Linear Regression - TTest FTest & Assumptions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear Regression\n",
    "\n",
    "* Lets Understand the importance of F Test in Regression\n",
    "* T tests for Slope\n",
    "* Linear Regression Assumptions\n",
    "\n",
    "\n",
    "### Deploying a Regression\n",
    "\n",
    "* Import the Data\n",
    "* Univariate Analysis\n",
    "* Bivariate Analysis\n",
    "* Missing Values\n",
    "* Outlier Analysis and Removal of Outliers.\n",
    "* Transformation & Scaling (If required)\n",
    "* **Data Preprocessing Stage**\n",
    "\n",
    "It means that the data is ready for Modelling\n",
    "\n",
    "* Modelling\n",
    "* Linear Regression\n",
    "* Lasso & Ridge Regression\n",
    "* Decision Trees, Random Forests, KNN Regressor, Naive Bayes, Bagging, Boosting\n",
    "* Ensemble Techniques - Random Forests, Stacking..\n",
    "* Hyperparameter Tuning & Use Lot of CVs.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "from statsmodels.formula.api import ols\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.metrics import mean_squared_error, mean_absolute_error\n",
    "from warnings import filterwarnings\n",
    "filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "premium = pd.DataFrame({\"Mileage\":[15,14,17,7,10,7,20,21,18,11,7.9,8.6,12.3,17.1,19.4], \n",
    "                        \"Engine\":[1.8,1.2,1.2,1.8,1.6,1.4,1.2,1.6,1.2,1.6,1.4,1.6,1.2,1.6,1.2],\n",
    "                        \"Age\":[2,10,8,3,4,3,7,6,2,5,3,3,2,1,6],\n",
    "                        \"Premium\":[392.5,46.2,15.7,422.2,119.4,170.9,56.9,77.5,214,65.3,250,220,217.5,140.88,97.25]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>Premium</td>     <th>  R-squared:         </th> <td>   0.226</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.166</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   3.789</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 17 Jan 2021</td> <th>  Prob (F-statistic):</th>  <td>0.0735</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>08:24:45</td>     <th>  Log-Likelihood:    </th> <td> -90.831</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    15</td>      <th>  AIC:               </th> <td>   185.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    13</td>      <th>  BIC:               </th> <td>   187.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>  327.0860</td> <td>   87.035</td> <td>    3.758</td> <td> 0.002</td> <td>  139.057</td> <td>  515.115</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mileage</th>   <td>  -11.6905</td> <td>    6.006</td> <td>   -1.947</td> <td> 0.074</td> <td>  -24.665</td> <td>    1.284</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.225</td> <th>  Durbin-Watson:     </th> <td>   2.347</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.199</td> <th>  Jarque-Bera (JB):  </th> <td>   1.770</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.841</td> <th>  Prob(JB):          </th> <td>   0.413</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.057</td> <th>  Cond. No.          </th> <td>    44.3</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                Premium   R-squared:                       0.226\n",
       "Model:                            OLS   Adj. R-squared:                  0.166\n",
       "Method:                 Least Squares   F-statistic:                     3.789\n",
       "Date:                Sun, 17 Jan 2021   Prob (F-statistic):             0.0735\n",
       "Time:                        08:24:45   Log-Likelihood:                -90.831\n",
       "No. Observations:                  15   AIC:                             185.7\n",
       "Df Residuals:                      13   BIC:                             187.1\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept    327.0860     87.035      3.758      0.002     139.057     515.115\n",
       "Mileage      -11.6905      6.006     -1.947      0.074     -24.665       1.284\n",
       "==============================================================================\n",
       "Omnibus:                        3.225   Durbin-Watson:                   2.347\n",
       "Prob(Omnibus):                  0.199   Jarque-Bera (JB):                1.770\n",
       "Skew:                           0.841   Prob(JB):                        0.413\n",
       "Kurtosis:                       3.057   Cond. No.                         44.3\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Build the model using Mileage and Premium\n",
    "model = ols(\"Premium~Mileage\", data = premium).fit()\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hypothesis Testing: Anova for Regression\n",
    "\n",
    "* H0: F test assumes that the model coefficients are 0.\n",
    "* H1: F test assumes that the model coefficients aren't 0.\n",
    "\n",
    "* F test is a test of significance in regression. If the pvalue > 0.05 then we fail to reject the Ho.\n",
    "* It means that the feature used to build the model is not significant.\n",
    "* It means that it is not a significant contributor to the model.\n",
    "\n",
    "#### Difference between F test & T Test in Regression\n",
    "\n",
    "* F test shows the overall significance (considering all the variables) where as T Test shows whether each and every feature is individually important or statistically significant.\n",
    "\n",
    "### Calculate F Statistic\n",
    "\n",
    "F Stats = MSR/MSE\n",
    "\n",
    "* Mean Square Regression = Sum of Square Regression/Predictor Count)\n",
    "* Mean Square Error = SSE/(n-p-1)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Sum of Sq Regression = yhat-ybar\n",
    "# SSE\n",
    "\n",
    "yhat = -11.6905*premium[\"Mileage\"]+327.0860 # Y hat\n",
    "\n",
    "SSE = np.sum((premium[\"Premium\"] - yhat)**2) # SSE = yi-yhat\n",
    "\n",
    "SSR = np.sum((yhat-premium[\"Premium\"].mean())**2) # SSR = yhat - ybar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "FTest Statistic:  3.789239534705334\n",
      "PValue(F):  0.0735202665782958\n"
     ]
    }
   ],
   "source": [
    "# Mean Square Regression\n",
    "MSR = SSR/1 # here 1 is the no of predictors::Mileage\n",
    "\n",
    "# Mean Square Error\n",
    "n = premium.shape[0]\n",
    "\n",
    "MSE = SSE/(n-1-1) #n-p-1\n",
    "\n",
    "Fstats = MSR/MSE\n",
    "\n",
    "print(\"FTest Statistic: \", Fstats)\n",
    "\n",
    "# Pvalue\n",
    "\n",
    "print(\"PValue(F): \",1 - stats.f.cdf(Fstats, 1, n-1-1)) # Dfn, DFd\n",
    "\n",
    "# Inference: F Test suggests that Mileage is not a Significant Variable."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hypothesis Testing: Slope\n",
    "\n",
    "* HO: Beta1 = 0. It means that the Predictor is not contributing significantly.\n",
    "* H1: Beta 1 !=0. The Feature is significant for the Model.\n",
    "\n",
    "Note: T tests are always a two tail test thus, when we calculate the PValue,\n",
    "we have to Multiply by 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "T Test Statistic -1.9464701964701965\n",
      "Pr(t-stats) 0.07353681873117468\n"
     ]
    }
   ],
   "source": [
