque3Y1r67ex+3nj+H5m7KI6qd/3SgVyG45N43XfnIWR+qamff4Khat3d/vbjjUAhIgjDG8mXuAuQs/Y3vJER6//nT+16UTCXXpf5FSgerssXG8d/d5nD4qlvlvfc3NL66jpKbO6bR6jf52CgAFFbXc8tI6frlkCxOTBvPBPefz3VP1DnOl+oLEwZH85dbpPDxvEmsLKpn9x5X8+dM9NDQH/4Op9NiIg6qPN/LnlXt44YsCIkJd/Oa7mdx8TiouvUFQqT4lJES48exULhiXyMPv5rHggx0sWrefey8ex3dPHRG032ktIA44fKyBl74s5MVVhRxraOaqqcncd8l4vURXqT5uVNxAnv1RFp/tKuf/vLedexZt4rFPdvPTC8Zy+Wkjgu4GYC0gvcQYw4b91by2Zh/vbC6hsaWVy05J4u5ZGYwfrqPpKhVMzh+XwHnp8SzbdojHPtnNr5Zs4f++t51rz0zh6qnJZATJCNpaQHpQa6vh6+IaPsorJWfzQfZXHicq3EX2tBR+dPZo0hODYyNSSv2rkBDhklOSmDt5OF/tOczLXxXy7Gd7eXrlXiaNGMwlk4cza+IwJgyPRqRvHuLyqYCIyFzgMcAFPGeM+c9270cArwBnAIeBHxhjCu179wO3Ai3A3caYZR3FFJE0YBEwFNgA3GiMaexoGYGisbmV/LJjrN9fxbqCSlblV3C4tpEQgXPT4/nZzHTmTh5OdGSY06kqpXqJiHBOejznpMdTdrSedzaXsHTzQf7w4S7+8OEuEqMjmDpqCGeMHsLU0bFMGhHTZw51dVpARMQFPAFcDBQB60QkxxiT16bbrUCVMSZdRLKBBcAPRCQTyAYmASOAj0VknJ3HW8wFwEJjzCIRecrG/rO3ZZzsB9BV9U0tlB1poPRoPYdq6imoqGVn6VF2HTpKQUUtzXZog8ToCM5Nj+eiCQlcMC6RoVHhvZ2qUirAJEZH8uPz0vjxeWmUHaln+Y4yVu89zPr9VXyw7RAA4a4QxiREkRYfRWp8FGlx7n+HDY4gblAEUeGugNlj8WUPZBqQb4zZCyAii4B5QNsCMg940E4vAR4X9xrOAxYZYxqAAhHJt/HwFFNEtgMzgettn5dt3D97W4bpgTt3Ptleyt83FlPb0ExtQwu1jc3UNjRTdbyJmrqmf+k/auhAxg2L5uLMYYwfHs2UlFhGDR0YMP/JSqnAkzg4kuxpo8i2w8OXHa1n4/5qNuyrYnfZMXYeOspHeaX//KP0hIjQEOKiwhkSFU5UeCgRYSFEhrkYEOYiPDSEEAFBuOL0kZw9Nq5H18GXAjISONDmdREw3VsfY0yziNQAcbZ9dbt5R9ppTzHjgGpjTLOH/t6WUeHDOnRJ+dEG8kqOEBUeSlSEi6SYSAaGhxIzIIzhMZEkRkcwbHAkiYMjSBkyUO8UV0qdtMToSOZMGs6cScP/2dbc0kpxdR0FFbVUHGvk8LEGKmsbqTjWSNXxRuoaWzha30z50Qbqm1pobG7FAK3GMH3M0B7P2ZfffJ7+jG7/V7+3Pt7aPd3A2FF/X/NARG4Hbrcvj4nITg/znRBPDxSgbhKouWleXReouQV8Xj90OJF2AvXzAg+5XfXAScUb7UsnXwpIEZDS5nUycNBLnyIRCQVigMpO5vXUXgHEikio3Qtp29/bMr7FGPMM8IwP64WI5Bpjsnzp29sCNTfNq+sCNTfNq2sCNS9wLjdfhjJZB2SISJqIhOM+KZ7Trk8OcJOdvhpYbs9N5ADZIhJhr67KANZ6i2nnWWFjYGMu7WQZSimlHNDpHog933AXsAz3JbcvGGO2ichDQK4xJgd4HnjVniSvxF0QsP0W4z7h3gzcaYxpAfAU0y7yPmCRiDwCbLSx8bYMpZRSzvDp7K8x5j3gvXZtv20zXQ9c42XeR4FHfYlp2/fyzZVabdu9LuMk+HSoyyGBmpvm1XWBmpvm1TWBmhc4lJvoUSCllFL+0OHclVJK+SXoCoiI/F5EdojIFhH5u4jEtnnvfhHJF5GdIjKnTftc25YvIvPbtKeJyBoR2S0ib9gT/tiLAt6w/deISKoPeV0jIttEpFVEstq0p4pInYhssj9PtXnvDBH52i7nv+zNmYjIUBH5yOb1kYgMse1i++Xb9Z/qb15Of14e8nxQRIrbfE6Xdnee3c3b8nuSiBTabWaTiOTati5vLyJyk+2/W0Ru8ra8TnJ5QUTKRGRrm7Zuy8Xb98PPvBzfvkQkRURWiMh2+528J1A+M6+MMUH1A3wHCLXTC4AFdjoT2AxEAGnAHtwn8F12egwQbvtk2nkWA9l2+ing3+z0HcBTdjobeMOHvCYC44FPgaw27anAVi/zrAXOxn0PzPvAJbb9d8B8Oz2/zTpeavsJcBaw5iTycvTz8pDng8C/e2jvtjy7eTv0uvwe3v4Lgfh2bV3aXnCPQ7fX/jvETg/xI5fzgaltt+/uzMXb98PPvBzfvoAkYKqdjgZ22eU7/pl5+wm6PRBjzIfmmzvZV+O+lwTaDKtijCkATgyr8s+hWowxjbgHcpxnK/NM3MOmgHtYlSvaxHrZTi8BZnVWyY0x240xHd3U+C0ikgQMNsZ8Zdz/8694WX77vF4xbqtx31OT5Gdejn5eXdCdeXYnj8vvgeX4oqvbyxzgI2NMpTGmCvgImNvVhRpjPuNf79Xqllw6+X74k5c3vbZ9GWNKjDEb7PRRYDvuETgc/8y8CboC0s6PcVdZ8Dwky8gO2n0eVgU4MayKv9JEZKOIrBSRGW2WUeQhL4BhxpgSu/wSILGTdfRHIH5ed9ld9RdO7MZ3c57dqTv/L7rCAB+KyHpxj8oAXd9eejL37sqlo++HvwJm+xL3Yd7TgTUE8GfWJwdxEpGPgeEe3nrAGLPU9nkA970nr52YzUP/bh1WxZe8PCgBRhljDovIGcDbIjKpk+V70515OTEMjdc8cQ+o+bCd72Hgj7j/QOjOPLtTby2nvXONMQdFJBH4SER2dNC3q0MQ9aSu5tLdOQbM9iUig4C/AT83xhzpYGfd6c+sbxYQY8zsjt63J42+C8yyu2rQC8OqdJaXl3VpABrs9HoR2QOMs8tIbtO17fJLRSTJGFNid0vLOlpHf/LyFstO99QwND7lKSLPAu/0QJ7dyZchgLqdMeag/bdMRP6O+1BLl7YX235hu/ZPuynF7sqlo+9HlxljSk9MO7l9iUgY7uLxmjHmLdsckJ8ZEJQn0efivvM9oV37JL59Mmwv7hNhoXY6jW9Ohk2y87zJt0+G3WGn7+TbJ4UXdyG/T/n2yeoEwGWnxwDFwFD7eh3uk2MnTnhdatt/z7dPqv3OTl/Gt0+qrT2JvALi82qTT1Kb6V/gPi7drXl283bodfk9uO1HAdFtpr+034cubS+4T74W4D4BO8ROD/Uzp1S+fbK623Lx9v3wMy/Hty+7Hq8Af2rXHhCfmcece3KDduIH90muA8Am+/NUm/cewH3lxE7aXH2A+2qGXfa9B9q0j8F91UK+3SgibHukfZ1v3x/jQ15X4v4LoAEoBZbZ9quAbXYD3AB8r808WcBWm9fjfHPjZxzwCbDb/nti4xDcD+raA3xNm4LQ1byc/rw85PmqXactuMdFS+ruPHtgW/S4/B7c9sfY7Wiz3aYe8Hd7wX34Jt/+3OJnPn/FfYi2yW5jt3ZnLt6+H37m5fj2BZyH+5DSFr75/XVpIHxm3n70TnSllFJ+CfarsJRSSvUQLSBKKaX8ogVEKaWUX7SAKKWU8osWEKWUUn7RAqKUUsovWkCUUkr5RQuIUkopv/x/dD7eUGZWt0kAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(residual)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Residual looks normally distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0xcdd1278>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "sns.scatterplot(X_train,residual)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is no pattern to residual."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Predictions on the test data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test_sm = sm.add_constant(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = model.predict(X_test_sm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Root mean squared error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5505.479002176114"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "RMSE = np.sqrt(mean_squared_error(y_test,y_pred))\n",
    "RMSE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RMSE won't suggest anything as we do not have any model to compare."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### R2 score:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9627668685473272"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r2_score(y_test,y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model explains 96.27% of variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "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": [
    "# Let us show the line fitting:\n",
    "plt.scatter(X_test,y_test)\n",
    "plt.plot(X_test, 25200 + X_test * 9731.2038,'r')\n",
    "plt.show()"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}