    "# Calculate the T Test Statistic Value\n",
    "# tstats = Model Coefficient/Std Error\n",
    "\n",
    "# Pvalue as per the table - 0.074\n",
    "\n",
    "tstats = -11.6905/6.006 #(Coeff/Std Error)\n",
    "print(\"T Test Statistic\", tstats)\n",
    "\n",
    "df = premium.shape[0] - 2 # n-2\n",
    "\n",
    "print(\"Pr(t-stats)\", (1-stats.t.cdf(np.abs(tstats), df))*2)\n",
    "\n",
    "# Inference: If the PValue is less than 0.05, we reject Ho meaning that\n",
    "# Variable is significant.\n",
    "\n",
    "# As a groundrule, we always check the PValue of all the Predictors\n",
    "# to decide if the variables are contributing towards the model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Confidence Interval for Slope"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TCritical:  2.160368656461013\n",
      "Confidence Interval 0.025 -24.6657\n",
      "Confidence Interval 0.975 1.2847\n"
     ]
    }
   ],
   "source": [
    "alpha_by_two = 0.05/2\n",
    "\n",
    "df = premium.shape[0]-2\n",
    "\n",
    "# xbar +/-tcrit*SE\n",
    "\n",
    "# xbar - Model Coefficient\n",
    "\n",
    "beta1 = -11.6905\n",
    "se = 6.006\n",
    "\n",
    "tcrit = np.abs(stats.t.ppf(alpha_by_two, df))\n",
    "print(\"TCritical: \", tcrit)\n",
    "\n",
    "print(\"Confidence Interval 0.025\", np.round(beta1-tcrit*se,4))\n",
    "print(\"Confidence Interval 0.975\", np.round(beta1+tcrit*se,4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression Assumptions\n",
    "\n",
    "Fit the Model and Check the Assumptions\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>Premium</td>     <th>  R-squared:         </th> <td>   0.591</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.480</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   5.309</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 16 Jan 2021</td> <th>  Prob (F-statistic):</th>  <td>0.0166</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>09:53:04</td>     <th>  Log-Likelihood:    </th> <td> -86.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    15</td>      <th>  AIC:               </th> <td>   180.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    11</td>      <th>  BIC:               </th> <td>   182.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>  138.3977</td> <td>  218.865</td> <td>    0.632</td> <td> 0.540</td> <td> -343.321</td> <td>  620.116</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mileage</th>   <td>   -4.8756</td> <td>    5.252</td> <td>   -0.928</td> <td> 0.373</td> <td>  -16.436</td> <td>    6.684</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Engine</th>    <td>  137.6328</td> <td>  118.936</td> <td>    1.157</td> <td> 0.272</td> <td> -124.143</td> <td>  399.409</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age</th>       <td>  -23.7176</td> <td>   10.444</td> <td>   -2.271</td> <td> 0.044</td> <td>  -46.704</td> <td>   -0.731</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.101</td> <th>  Durbin-Watson:     </th> <td>   2.374</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.951</td> <th>  Jarque-Bera (JB):  </th> <td>   0.285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.143</td> <th>  Prob(JB):          </th> <td>   0.867</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.388</td> <th>  Cond. No.          </th> <td>    167.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                Premium   R-squared:                       0.591\n",
       "Model:                            OLS   Adj. R-squared:                  0.480\n",
       "Method:                 Least Squares   F-statistic:                     5.309\n",
       "Date:                Sat, 16 Jan 2021   Prob (F-statistic):             0.0166\n",
       "Time:                        09:53:04   Log-Likelihood:                -86.035\n",
       "No. Observations:                  15   AIC:                             180.1\n",
       "Df Residuals:                      11   BIC:                             182.9\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept    138.3977    218.865      0.632      0.540    -343.321     620.116\n",
       "Mileage       -4.8756      5.252     -0.928      0.373     -16.436       6.684\n",
       "Engine       137.6328    118.936      1.157      0.272    -124.143     399.409\n",
       "Age          -23.7176     10.444     -2.271      0.044     -46.704      -0.731\n",
       "==============================================================================\n",
       "Omnibus:                        0.101   Durbin-Watson:                   2.374\n",
       "Prob(Omnibus):                  0.951   Jarque-Bera (JB):                0.285\n",
       "Skew:                           0.143   Prob(JB):                        0.867\n",
       "Kurtosis:                       2.388   Cond. No.                         167.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols(\"Premium~Mileage+Engine+Age\", data = premium).fit()\n",
    "\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression Assumptions\n",
    "\n",
    "* Linearity - The Data should be **linear** in nature. It means that the predictors should have a linear relationship with the Target variable.\n",
    "\n",
    "* Normality - The Data should be **normal**. It means after fitting the model, the residuals/errors should be normally distributed.\n",
    "\n",
    "* Multicollinearity - The **predictor variables should not have a strong correlation** amongst themselves. Having a strong correlation with target variable is awesome but amongst predictors is a sign of multicollinearity.\n",
    "\n",
    "* Heteroskedasticity - It simply means **unequal variances**. The residuals should not have unequal variances.\n",
    "\n",
    "* Autocorrelation - The **errors should not be autocorrelated**. If there is autocorrelation, we would run into assumption that the feature is significant where in reality, it won't be."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.677948550044173, 0.11587562145871054)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Linear Assumption:: Rainbow Test\n",
    "\n",
    "# Ho: Data is Linear or the Model shows signs of Linearity.\n",
    "# H1: Models is not linear. Since it is not linear so regression cannot be applied.\n",
    "\n",
    "import statsmodels.api as sma\n",
    "\n",
    "sma.stats.diagnostic.linear_rainbow(model) # test stats, pvalue.\n",
    "\n",
    "# Rule: PValue< 0.05: Reject the Ho. \n",
    "# Inf: Data is Linear."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Residual Plot\n",
    "\n",
    "* A Residual Plot shows the **Residuals on Y axis** and **Fitted Values(Predicted Values) on the X-Axis.**\n",
    "* If the points in Residual Plot are randomly scattered showing no pattern then LR is a well built model.\n",
    "* If the Residual Plot shows some pattern then LR is not a good fit. We must deploy another model.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Residual and Fitted Values\n",
    "residual = model.resid #(Error: Act-Pred)\n",
    "fitted = model.fittedvalues # predicted values\n",
    "\n",
    "# Plotting the Residuals.\n",
    "sns.set_style(\"whitegrid\") # theme of the plot\n",
    "\n",
    "sns.residplot(fitted, residual, color = \"m\") # plt.scatter(fitted, residual, color = \"m\")\n",
    "plt.xlabel(\"Fitted Values\")\n",
    "plt.ylabel(\"Residuals\")\n",
    "plt.title(\"Residual Plot\")\n",
    "plt.show()\n",
    "\n",
    "# Inference: The plot is showing randomness with no pattern and hence, LR is a good fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 02nd Assumption: Normality | Tests: Shapiro Wilk test of Normality & Jarque Bera Test\n",
    "\n",
    "* Probplot\n",
    "\n",
    "* Shapiro Wilk Test of Normality - Applicable till 5000 Rows of Data.\n",
    "* Jarque Bera Test of Normality (>5000 Rows) - Large Datasets\n",
    "\n",
    "* **These tests are telling us if the sample pulled out randomly are normally distributed or not.**\n",
    "\n",
    "* Ho: Data is normal\n",
    "* H1: Ho is False: Data or Residuals are not normally distributed.\n",
    "\n",
    "* Inference: If the PValue<0.05, We reject the Ho meaning that the Data is not Normal.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "ShapiroResult(statistic=0.9564691185951233, pvalue=0.6313204169273376)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Shapiro Wilk Test of Normality: TGT & Residual.\n",
    "\n",
    "stats.shapiro(model.resid) # Residuals are Normally Distributed.\n",
    "#stats.shapiro(premium[\"Premium\"]) # Tgt Variable is normally Distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Probplot\n",
    "from scipy.stats import probplot\n",
    "\n",
    "probplot(model.resid, plot = plt)\n",
    "plt.show() \n",
    "\n",
    "# Inferece: Since most of the points are closer to the red line hence, the data is normally distributed.\n",
    "# If the points deviated from the red line, we can conclude that the data is not normally distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test Stats:  0.2852794190012313\n",
      "PValue - Jarque Bera:  0.8670664084149167\n"
     ]
    }
   ],
   "source": [
    "# Jarque Bera Test\n",
    "\n",
    "# JB test of normality\n",
    "# Samples pulled out are normally distributed.\n",
    "# Meant for Samples greater than 5K rows of the data.\n",
    "# This Test uses Skewness and Kurtosis to find that the data is normal.\n",
    "# For a Normally Distributed Data, skewness is 0 and Kurtosis is 3.\n",
    "# Any Deviation from these values is considered to be not normal.\n",
    "\n",
    "# Ho: Data is Normal & H1: Data is not Normal.\n",
    "\n",
    "# Applying Jarqe Bera Test on Residuals\n",
    "print(\"Test Stats: \", stats.jarque_bera(model.resid)[0])\n",
    "print(\"PValue - Jarque Bera: \", stats.jarque_bera(model.resid)[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 03: Assumption of Multicollinearity | Condition No, Correlationplot, Variance Inflation Factor (VIF)\n",
    "\n",
    "* Correlationplot - Create a Heatmap that has correl values for all the variables. We can easily see if there is a strong correlation between the predictors. \n",
    "\n",
    "* Condition No: **<100: No Multicollinearity, 100-1000: Moderate Multicollinearity, >1000: High**\n",
    "* Condition no will tell you if there is Multicollinearity or not but if we really wanna know what all variables are multicollinear, I need to apply VIF.\n",
    "\n",
    "#### Why there is a Multicollinearity (Causes)\n",
    "\n",
    "* It exists because maybe the data was not captured correctly.\n",
    "* For e.g. Income vs Expenses, No of Gadgets vs Income. These things cannot be removed from data.\n",
    "* It is also seen because of the **variable extracted/created as a part of Feature Engineering.**\n",
    "* For e.g. BMI on the basis on weight and height. This variable might be important for the model, however, this leads to introduction of Multicollinearity in the data.\n",
    "* Temp in Celsius & Temp in Farenheit.. (0.90 Correlation)\n",
    "* **Dummy Variable Trap - Gender (Male/Female):: Gender_Male(0,1) & Gender_Female(0,1). You can have only 1F.**\n",
    "* Insufficient Data...\n",
    "\n",
    "\n",
    "#### Is this a Problem\n",
    "\n",
    "* It is a big problem because if the variables are highly correlated, we would never come to know the contribution of the variables individually. \n",
    "\n",
    "* It is because Multicollinearity does not really impact the overall efficiency of the model but it does impact the calculation of SE, T-Test Stat and in turn, PValue. In a nutshell, the model will lose reliability in determining the effects of the predictors on the target.\n",
    "\n",
    "* What is to be done - Drop one Variable out of the Two.\n",
    "\n",
    "\n",
    "### Role of VIF\n",
    "\n",
    "* VIF determines the strength of the correlation between the predictors(ind var). It will take one variable as target vs other predictors (mileage: tgt and age and engine: predictors)\n",
    "* It is calculated using a variable as target and regressing it against predictors.\n",
    "* Note: The Original Target Variable is not used in VIF Calculation.\n",
    "* VIF score tells us how that vairable is explained by other predictors.\n",
    "\n",
    "* **Thumb Rule: VIF = 1, No Collinearity, 1-5: Moderate, > 5: Highly Collinear**\n",
    "\n",
    "Tip: Try Feature Selection. Sequential Feature Selector - mlxtend \"r2\" | CV -10, 15\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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>Features</th>\n",
       "      <th>VIF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Engine</td>\n",
       "      <td>3.080527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Age</td>\n",
       "      <td>3.080527</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Features       VIF\n",
       "0   Engine  3.080527\n",
       "1      Age  3.080527"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the VIF (1/(1-R2))\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor\n",
    "\n",
    "# VIF is applied on Predictors\n",
    "x = premium.drop([\"Mileage\",\"Premium\"], axis = 1) #Now, I will remove Mileage too...\n",
    "\n",
    "mylist =[]\n",
    "\n",
    "for i in range(x.shape[1]):\n",
    "    mylist.append(variance_inflation_factor(x.values, i)) # values of the data, instance\n",
    "    \n",
    "\n",
    "pd.DataFrame({\"Features\":x.columns, \"VIF\": mylist})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1759e20f8e0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Correlation plot\n",
    "sns.heatmap(x.corr(), annot = True, cmap = \"YlGnBu\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>Premium</td>     <th>  R-squared:         </th> <td>   0.559</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.486</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   7.621</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 17 Jan 2021</td> <th>  Prob (F-statistic):</th>  <td>0.00731</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>08:24:54</td>     <th>  Log-Likelihood:    </th> <td> -86.600</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    15</td>      <th>  AIC:               </th> <td>   179.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    12</td>      <th>  BIC:               </th> <td>   181.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>   39.1681</td> <td>  189.882</td> <td>    0.206</td> <td> 0.840</td> <td> -374.548</td> <td>  452.884</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age</th>       <td>  -25.8293</td> <td>   10.134</td> <td>   -2.549</td> <td> 0.026</td> <td>  -47.909</td> <td>   -3.749</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Engine</th>    <td>  166.5562</td> <td>  114.119</td> <td>    1.459</td> <td> 0.170</td> <td>  -82.087</td> <td>  415.200</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.077</td> <th>  Durbin-Watson:     </th> <td>   2.446</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.962</td> <th>  Jarque-Bera (JB):  </th> <td>   0.139</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.109</td> <th>  Prob(JB):          </th> <td>   0.933</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.582</td> <th>  Cond. No.          </th> <td>    51.2</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                Premium   R-squared:                       0.559\n",
       "Model:                            OLS   Adj. R-squared:                  0.486\n",
       "Method:                 Least Squares   F-statistic:                     7.621\n",
       "Date:                Sun, 17 Jan 2021   Prob (F-statistic):            0.00731\n",
       "Time:                        08:24:54   Log-Likelihood:                -86.600\n",
       "No. Observations:                  15   AIC:                             179.2\n",
       "Df Residuals:                      12   BIC:                             181.3\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     39.1681    189.882      0.206      0.840    -374.548     452.884\n",
       "Age          -25.8293     10.134     -2.549      0.026     -47.909      -3.749\n",
       "Engine       166.5562    114.119      1.459      0.170     -82.087     415.200\n",
       "==============================================================================\n",
       "Omnibus:                        0.077   Durbin-Watson:                   2.446\n",
       "Prob(Omnibus):                  0.962   Jarque-Bera (JB):                0.139\n",
       "Skew:                           0.109   Prob(JB):                        0.933\n",
       "Kurtosis:                       2.582   Cond. No.                         51.2\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "newmodel = ols(\"Premium~Age+Engine\", data = premium).fit() # Age Adj R2 Score - 0.441\n",
    "newmodel.summary()\n",
    "\n",
    "# With Engine & Age, Adj R2 Score has increased.\n",
    "# Regression Model is significant"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 04: Assumption - Autocorrelation of Errors\n",
    "\n",
    "* Error should not be correlated. It means that the Errors in the first instance are related with the 02nd Instance and so forth...\n",
    "\n",
    "* It might run into a Type 1 error where the analyst feels that the Features are significant wherein they are not.\n",
    "\n",
    "* The test of Autocorrelation is **Durbin Watson Test**\n",
    "\n",
    "* The test statistic can throw a value between 0 and 4.\n",
    "* **Parameters: DW Test Stat = 2, No Correlation, 0-2: +ve ACorrelation, >2 to 4: -ve ACorrel.**\n",
    "* Thumb Rule - Test Stats is **between 1.5 to 2.5** then we consider it to be normal. Values beyond this range is a sign of Autocorrelation\n",
    "\n",
    "* Ho: No Autocorrelation in errors/residuals\n",
    "* H1: Autocorrelation in errors/residuals exist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>Premium</td>     <th>  R-squared:         </th> <td>   0.591</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.480</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   5.309</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 16 Jan 2021</td> <th>  Prob (F-statistic):</th>  <td>0.0166</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>10:23:27</td>     <th>  Log-Likelihood:    </th> <td> -86.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    15</td>      <th>  AIC:               </th> <td>   180.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    11</td>      <th>  BIC:               </th> <td>   182.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     3</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>  138.3977</td> <td>  218.865</td> <td>    0.632</td> <td> 0.540</td> <td> -343.321</td> <td>  620.116</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Mileage</th>   <td>   -4.8756</td> <td>    5.252</td> <td>   -0.928</td> <td> 0.373</td> <td>  -16.436</td> <td>    6.684</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Engine</th>    <td>  137.6328</td> <td>  118.936</td> <td>    1.157</td> <td> 0.272</td> <td> -124.143</td> <td>  399.409</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Age</th>       <td>  -23.7176</td> <td>   10.444</td> <td>   -2.271</td> <td> 0.044</td> <td>  -46.704</td> <td>   -0.731</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.101</td> <th>  Durbin-Watson:     </th> <td>   2.374</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.951</td> <th>  Jarque-Bera (JB):  </th> <td>   0.285</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.143</td> <th>  Prob(JB):          </th> <td>   0.867</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.388</td> <th>  Cond. No.          </th> <td>    167.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                Premium   R-squared:                       0.591\n",
       "Model:                            OLS   Adj. R-squared:                  0.480\n",
       "Method:                 Least Squares   F-statistic:                     5.309\n",
       "Date:                Sat, 16 Jan 2021   Prob (F-statistic):             0.0166\n",
       "Time:                        10:23:27   Log-Likelihood:                -86.035\n",
       "No. Observations:                  15   AIC:                             180.1\n",
       "Df Residuals:                      11   BIC:                             182.9\n",
       "Df Model:                           3                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept    138.3977    218.865      0.632      0.540    -343.321     620.116\n",
       "Mileage       -4.8756      5.252     -0.928      0.373     -16.436       6.684\n",
       "Engine       137.6328    118.936      1.157      0.272    -124.143     399.409\n",
       "Age          -23.7176     10.444     -2.271      0.044     -46.704      -0.731\n",
       "==============================================================================\n",
       "Omnibus:                        0.101   Durbin-Watson:                   2.374\n",
       "Prob(Omnibus):                  0.951   Jarque-Bera (JB):                0.285\n",
       "Skew:                           0.143   Prob(JB):                        0.867\n",
       "Kurtosis:                       2.388   Cond. No.                         167.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3735258408206343"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from statsmodels.stats.stattools import durbin_watson\n",
    "\n",
    "durbin_watson(model.resid)\n",
    "\n",
    "# Inf: Since it is between 1.5 - 2.5, we fail to reject the Ho."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 05 Assumption : Heteroskedasticity\n",
    "\n",
    "* It means that the residuals do not have uniform variance. The variance changes at different points.\n",
    "\n",
    "#### Why it occurs\n",
    "\n",
    "* It occurs because of the increasing or decreasing patterns in the data. For e.g. Income vs Expenses.\n",
    "* If observations have mixed scale - ratio scale, weight in kgs, area in square foot, doors in a house. \n",
    "* Maybe we have outliers in the data and hence it can contribute to heteroskedastic\n",
    "* Incorrect Transformation is done on the data\n",
    "* Skewness is another factor that contributes to Heterskedasticty..\n",
    "\n",
    "###### Shape: Inward or Outward Funnel showing in residual plot\n",
    "\n",
    "**Statistics Test**\n",
    "\n",
    "* Breusch Pagan Test\n",
    "* GoldFeldQuandt Test\n",
    "\n",
    "* Ho: Data is Homoskedastic (Uniform Variance) & is not Heteroskedastic(Uneven Variance)\n",
    "* H1: Data isn't Homoskedastic (Uniform Variance) & is Heteroskedastic(Uneven Variance)\n",
    "\n",
    "About Breusch-Pagan Test: It will test whether the variance of errors from regression (residuals) are independent of any predictor. Because if it does not, then it will lead to Heteroskedasticity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.006453649980378762\n"
     ]
    }
   ],
   "source": [
    " # Heteroskedasticity\n",
    "    \n",
    "import statsmodels.stats.api as ssa\n",
    "\n",
    "predictors = premium.drop(\"Premium\", axis =1 )\n",
    "\n",
    "# residuals, predictors:: endog, exhog\n",
    "# Generate 04 statistic - Test Stat of BP, PValue(BP), Ftest & Pvalue(Ftest)\n",
    "teststats, pvalue, ftest, f_pvalue = ssa.het_breuschpagan(model.resid, \n",
    "                                                          predictors) \n",
    "print(pvalue)\n",
    "\n",
    "teststats, pvalue, ftest, f_pvalue = ssa.het_breuschpagan(newmodel.resid, \n",
    "                                                          x) \n",
    "print(pvalue)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "\n",
    "* Data is Linear & Normal too.\n",
    "* Data was suffering from Multicollinearity. We removed the variable and saw that R2 value improved.\n",
    "* There was no Autocorrelation in Residuals.\n",
    "* However, the Heteroskedasticity is present. \n",
    "* Recommendation: One must scale or try transformation on the data and rerun the test.\n",
    "* We can also check Heteroskedasticity on the newmodel which did not have mileage. Maybe the results are different."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Linear Regression vs Random Forest\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.ensemble import RandomForestRegressor\n",
    "\n",
    "rf = RandomForestRegressor()\n",
    "lr = LinearRegression()\n",
    "\n",
    "predictors = premium.drop(\"Premium\", axis =1 )\n",
    "tgt = premium.Premium\n",
    "\n",
    "pred_lr = lr.fit(predictors, tgt).predict(predictors)\n",
    "pred_rf = rf.fit(predictors, tgt).predict(predictors)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(premium.Premium, label = \"Actual\")\n",
    "plt.plot(pred_lr, label = \"LR\")\n",
    "#plt.plot(pred_rf, label = \"Rf\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CEx83dSn7Y5re6PcleGuMFsYHdaUpRl7G1LsWS/XNR1EIsqnLyAQqvm3qkVK1xkmhTX7d1s7ucFJnsjBG3SgduNxMHSBxMoq6Yxgi1ZyWTV1GJiDxbVPvKsE7Tt3o17tK681WnCIkCd3NMXox9a7F0tlh9ZTJpi4jE5D4tqmHREFQOGmKWupMViw2h6cVuYXuHPVRzhqp2XToqMuf2LVYOkNTRmlDW8DUmZeRkTmHb5s6QFQ68Q4prdFfC3t156hHdFZDRDIoevmxdS2WjnOW0N7poM5kHUGVMjIy3oDvm3qkgfAOqZCVv9ZVr2qR3qxC2ip7j6dDz2JpQruUAXO6Xg7ByMgEGr5v6lHpaNvOosLut2mNNUYLwWolytby3uPp3SROJtR4AjV2OQNGRiYA8QNTNyA47aSqmvw2rbG61UJGmBOho7nvmTpAwmQERyfZqrOUNcqmLiMTaPi+qXelNU7Tt/htBkyN0UKOrll6MICZOsA1+go5/CIjE4D4vql3bUDKDmr025h6jdFCpqZJehCR0vfJXYulU9Vn5GqNMjIBiO+bun4UqIIZo6qnosn/wi8Op0htq4U0ZYN0ICKt7wu6FkvHOkoob2rH7nC6XaOMjIz34PumLggQZWC0WI2xw0arxeZpRS6l0WzF7hRJFOtAEyrl5vdH4mTiOkrAYeNsi/+90cnIyPSO75s6SCV4O7tL8PpXCKaqK0c92t5VyEsQ+r8oYTJKp41MoULOgJGRCTD8w9SjDOjayhFw+l0Ipqar+Ye+42z/i6TddC2W5ipOy6YuIxNg+I2pKxxW4mih0s8WS6USASJacz8bj84n0oAYFM5U1RnZ1GVkAox+m2Q4HA5WrVpFaWkpSqWSZ555BlEUefTRRxEEgbFjx/LUU0+hUCjYsGED69evR6VS8cADD3DttdeOxPfQkwEzIajB78IvNUYLo1RmBFv7wGfqgoCQMJnJFWVskk1dRiag6NfUt26VOgutX7+e3bt395j68uXLueKKK3jyySfZvHkzkydPZu3atWzcuBGr1Up+fj6zZ89GoxmB7jtdueq5IU0c9rMNSNVGC5NDjWBh4DN1gMTJGMp2UF7X4jZtMjIy3ke/4Zd58+axevVqAKqqqoiJieHo0aPMnDkTgLlz57Jjxw4KCwuZMmUKGo0GvV5PSkoKxcXF7lXfTXgyKFSM19T75Uw9K6grR32gM3WAhMmoRBt600m/rV4pIyNzKf3O1AFUKhUrV67k888/54UXXmDr1q0IXVkYOp0Ok8mE2WxGr9f3XKPT6TCb+978YrVaKSoqGpJwi8VywbUZIaMYZauk3NjGsWPHevR5CxfrHShnGlrJC5Yye4prLYhNA7uHukPPGGCicJpte4+QGjnwT0xD1eopfEmvL2kF39LrS1rBfXoHZOoAa9as4Ze//CV5eXlYredKura1tREWFkZoaChtbW0XHD/f5C+HVqslKytrCLKhqKjowmv3jyel9ixWu0hscgaxeu2Q7usuLtE7AJxOkaaOUsZEtYIjmvG50wZ+sTge++dhTLSXQlg8WVm91GB3kVZP4kt6fUkr+JZeX9IKw9Pb15tBv+GX9957jz//+c8ABAcHIwgCOTk57N69G4Dt27czffp0cnNz2b9/P1arFZPJRElJCZmZmUMSPCQiDYRZKgHRb1rbNbZ1YnOIxDlqBhdPh56dpTmKUjkDRkYmgOh3pj5//nwee+wxli1bht1u5/HHHycjI4MnnniC5557jvT0dBYsWIBSqaSgoID8/HxEUWTFihVotSM4W45KR20zEYmJyuZ2pqVGjtzYbqK7OUa4tRpGTR309aqkKYw/s4P18mKpjEzA0K+ph4SE8Pzzz19yfN26dZccy8vLIy8vzzXKBktXv9JUoc5vFkurjR0ocBLcXgURiwZ/g4TJaLDjqD0KDCJ0IyMj47P4x+Yj6MlVzwlu9JtdpTWtFuJpRuG0DS7zpZuunaVhzUdcrExGRsZb8R9Tj0gFBLKD/acEb1WLBYOqXnow2Jg6QKQBq0qPofOk3xU6k5GRuTz+Y+rqIAgbTYayzm9MvcbYQXZId3OMtMHfQBAwReWQoyilTF4slZEJCPzH1KGrBG8NVS0Wv6gjXm20kKluAgQITxrSPRSJkxknVFBW1+xacTIyMl6J35l6tLUSh1PsKoTl29S0WkhRNkBYIqiGlkkUapiOVrBjKj/sYnUyMjLeiH+ZeqSBoM4mdHT4fAhGFKU3pgSxdmjx9C40yVIqpLLmoKukycjIeDH+ZepdGTCpQi2VPp4B09xuo9PuJLqzemiZL91EGmgTQoloOeo6cTIyMl6Ln5m6lKuepvD9xdJqYwcabIRY6/pvNt0XgkCNbjzJHScQRdF1AmVkZLwS/zL1rhK8Uq66j5t6i4VEoQEBcVjhF4D2mBzGUE5ja98F1mRkZHwf/zL1oDAIiWGcpoEKH6+rXt1qIVnoylEfTvgFEEZPQSvYqT11wAXKZGRkvBn/MnWAqHRShRqfn6nXGDtIVQxj49F5RGbMAKCjbN9wZcnIyHg5fmjqBuLs1dSZrD7dHKLaaGGctgkUaimlcRjEp4zHKOpQ1h5ykToZGRlvxQ9NPR29tRYNNip9OARTY7SQrmqUNh0plMO6l0ql5JQqgyjjMRepk5GR8Vb8z9QjDQiIJAu+nQFTY7Qwmrphx9O7qQvNIsF6GuydLrmfjIyMd+J/pn5BrrpvmrooilQZO4gdSnOMXuiIyUGDHWetnK8uI+PP+KGpS2mNUmEv3wy/GDtsKGzt6OwtLpupK5OkeurGkj0uuZ+MjIx30meTDJvNxuOPP87Zs2fp7OzkgQceYNSoUfzkJz8hLS0NgKVLl3LTTTexYcMG1q9fj0ql4oEHHuDaa68dCf2XEhIN2jAmOBv5tNE3Z+rVRgtJgmsyX7qJSx5Hi6jDUv6tS+4nIyPjnfRp6ps2bSIiIoJnn32W5uZmFi1axIMPPsi9997Lfffd13NefX09a9euZePGjVitVvLz85k9ezYazcA72LsMQYDINNJbfDemXmO0kCzUSQ+GUnL3MqTHhXLEmcb4ukKX3E9GRsY76TP8cuONN/Lwww/3PFYqlRw5coRt27axbNkyHn/8ccxmM4WFhUyZMgWNRoNeryclJYXi4mK3i++VrhK8vpqrXm08b+ORq2bqei3FigwiTCflxVKZfnE4RR57t5DPTprk8hI+Rp8zdZ1OB4DZbOZnP/sZy5cvp7OzkyVLlpCTk8Mrr7zCSy+9xPjx49Hr9RdcZzb3vyXdarVSVFQ0JOEWi6XXa2PFcCI7qzFbOtl76AihmuGlBLqCvvRezOGSJsYK9TiVQRwvrwehwSUazmrHoOq0Ubr7QyxR412i1RvwJb2+ovVEg5V/7jkLwFdntvLwrFhidP22NPYovvLaduMuvf3+lKqrq3nwwQfJz89n4cKFtLa2EhYWBsANN9zA6tWrmT59Om1t5zrrtLW1XWDyvaHVasnKyhqS8KKiot6vbZ8ORf8gUWgkOGYuWaPDhzSGK+lT70XYjhwiQ92IIspA1oQJLtPg2D0NysCgbYE+tAxGqzfgS3p9Res3X50GzvL9SZFsPNbKT/9dxVMLs7l96mgEQfC0vMviK69tN8PR29ebQZ/hl4aGBu677z4eeeQR7rjjDgDuv/9+CguluOzOnTvJzs4mNzeX/fv3Y7VaMZlMlJSUkJmZOSSxLqEnrbGGSh+Mq9cYLaQo6l2W+dJNeMIYWkQdjrNyDRiZvtld2kRadAjLJkfy8cNzGD9Kzy/fPsQP/76P2lbfb0Djz/Q5U//Tn/5Ea2srL7/8Mi+//DIAjz76KL/97W9Rq9XExMSwevVqQkNDKSgoID8/H1EUWbFiBVrt0Dr1uISutMZUoY4KH6yrXt3SziixFiLmu/S+hlhpsXR65QE8H5CS8VacTpF9ZU3cMCEegLQYHW/9eBZ/3VHGs58WM/+P2/nVrdncNjnRa2ftgUyfpr5q1SpWrVp1yfH169dfciwvL4+8vDzXKRsO+kRQahlLHaU+NlMXRZH21gaCFe0un6kbYnTsFtP5TuMn0mKpygPZSTJez6l6M83tNmYaogETAAqFwP1XGbh2XCyPvFPI8rcO8uHhan6zKIc4fZBnBctcgP9tPgJQKCAyjUx1g89lwJisdmJsNdIDF2W+dGOI0XHYaUDhtEGdXAdG5vLsLm0CRK4z/5vIk+9A6XYw1YIokh4byob/mMV/3pTFlyfqmf/H7Ww6VCVnyHgR3r2cPRyi0kltLfa5XaUX5qi71tQjQjSc0WaCCFQdgMTJLr2/jH+wp7SJWfoGoraulA58+wfp/6BwiBmHMjaTH8WM4+ZbU/jVLjsP/3M/Hx9OZPX3cogJ9WDYVQbwa1M3EHdqK5XNbYii6DOxP3fkqJ+PJsaAuSGU0Gq5EbXMpYiiyJ7SRh6NPA51UHr9/2JIiIKGE1B/HBpOwolP4cA6EoE/A/YQLSdPjmLffyVhGD+VcTnTIGYcRGeASjb5kcaPTT0djdOC3tZEvdnqM3G/6pYOkoU6HEGRKIPCXH5/Q6yeooZ0ZlTJpi5zKeVN7dS2WrlSfwBixmGJyYExWTDm+gtPbG/qMXpVwwlSzh4lqvIYscd2QFFXKEZQSjuiY8dBTGbX/+MgNhO0/ac8ywwN/zX1yO4MmFoqmjp8x9SNFqYq6lEMp9l0H6TH6thfmMr0uk8R5MVSmYvYXdpEMBZGNe+HmT/q/cSQKEi5UvoH6ACtw8lrW4/y0dbt5GhruTezkzHCWWl2f/JzcNq6LhYgcYr0RpFxPSRNB6Xa7d9boOC/pt6V1pimqKWyuZ1pqZEeFjQwaowW0hQNCJHT3XL/tGgdHzkNCI5OabFUjqvLnMee0ibmhZxCcHZKpmvr/5puVEoF/zFvIlfnpPLLtw8x72Art05K5Fc/yCYySAHNZdBwHKoLoWQLfPVfsP1Z0IaBYS5kXCeN6aJ6R4GK/5p6RAqioCRFqPWpDJgaYzuJLmyOcTGGGB2FovSGJy+WylzMntImntYXQVswpM6GU6WDvsf4UWH866ezeWVbCS9sPsmOkkaeWTyRGyaMgZgxMP5muPYx6GiB0i/h1GbJ5Iv/Ld0gKuPcLD7tKtCGuvi79G/819SVaoSIZMa11LPFhzYgdbZUocbulkVSgLSYECrEOCyqMILkxVKZ86g2dlDe1M60qP2SmaqHHrJUKxX87PqxzMuK5xdvH+JH/9jH4imjeWphNuEhXaGW4AiYcJv0TxSh8VSXwW+GA+tgz6tSj96UK8/N4uMnSinLMr3iv6YOEGkg3XSWv/vQBiS1qUL6wk0fQUM0KhLCgylXjSVTXiyVOY89pU0kC7WEt5fDmAddcs8JiWG8/+BsXtp6ipe2nuLrUw386tZsckaHow9SEapVoVIqpJLZMWOlf1f+BOxWKN8pzeBPbYHNv5L+6WIh/dqumfx1EBrnEp3+hH+belQ6iWX7fKauutlqJ7qzGjS4baYOUgjmSLOBzLpN8s5SmR72lDYxX9PV7nDMPJfdV6NSsOKGTG6YEM8v3z7EA29c2KglWK0kNEiFPkiFXqsitMvs9UGRhGrvRJ+xjLgxLYwx7SW5eRdxJ75Ac3gDAJ2xOYjp16LKnIfg8I11M3fj56ZuQOc00dbSgN3hlGYEXkyNseO8HHX3ZL+AVMtjV1Uyi0V5sVTmHHtKm1gTchS0qVKOuYvJGR3O+w/N5qsTDTS1d2K22DFb7Zgstq7/pX9mq50GUzsmiw2TVXosbVg1AAYE7mSCcIarFYXMqTnMtLqXUe5+kWghms6Id9EkBfbvs5+bulStMUmskTb1RIV4WFDfdLex6wyOQzOMeGZ/pMfo+LslBbTIi6UjiMXmoNZswxuLwzaarZTVtTAx5CBk50vhEDegVSmZ11UobKA4nSLtNkfXm4CNVosds+VKzNbbKbfYOGE2oq38irmnnoW/fheWrnXpJw1fw79N/YJc9XafMPVkoR7RjaEXkMIvFWIcdk04KnmxdMRY80kx6/dU8u2kbIK9oHHL+ewta2a64jhqZ4fXGaJCIRCqlUIy0NtkZyI/eT6OFU2/IvONPISFz8PUgpGU6TV4dzxiuHQtNqYKtUYv58oAACAASURBVD4RV68xWkhW1KGKTnPrOIYYHSDQFJYF8mLpiOB0ivy7sJoOm8jXp1zTycqV7Clt4jpVIaJCDYY5npYzJJZcmcld9qc5ETIFNj0EW38LAVhozL9NXROCqE8gTeEbddVrW8wkCE0oo9LcOk5yVAhKhUCZZqwUU5d7lrqd/eXNNJo60NHB5qJaT8u5hD1ljczXHEFIudJnt/Anhqm5a042Nzf+jIaxS+DLNfDeTwPu99u/TR0QotIZq67ziZm6rbEcJU63Zr6AlEOcHBnMYacBuneWyriVjw5X8wvNRr4J/jlfFVXidHrPDLLVYqOh6gyp9tJLa7z4GA9eO4YovY77m+7BefVjcOhNeHMJWIyeljZi+L2pE2kgBd/YVaowlktfuGk36fkYYnR83d6VYVMlt7dzJ06nyKeHq7hL/Q0RopGc9t0cPus9JrP/TDNzFIekB14WTx8soVoVj353PIfOtvKOfhl87xUo+xr+8l0wnvW0vBGhT1O32Ww88sgj5Ofnc8cdd7B582bOnDnD0qVLyc/P56mnnsLpdAKwYcMGFi9eTF5eHlu3bh0R8QMiykCks4n6pmZPK+mXoLZK6Qs3z9QBDDGh7GoORQyKAHmx1K0cqmxhlOkI0Q6pTv6typ1eFYLZU9rENYpCRF08xOd4Ws6w+d7k0UxNieD3nxyndfwSWPY2tJTD/86DmsOelud2+jT1TZs2ERERwZtvvslrr73G6tWreeaZZ1i+fDlvvvkmoiiyefNm6uvrWbt2LevXr+f111/nueeeo7PTS+JYXYW9QtoqsNgcHhbTO+2ddmLs1ThRQthot49niNXRYXPSGTtRXix1Mx8fqeFW1S5EpZaW1O8yT3mQb46VeVpWD/tO1zNXdQRh7Dy3pTKOJAqFwNO3ZtPYZuXFzSelnaf3fSI9+ZfvSrtU/Zg+UxpvvPFGFixY0PNYqVRy9OhRZs6cCcDcuXP55ptvUCgUTJkyBY1Gg0ajISUlheLiYnJzc/sc3Gq1UlRUNCThFotlQNcGGRUYgDShli/3HSElwjO7J/vTW2nsJFmox6SJperESbfrUbZLC8enxdGMq93I8SOFPeVPB/raDgqnHUF0ICpd3zTBLXpdhCiKbNp/ho/UezCPuoK65O+SeeZjkuq2sX1fIrE6z2YVW+xOxLP70avNVAaPx3TR6+jNr+3FnK9VDcwfo+cvX5cyM9pGUrgG1TV/Inn7CrTr7qB6xmMYDbd4jV5X0udvlE6nA8BsNvOzn/2M5cuXs2bNmp4uQjqdDpPJhNlsRq/XX3Cd2Wzud3CtVktW1tC2YhQVFQ3s2o4E+BxShFo0kQlkjfdMrYj+9DafaiBaqIMow5Bfk8EQltABn1XTEDONrMr1ZEU5ITFrQFoHTV0xvJEvNUn4/juuu28XLtfrQg5XGklu/5gobRNceQ+VyixsugQWOnZSbv8Jc7PcH2rrix0lDVwlHEIUFCTN+b5UJ/08vPm1vZiLtf4mOZ0dz25j3TErf7s3F0HIguytsOFuEvf8msQQB1y90mOfTobz2vb1ZtDvQml1dTV33303t912GwsXLkRxXoW0trY2wsLCCA0Npa2t7YLj55u8RwmOwBkURZqX56p3bzxSuDmdsZuEsCC0KgWHHOeV4XUHpV/B6/PBWA6nvoDWaveM46V8dKRaCr2ogiBzAQgKVLl3cLXyMLuOuP8TWX/sKW3iakUhjoSplxi6rxMTquXheWP58kQ9W4q7+v4GhUP+2zApH7Y9A+8/CI5BFI33Afo09YaGBu677z4eeeQR7rjjDgAmTJjA7t27Adi+fTvTp08nNzeX/fv3Y7VaMZlMlJSUkJmZ6X71A0SINnTlqnuvqdc3NRMrGAmKTR+R8RQKAUOMjgOt4eCuxdLCDbB2EehHwbKNgAhFm1w/jpciiiKfFlayUL0XYez8nvxvYeLtqLETfuZT2jvtHtV47FQZkxQlqDJv8KgOd3H3rDQyYnWs/vcxrPauNTWVBr73Mlz9KBx8A95YApZWzwp1IX2a+p/+9CdaW1t5+eWXKSgooKCggOXLl/Piiy9y5513YrPZWLBgAbGxsRQUFJCfn88999zDihUr0Gq9p+GsEJVOurLWqzcgWRqkZgTqaMOIjWmI0VHa1A4Jk1y7WCqKsP0P8O6PpFrY938KY+dB3AQ4+i/XjePlFFWbiG/5lghnM+QsPvdEwmQ69Kl8l2/4+qTndpd22p2EVn2FAtHnUxl7Q6NS8OTCbMoa2/nL12XnnhAEqVHHbS9B2VdSzZjWKo/pdCV9xtRXrVrFqlWrLjm+bt26S47l5eWRl5fnOmWuJNJAvLiR6ibvyQ2+GKH5jPTFCOSod2OI0fH5sVqcOZNQ7PmTa8rwOuzw4c/h27/DxCXSH013R/nsRbD1N9IfT1ji8L8BL+eTI9XcotyFqAqRZurdCAKaSXnM+uoP/LawiPnZozyi7/BZI98RD9KpCUeTOMUjGkaCqzNjmZcVz/9sOcntU0cTF3Ze/Zgp3wd9Amy4R0p5XPY2xGd7TqwL8P/NRwBR6Shw4uw2Ti+kpzmGG0vuXkxajA67U6QhbIJrdpZaTfDPuyRDn/MLWPzaOUMHmPA96f9j7w9vHB/hk8NnuUW9D2HcjaDRXfCcMvcOlIJI0MkPPLa7dM/pBq5WHEJMvw4U3lVgzNU8cUsWNofI7z4pvvTJMdfDfR+D6IS/3AglXrTPZggEiKlLIY3oziqMHd65KKK3VGETNBA6uLKkwyE9RjKaEvVY6cBwFktbq+GvN0k5wLf8N1z/5KVZBbGZ0uaWAAjBnKw1Ede4h3CnUfqEcjFx4zGGZXKt/SsKPbS7tPrEXmIFI9rx8/s/2cdJjdZx/xwD7357lm/LL7MRcdRE+OEXEJ4Eb9wBB98ceZEuIjBM/aISvN6GxeYg1l6DKShxRNOrDF2mfqwjaniLpXVF0kfXxhLIfwum39v7udmLoGI3GCuHNpaP8NHhGm5R7sKp1sHYyy9CaiYtYbriBHsOjPzmL4dTJKrqK+lBxnUjPr4neOjaMcSHafnVpqOX/3QUniRtUkqdDe89ANvW+GSVx8Aw9dA4HKoQUoVaKr0wrbHGaCFZqMOqTx7RcaN0GsKCVJQ1DmOxtHQ7vL4AnDa496NeDayH7lnr0fcGP5YP8dnhCm5W7UMx/mZQB1/2nOApSwBQFo38J5fimlauFA9gDBsnZScFALruujCVRt75tpdJRVA4LHsHJi2Fbb+VSvj6WMpjYJi6IECkoWum7n0ZMN056iNR8+V8BEHAEBtKaUOb1P1osGV4D70FaxdDWIL00XUgHZSiM2BUrl+HYErqzcTU70Ivmi4feukmykCtPocr2rZxtmVkfy8PnCxnmnAChZ+mMvbGubowxbRaejFrlUYqBHb1SjiwDj56ZGRFDpPAMHVAGZOOQVlHuReGXxobaggT2lHHjFw6YzeG6BDJ1BMmD3yxVBRh+7Pwrx9LKYv3fTq4Bd7sRXB2H3jxwvVw+ORIDbcoduLU6PstZavIvYMcRRn79u0eIXUSpqKtqAUH+uwbR3RcTyMI3XVhOqW6ML2fCNc+DjN+KBm7D6U7BoypE2kgmVoqm0yeVnIJ7XVSjrp+1MhsPDofQ0woZ1s6sMZNkg70t1jqsMEHP4Mtv4bcO+H770JwxOAGzfbvLJjPD5dzk3o/iqxbLsz+uQwxM/NwIuA8vHGE1EmbomJrv8KiCIbkK0ZsXG8hNymCvGnJ/PWbMk7V9VPO5Dv/B0QH7HplZMS5gMAx9ah01NixNHrfAp2jqQwAbYwHTD1WWiwtdcT0v1hqNcGbd8K3/4C5j8CiPw84r73BbKXBbJUeRKVLnwz8MART3thOVM036MQ2yF7c7/lC+GjKQyeT2/IFbb2FA1xMSZ2ZKxwHaIydNfx9CT7KIzeOI1itZPW/jyH2tRgamSal4u7/m8/sOg0gU5dCG5rWsr5/iB5AOYLNMS6mO62x38XS1mpp193pbbDwBbhu1YAzdc40trHgj9u5+/U951777EVQ9S00lw3/m/AiPu7acOTQRkD6NQO6xpG9mAyhioP7vnGrtm6KjnxLsqKeoCz/T2XsjcvWhemN2T8Da6tk7D5AAJm6NAtOcNZQb7J6WMyFhLSdpV3QQXDkiI+d1mXqp89fLL14tb/2mJSy2FQK+Rtg2j0Dvn9Leyf3/nUvTe2dHKtu5VBlV052TxaMf83WPz9czo2q/Sgn3DLgWXDKVUuxo8B6cIOb1UnYjn8GQFRuYMXTL+ae71ymLszlSJwCaXOkEIwP9DsNHFMPG41ToZYyYLwsrTGis4oWrWe2zYdqVcTqtZTWn1ssDTKWnDvh9JfwlwXgtMO9H0s1XAaIxebgx//YT2VzB3/5wQyC1Ure2nvep5LR0/zK1Cub24mq+pIQsWNAoZdu1PpYTuimM67hc5wOpxsVSvH0hPpvqFEnI0SN/MK8N6FWKnjqcnVhLsfsh8FUBUdGbu1jqASOqSuU2MNSvC6t0Wp3EO+opV2X5DENhhhdV1qjVP8jqLlrK/Wh9bDudqkT0w+/gIS+m56cj9Mp8sg7hewpa+K/8iZx7bg4Fk5KYNPBKtqsXZUJsxdB9SFp05If8MkRacORIygSDHMHda1l3PcYTR0nDrh3i/rZ+iamOI/QnDA4ff7K3PPqwtS2Wno/cUxXQbodL3j9hqTAMXVAGZ3udbtK64wWkoR6HOEjV/PlYtJjdJQ1tkmLQkERBDUVw5e/h3/9B6TOknbZRQxuY9R/fX6cDw5VsfLG8SycJH0KuXNGCm2dDv5d2JUeNuE26f9j/rERafPhMm5QHkCZfVtPF6mBkjHnLqyiGvO+t9ykTqJs/+cECTZCcwI79HI+3XVh1nx8mbow3QiClAlTd0zqC+DFBJapx2SQpqiloqmt/5NHiIbaSoKFTpRRnuuAY4jR0WDuxGixQ8IkIsr+LVVTnLRUqoM+yJTF9XvKeWlrCUtnpvCTq89l9ExNiSAzPpR/7jmveFnSDL8IwdQYLURUbiMYy6BCL92ER0ZzKGgG6bWfgdN9vXTFU19gQc3oSf5ZancopEbr+OEcA+8e6KUuTDc5d4A+Eb55fuTEDYGAMnUiDeiwYGyo8bSSHkw1pwAIicvwmIbuGjBlDW2QPBPBaYe5/1faVTfIlLcvT9Tzn+8d4erMWFbflt3T+hCkjR93zkjhYEULxTVd6WHZi6QO7w2nXPb9eIJPj9Zws3IX9uAYqXbIEDCNuY0osZn6I+5rjJzStJNTwZNRaEPcNoYv8mBXXZine6sLA9LfwpUPSPXX3dUpzAUElql3ZcAIzac9LOQctq7mGOGjx3hMQ7eplza0wVU/p/SGv8F1/zno4mLHqlp58I1vyYzX89KyqaiUl/56LZoyGo1Swfru2XpPCMa3Z+ubD51mnvIAqpzvgXJozaTTZ99Om6ilac8/XaxOoqHyJKliJaakq91yf19Gp1Xx2HezKKw08s7+PvayTPsBaMPgmxdGTNtgGZCpHzp0iIKCAgCOHj3KnDlzejohffTRRwBs2LCBxYsXk5eXx9atXlqPuGu1X9degd3NWQYDpmurvG6E2thdjpToEAShK61RE4Ilavyg71FjtHDf3/YSqlXx1x/MIFR7eWOL0mlYkDOKfx04i8XmkCrjJV/h0wW+6k1Wwis3E0Rn37Ve+sGQGMtO9RUkVn3mltS5qv0fAnIqY2/cNjmRaamR/P7TPurCBIVJxn7sPa/dY9Gvqb/22musWrUKq1XK7T527Bj33nsva9euZe3atdx0003U19ezdu1a1q9fz+uvv85zzz1HZ6cX5nNGpOBEQQo1VBv7WOkeQbTmCpqECNB47uOwVqUkKTJYCr8MAbPVzr1/24vZauev985gVHhQn+ffNSMZY4eNT492hcGyF0PtEag/MaTxPc2nR2u4WbEbe0g8pMwa1r2aDLegd5roOL7ZRerOoTq9mSoxhoysqS6/tz8gCAJPLxxAXZgrHwBBCTtfHjlxg6BfU09JSeHFF1/seXzkyBG2bdvGsmXLePzxxzGbzRQWFjJlyhQ0Gg16vZ6UlBSKi/tYSfYUKi2dugRSvCgDRm+polGd4GkZGGK6qjUOEpvDyYNvfMuJWhMvLZtKVkJYv9fMSo8mOSr4vBDMrYDgswum2wpPcZ3yIMqc7w27g1DqzFsxiiE07XZxCMZhI9W4l+LQmahU/t3laDhMTArnzun91IUJS5RaNR5YC+1NIytwAPQb/FuwYAGVlediTLm5uSxZsoScnBxeeeUVXnrpJcaPH49er+85R6fTYTb3UygHsFqtFBUVDUm4xWIZ0rXxQaNIM9Xy5bESIm31Qxp7KPSmN9pWTVXI+CG/Dq4iQmFlb52JY8eODfjnIooiL+xs4MuTJh6eFUOco4GiooE1Ur4uNYi/H2hk8+5CEsPUpMZOQvHtekrjbx209qH+LrgCo8WB/swXaNQ2ykKn0tGPjv606pwiX3AFN1d8RvHhA4iqvj/1DJiz+8mig9qIqYN6rTz52g4WV2m9zaDgg4MCj761h/93/agLFvu70Y66mfRDb1L30TM0Zt83pHHc9doOekXnhhtuICwsrOfr1atXM336dNrazs3y2traLjD53tBqtWRlZQ1WAgBFRUVDutZ5Mgex4V3s2giyssYNaeyhcDm9NlsngtjA2aiMIb8OrmJqUymbio8Rk5xOY2XpgPS8sq2ET06aePDaDFYsGFwc/qejLaw7tIV9zRpWXjEeWpfBx4+QFQ3EDe61GOrvgit4a285Nyl2YdMlkHZVHij6/vA7EK1fptxMUMVWxirOoMz6nkt0lh76KzZRSebcJWSNSxvwdZ58bQeLK7X+vF0qH1AtRHN91uVaTGZByQ3Elf6LuNtWg3rwb77D0dvXm8Ggs1/uv/9+CgsLAdi5cyfZ2dnk5uayf/9+rFYrJpOJkpISMjMzhyTW3SiiM4gWTNQ39FPEZwRorCpFJTgRRrDZdG8YYkMBpHIBA+CDQ1Ws+aSYWycl8osbBv/mGB8WxLXj4nhnfyU2h/O8EIxvLZhuO3SKa5SFqCYu7tfQB0rytBupF8Np3bveJfcDCC7fygEyyU4f2e5avsrds1IZExfK/+urLszsn0FbPRxyT7bSUBn0b+HTTz/Nb3/7WwoKCvj222/56U9/SmxsLAUFBeTn53PPPfewYsUKtNq+60h7jK5+pY4Gz6c1Gquk3GxtrOdrcJyr1ti/qe8ta+IXbx9iZloUzy7JRaEYWl/Vu2YkU2+ysrW4Tmqpljpbiqt7+TbsboztNkLLPkWNHSFn8BuOeuPqcaP42HkFoWe2uKbcq6mWUe0nOBV2BUFqOZ4+ENRKBU/eMoEzje28tKWXPRRpc6R6STv/B5xekk3HAMMvSUlJbNggVZDLzs5m/fpLZxB5eXnk5eW5Vp076MpVV7eWeVYH0FEnvbHoR3kuR72bxIhgNEoFpxvayA3t/bzT9WZ+9I99JEUE8+eCaWiHseh2zbhY4sO0rN9bwfzsUVLzjI9+KTWyjp8w5PuOFJ8X1XKTsJPO0CQ0o6e57L7hwWpK4m5E3fgZHP8YJt05rPtZjn9OEOAw9N2FSeZC5mbGsnjKaF7YcooQrYqfXH3RBkFBkGbr79wHxz+CrFs8I/QiAmvzEUj1TYBIy1k6Ot23HXsgOJvLcIgC0aM9t5u0G6VCIDU6pM/wS6PZyr1/24tSEPjrvTOI1A2vwYJKqWDJtGS2Ha+j2tghbUQSFD6TBbP94HHmKI+gzl086I1a/ZE86WrOitF0HBh+Od7Ww59QL4aTlhN4XY6Gy+/vyGXhpER+93Hx5dMcs26Tyl3s8J7NSIFn6tpQLNoYUoVaKj1cglfVWkkt0YTpLt9tfqRJ667WeBksNgc/+sc+aowWXrtnOqnROpeMmTc9GacIb++rhNA4SLsKjr7r9SGYVouN0NJPUOFwaeilm3kTEvjAMQvtmW3DS5tzOgg9u52vnLlMTY12mb5AQaVU8N93TmbxlNH81+cneO6z4xc22VGqYNZDULEbyke2z2xvBJ6pA/bwNFIVnq+rHtJeSZ3q8ilTniA9RseZxnYcF9W+cDpFfr7hIAcqWvjvOyczNcV1zTxSokOYPSaat/ZWSDU3shdB4ylpM5IXs6WojhuFnVj0qVJc1cWkxeg4EHYdCtEORZuGfqPqg4TYjZyOmIWul12+Mn2jVAg8u2QSd05P5oUtp1jzyUXGPuX7UoMbL5mtB6SpK2MzvKKuemRnNa0eao5xOQwxOjodThra7Rcc/90nxXx0uIb/vCmL7050/Uapu2akcLalg29KGiDrVp8IwXx1qIjvKI+izb3d5aGXblKzZ1EqjsJe+M6Q72E7/jlOUUA55joXKgs8lAqBZxZPZNkVKfzpyxJ+/WHROWPX6GDGD6H4Q68oTBeQph4Um0GC0ER1gwd3g9ksRDsb6fBgc4yL6S7sVWk8V/di7c4yXt1+mrtnpXL/Ve7J0pmfHU9kiFraYaqLkRpMeHEWTJvVjq7kY1Q4ESa6PvTSzfVZ8WxyfAflma/BNLTKopaizygU05k41nO1hfwFhULg19/L4QffSeP1r0t56vyKjjN/DEoN7Hyx75uMAAFp6kK0tDBpqfdcWqO9SSrk5cnmGBdjiJVM/WyrZOpbimt5atNR5mXF8dTCbLeFibQqJYunJvHZsRoazVYpBNN0GmoK3TLecNl6vI4F7KQjzADxOW4bZ1pqJNtUVyEgDi1/v6MZXf0BtjtzmZEW5XqBAYggCDy1cAI/npvOP3ae4T/fOywZe2gcTF4KB/8JZs/ugQlIU+/OVReayjwmobWrjroqOs1jGi4mNlSLTqPkbKuNI2eNPPTmAbITw3lh6RSUQ8xFHyh3zkjG5hB599uzMH6hVDDJS0MwXx84xpXKIrST7nBb6AWkRbrU8VM5QSriUHpjnt6GAielEbMIDxlcJyaZ3hEEgce+O54Hr83gn3sq+L8bC6V1qFn/BxydsOdVj+oLTFPvKsEb0nbGYxLMNVJfzpB47/lYLAgChlgdR+qkMrqRIRpev2c6IRr3L7BlxuuZmhLB+r3liCFRkH6NV4ZgOjod6Eo+RIkTxcTb3T7e9Vnx/Ms2C6FyT0+Z5oHiPPkFRlFHxBg5ldHVCILAL+ePY8W8TN7ZX8nPNxzEHpkO42+Gvf8LnZ7rrhaYph4ShVWlJ95ejbG9l7rJbsbWWIZVVBM9ynNt7C6HISaU002ddNgc/PXeGcSFuaig1AC4a2YKJfVt7DvTLIVgmsu8rsPMlyfqmM8O2sPHDrpGzVC4elwsH4td5XyPvjvwC0URx4nP+cqZw/T0y9UukRkugiDw8LyxPLJgHO8frOLh9QexX/kQdDTDgXUe0xWYpg5Y9KmkCTUeS2tUtJyhUowhIcK72oplJehRCvDn708jM77/omyu5OaJCYRqVdKC6fibQaHyuhDM1weOMENxHO3kO0ZkvLAgNYmG8RQpM2EwIZi6Y6jba/nSOYkZBteloMpcyoPXjuE/b8riw8PV/HS7GmfSTKl0gMPe/8VuIGBNXYw0kCLUeayuepC5kiohjvBg74p13n+Vgb8sTuE7Y2JGfGydVsXCSYl8eLiKVoUe0q+VFgi9JARjsTnQnfo3CkSUbthw1BvXZ8WzwXKF1Mt1oI1Eujrenwm/kjj9yH3aClR+NDedpxdO4LNjtbxkvRlayqHofY9oCVhTD4ofQ5JQT2Wj0SPj6y1VNKkTvGbjUTdalZK4UM9tUlk6MxmLzcn7B6ukEIyxHM5+6zE95/P1yQZuEHdgjhgPsSNXhXReVhwfOq5ERBjwbF08+QUnSCE9Y6yb1cl084PZBn6zKIfnKjKoViXh/PoFj0xIAtfU48agEpyYastGfnBLK6HOVtqCR4/82F7OxNHhZCWE8dbechh/EyjUg4slu5EdBw4xXXGC4CkjE3rpJjVaR1hcMkXaiZKp92cUVjOU72SLPZeZBjmVcSRZdkUqa26fzIsdC1DUHMRyctuIawhYU+9Oa3Q2loz82C1SFoMtTK5tfTGCILB0ZjJHzrZypEkBGdd5RQim0+4k+OQHACMaeunm+qw43mibCY0npTBMX5R9jeC08aVzkmzqHiBvRjJXLHqQBjGMY+/8BrN1ZGPrgWvq3SV4jSOf1ujoyo8XotJGfGxf4LZJo9GqFKzfWy6FYForoXKfRzV9U9LADc5vaI3MhuiRr6o5Lyuej+zTcQoqONJP2YBTX2AVgqjWTyIp0rsW4gOF26Zn0DDhB0zt3MuqP79Fq2XksuwC19T1o7AptIR1VFxYnGcEaK+VPh1oY70nR92bCA9Rc9PEBN4/UEVH+o3S9msPZ8Hs2v8tkxUlhIxw6KWbqSmREBJNccg0ONJ3FUvx1BfsJocpciqjRxm/cAV2ZTBz6tdT8L+7Ryx9ekCmfujQIQoKCgA4c+YMS5cuJT8/n6eeegpnV8ePDRs2sHjxYvLy8ti6dav7FLsKQcAckkySWEu9yTqiQ1vqSzGJwURHy390vXHXjGRMVjsfnmyDMfMkU/dQdxmb41zoReXGWi99oVQIXDsujjfaZ4CxAir3Xv7ExhKE5lI+65woh148TUgUqml3s0i9k6bqM+T/7y6a2zrdPmy/pv7aa6+xatUqrFbJ+J555hmWL1/Om2++iSiKbN68mfr6etauXcv69et5/fXXee655+jsdL/44WIPTyPVA7nqYvMZKsVYRkV4Rx11b2SmIYr0GJ20YJq9CExVULnHI1p2n27iesfXtETl9jRZ8QTXZ8XzfsdknAoNHO4lBHNqMwBfOuVFUq9g1k9RiA7emPgtJ+vMLH1tFw1m904i+zX1lJQUXnzxXOWxo0ePMnPmTADmzp3Ljh07KCwsZMqUKWg0GvR6PSkpKRQXF7tPtYtQxWRIueoD6MvpStSt5VSIsSSEaKWc5AAAFGtJREFUy/nDvSEIAnfOSGZvWTMlUVeBUuuxEMyu/XuZqChD56HQSzdzM2OwKnWcCP9O1yeXy3TuOvUFdZokOnTJPX1nZTxIZBpM+B4ppRv4e/54yhrbuOvVXdS1Wtw2ZL8JyQsWLKCysrLnsSiKPbnVOp0Ok8mE2WxGrz+3+1Cn02E2m/sd3Gq1UlRUNBTdWCyWIV/bTaigJ1KwcerotxQF9693OPToFUUy2is5y1iSykuo87I8dXDNa+sKJurtKAV4actpfjXqSoIOvcOp1Luleuvn4U69DqeIplh6MykLzsU+zHGGqzUnLog3TFNZbd/Gme1v0h4/vec5wWEl8/SXbHNew/g4tUsmVt7yuzAQvFVrUOKtGI6+S/rx1/nVdYt5anMNi/5nO7+9LgrcoHfQu0wUinN/UG1tbYSFhREaGkpbW9sFx883+d7QarVkZQ2tfkZRUdGQr+1BMxsO/gGdo2X49+qHHr3mehCtmIJGM2GCdzZXdslr6yJuONrJtrImghd+H9V7PyJLZ4TU71xwjjv17ixpZJ5zF80xkxk7/dph32+4Wm9tCmLNBy38Sq8jtXUPXFNw7smSreCw8HHnROblppKVNfz69970u9Af3qs1C06+Tvzpjdz58JNkGNJY/tZBGjuVXD0M/+uNQWe/TJgwgd27pV5827dvZ/r06eTm5rJ//36sVismk4mSkhIyM0dux92Q6cpVVzSPYF31lnIALKHe0xzDm7lrZjJNbZ184ZgCqqARD8Hs2beLCYoz6Kbmjei4vTEvKx4LWk5HXw3HNoH9vLWrU1/gUKjZ5cxipkHuR+pVzH5YWhc6spHpaVF8vfI6smLdE34dtKmvXLmSF198kTvvvBObzcaCBQuIjY2loKCA/Px87rnnHlasWIFWq3WHXtcSnowDJcHmipEbs6UMADHcu6ozeitzxsaSGB7EGwebYOx8OPb+5WPJbsDpFAk6/j5OBDS5i0ZkzP5IjgohMz6UdzuvAEsLnD4v0+zUZk6HTEIdFMq4USNbjE2mH8bMg7gJsONFt2+kG1D4JSkpiQ0bNgBgMBhYt+7SspJ5eXnk5XnHbGbAKFW0BiUS3VaJzeFErXR/2r6z6QwKQBXjntZw/oZSIbBkejIvbDlJw203E1O0Ccp3QtpVbh97f3kz19i/oSl2KjFh3tNL9vqseP66PZ1fhkWgOPwOZC4AYyXUF7FZey8z0qLc3tREZpAIAnzn/8B7D0gZSmPnuW2owN181IVFn0qKUEt1i/tWo8/H2nCaRlFPTJScbjZQ8mZI5RTebB4PqmBp880IsG/PDsYpKgn1ktBLN/Oy4uhwKqmInwfHP4LOdijZAsDG1iw5ldFbybkD9Imw43m3DhPwpk6UgVShloqmkUlrtDeWUSHGMkpOZxwwoyOCmTs2ljcPNOLMXABFm9xeq9rpFNEcfx8nCoK8JPTSzeTkSKJ0Gv7tnAWdZjj5GZz6go7gUZwURzNDNnXvRKWBK38Cpduh6qDbhgl4Uw+KG0OY0EFtbdWIjKcwllMpxsk56oNk6cxkalotHI28Dtrq4cw3bh3vUEUz19i+oiFmOuj/f3v3HhVlve9x/P0wzICAMBCgIkiMiuIp8wbqUdF2m0jPsasFsg7lZWuWx/tpaZrg2aXZWWXtXdvlpXVWiVkeLRXLrWfrIUndi9yWljhqaRBXRUTuMzKX8wdImYKK8/gw+H2t5XKNML/ns0b8zOMzv+f3a193/l65u/T9gu44fUPhu81w5ktO+MTSSe/JfWEBWkcULRk8CQyd4dCfVTvEXV/q/mGN603Xlf6g/sEcdrxri+RMvQ1+17cLwX4G1hb1BL2P6rNgjhw+QE+PEjoPbl+XXq74fUwoFRYHpRFjGy/BWCvZbbmPQZFGDJ53/T/r9ss7AIZMgtzt6GvUOZG86//2dcG9AHCU34FpjdUl6Jw2ipVQgn3dYHZQO2Lw9OCpQeH89XQVFlOCqpdgnE4nhpPbseNBp3Z26eWKUdEhGHQe7KFxzr5T0bH5oom4e2UqY7s37EXwC0VfV6rK8Hd9qWOMxIGCvuoOLMHbtBt8TadwPGR2wi1Lio3A7nCS5TkS6soh7yuXH6Os2srKXWbiLx+gLHgo+N75bf1uhp+XJ0NNQWwo6ALGHlQGD6TK6SsfkroD/zCYd4K60EGqDK/dvmXthd6bKn0I/nV3YK560+YYNtkco01MIX7ERQWx6icdjxj8UHK3Qc/bv8sT4KeyajL/to9KcxZDOc69unNY4152ydhq+X1MF9Izc/l56kfszC1HX1zPwB5GrWOJm+Gh3vm0lDpQ4xNBl4oS6i/b6WTQqXeginwcKHgG9lDvGB1ccmwE8//nIhf6/o4Qcyb8y1ttG8hhh9LvKTq2l7Lj/0dkzTHmKDWggwa/7tBnMl4Dklwb3sUeigklPTOXPSV+7C2u5oFwL7z1Kv78CrcgpQ7YjFFEXvpfCivq6N1FvTvxnJfyOOcMJCTQX7VjdHTj7u9GemYu2xvimFafCT/tB25ir1e7DUqOQf4BnHkHseUdQt9QTXfAQRcKQ8egG/ww/n3GoA90j7t9wwN96Nu1M59/V0xucRXT42XTFSGlDoBnsImQ/CpOnD+vaqnbyvP42RlKV3+Z+dJW3nodTwzszp8OW/iDT9MlmOh/v/YbbZeh+FvIPwB5B6Egp3FON1Do0Z2vLg/hlHd/+gwdy6PxsUR4uec/hYdiQvlLVuNOWnI9XYCUOgCdw6LhCFQW/QD3q7j/ZEU+hc5ehBml1G9HcmwPNvw9nzP3jKaX+XPo+Tw0WKDoSOP89bwDUPA12OoBsAf35VTIWDadi2BPTU+CuvTg+dEmXnkg7I4sDaGmh2K68JesM3goMDgyUOs4oh2QUgf8uzXOVb9cdka1Yyj2y3jWllLgHM6YANnx6Hb0C/Onf3gAGyoH8UfLF0TtnQLbfga7FVCgy30w+DkqQ+P4sDiM9UeqqLbYGGYK4r+e7smY6JDmPQHc3YBwI8F+BroGeNPZW691HNEOSKkDSlDjtUg1l+D1rCtFwUmBQ+4mdYWk2Aj+c9sFFoXFoDidEDcNIkdAj2GcqTWwPvssn31WhM1xkbH3dWN6vIkHIjrezBAPD4W3kwbgo+YH/MKtSKkDePtT5WFUdQleQ20JAEVKKMF+cuPR7Xr0gTBe+9zMH7uv47l+emJiYjiSX8HarWf4m/kcBp0Hz8SG84eRJu7t4Nu6jeodonUE0Y5IqTe51CmcoJrCq7brc6UrtwRbfMNlWVQX6Oyt51/7dyPzWDEmn3tI23+Iw3kVBHTSM+vBXjz7z/fKm6e4K0mpN7H6RdK9JofK+gaMPgaXj6+vLcaGJ54B3Vw+9t0qOS6CLUcKWbH/PN2NnUgf349nhkTg66YzWYRwBfnpv+KeKMJKd3Gi7BLGyFCXD2+oLeacEkwXo5/Lx75bDeoRyEuJfaDuItMfGeL2M1mEcIU2l/rjjz/evLl0eHg4M2bMYNGiRSiKQu/evUlPT79qk+r2zju0Fx4nnJQX/gAqlLq+toR8R4h8SOpCiqIw88FemM1mKXQhmrSp1K1WKwAZGRnNfzZjxgzmzp3L0KFDSUtLY9++fSQkJLgm5R0QGN4XgLrS08AIl4/vWVNMnn2gLLkrhFBVm0r95MmT1NfXM2XKFGw2G/Pnzyc3N5e4uDgA4uPjOXjw4A1L3Wq1Yjab2xIBi8XS5udej87iJBqoKcx16bgASkMdfS9fotAZirGmHLPZ6tLxXc3Vr63a3CmvO2UF98rrTllBvbxtKnVvb2+mTp3K008/TV5eHtOmTbtq1oivry/V1dU3HMfLy4uYmJi2RMBsNrf5udfldFKX2QkfSym9ovu49r/z504AUOAM4aF+vYhp53f+ufy1VZk75XWnrOBeed0pK9xe3tbeDNrUXFFRUTz66KMoikJUVBRGo5Hy8vLmr9fW1uLv72aLVikKtb49iKk9zJq3lvJT7teNK/m5QtOSuwWyjZ0QQmVtKvWtW7eycuVKAM6dO0dNTQ0jRowgJycHgOzsbIYMGeK6lHdIyIhJhHtbmFX3HlFbEri8PBznB+Nh36twajfUXmjbwE2bYxQRQmhnmTsthFBPmy6/TJgwgZdffpmJEyeiKAorVqwgMDCQpUuXsmrVKkwmE4mJia7Oqr7hL2IY9gIXC0+yfed2PIuPMKLwJ0z5b6M4m87aA6MgIg7CYyF8SOM6I7obrLlxKR+r4oXOLxRPmaUhhFBRm0rdYDDw1lvXbk6wcePG2w6kOUUhKCKGyS/0ZfvRIh7fkYun3cLK4TYe9i9AKTwMZ79s3MEdwLMThA1sLPjw2MbC79z16jEr8jmnhNLVKAt5CSHUJTcftUBRFJ4YGM4w0z0s/PR7ns8uY1Tv4bzx1POEBXhDZQEUHobCfzT+nrMGDv258ckBEU0l33RGf/EsBcj1dCGE+qTUb6BbQCc+nBzLRzk/s2KXmcR3slk2/p94clAEirEH3PdU4zfarFDyXVPRN/3K3dY8zllHosxRF0KoTkr9JiiKwr8Ni2RU72D+Y8sxFmw5xp7cUlY8ef8vi0Z5ekFEbOOvK6pKoOgfWAu+5YOsriRJqQshVCaf2t2CyHt8+WT6cJaMi+HL02Ukvp3N7uOlLT/BvxvEjCf/gXmccXanq2yOIYRQmZT6LdJ5KEyLN/H5rJF0M3ozY+MR5m0+SmVdQ4vPKam0AMg1dSGE6qTU2yi6S2e2vTiCOQ/1JvNYMYnvZLP/dNl1v7e0snGvTCl1IYTapNRvg17nwbyEaLa/OILO3p48999fs2Tb99RabVd9X0mlBQUI7SylLoRQl5S6C9wfHsDOWSOZHm9i09c/M/ZPX3E472Lz10suWTB20mHwlJdbCKEuaRkX8dbrWDwuhs3ThwPwzNq/s2KXGUuDnZIqC8E+MtFICKE+aRoXi4sK4q9zRrFil5l12WfJOnmeKksDpgDZ7V0IoT45U1eBr5cny5+4nw+nxFFtsXGuykqwr7x/CiHUJ02jotHRIeyZG8/7B87S17de6zhCiLuAnKmrLMBHz4KH+2AKkiV3hRDqk1IXQogOREpdCCE6ECl1IYToQFz6QanD4WDZsmWcOnUKg8HAa6+9RmRkpCsPIYQQohUuPVPfu3cvly9fZvPmzSxYsKB5H1MhhBB3hktL/ciRI4waNQqAAQMGcPz4cVcOL4QQ4gZcevmlpqYGPz+/5sc6nQ6bzYan5/UPY7VaMZvNbTqWxWJp83O14E553SkruFded8oK7pXXnbKCenldWup+fn7U1tY2P3Y4HC0WOoCXlxcxMTFtOpbZbG7zc7XgTnndKSu4V153ygruldedssLt5W3tzUBxOp3Otob6rT179pCVlcXKlSs5evQo7733Hu+//36L33/06FG8vOSmHCGEuBVWq5UBAwZc92suLfUrs19Onz6N0+lkxYoV9OzZ01XDCyGEuAGXlroQQghtyc1HQgjRgUipCyFEByKlLoQQHYiUuhBCdCBS6kII0YG4Xak7HA7S0tJISkoiNTWV/Px8rSO1qKGhgZdeeomUlBQmTJjAvn37tI50U8rLyxk9ejRnzpzROkqr1q5dS1JSEk8++SRbtmzROk6rGhoaWLBgAcnJyaSkpLTb1/bYsWOkpqYCkJ+fz8SJE0lJSSE9PR2Hw6Fxumv9Oq/ZbCYlJYXU1FSmTp3KhQsXNE53tV9nvWLnzp0kJSW59DhuV+rutGhYZmYmRqORTZs2sX79el599VWtI91QQ0MDaWlpeHt7ax2lVTk5OXz77bd8/PHHZGRkUFpaqnWkVu3fvx+bzcYnn3zCzJkzeeedd7SOdI3169fzyiuvYLVaAXj99deZO3cumzZtwul0truTkt/mXb58OUuXLiUjI4OEhATWr1+vccJf/DYrNL4Jbd26FVfPKne7UnenRcMeeeQR5syZ0/xYp9NpmObmvPHGGyQnJxMaGqp1lFYdOHCA6OhoZs6cyYwZMxgzZozWkVoVFRWF3W7H4XBQU1PT6vIZWunRowfvvvtu8+Pc3Fzi4uIAiI+P59ChQ1pFu67f5l21alXzbfd2u71d3a3+26wVFRW8+eabLF682OXHan8/WTdwq4uGacnX1xdozDx79mzmzp2rcaLWffbZZwQFBTFq1CjWrVundZxWVVRUUFxczJo1aygsLOSFF15g9+7dKIqidbTr8vHxoaioiLFjx1JRUcGaNWu0jnSNxMRECgsLmx87nc7m19PX15fq6mqtol3Xb/NeORH55ptv2LhxIx999JFW0a7x66x2u50lS5awePFiVd543O5M/VYXDdNaSUkJzz77LI899hjjx4/XOk6rPv30Uw4dOkRqaipms5mFCxdSVlamdazrMhqNjBw5EoPBgMlkwsvLi4sXL2odq0UffPABI0eOZM+ePezYsYNFixZd9V/x9sjD45d6qK2txd/fX8M0N2fXrl2kp6ezbt06goKCtI5zXbm5ueTn57Ns2TLmz5/Pjz/+yPLly102fvttwxYMGjSIrKwsxo0bx9GjR4mOjtY6UosuXLjAlClTSEtLY/jw4VrHuaFfn9mkpqaybNkyQkJCNEzUssGDB7NhwwYmT57M+fPnqa+vx2g0ah2rRf7+/uj1egACAgKw2WzY7XaNU7WuX79+5OTkMHToULKzsxk2bJjWkVq1Y8cONm/eTEZGRrv+Wejfvz9ffPEFAIWFhcyfP58lS5a4bHy3K/WEhAQOHjxIcnJy86Jh7dWaNWuoqqpi9erVrF69Gmj8wKS9fwjpDh588EEOHz7MhAkTcDqdpKWltevPLCZNmsTixYtJSUmhoaGBefPm4ePjo3WsVi1cuJClS5eyatUqTCYTiYmJWkdqkd1uZ/ny5XTr1o1Zs2YBEBsby+zZszVOdufJgl5CCNGBuN01dSGEEC2TUhdCiA5ESl0IIToQKXUhhOhApNSFEKIDkVIXQogOREpdCCE6kP8H6lcd9703q3EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(premium.Premium, label = \"Actual\")\n",
    "#plt.plot(pred_lr, label = \"LR\")\n",
    "plt.plot(pred_rf, label = \"Rf\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interaction Effect\n",
    "\n",
    "1. IE occurs when the effect of one variable influences the other.\n",
    "2. Lets say if the fuel efficiency along with car types would have been given then a legit interaction effect would be Engine*Fuel_Efficiency.\n",
    "3. In simple words, if a variable or its properties are complimenting the other variable(s) then such an effect is called Interaction Effect.\n",
    "\n",
    "Here in this data, we can take engine and age to create an interaction effect.."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1e37c081c10>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Interaction Effect\n",
    "premium[\"Int_Eng_Age\"] = premium[\"Engine\"]*premium[\"Age\"]\n",
    "\n",
    "sns.heatmap(premium.corr(), annot = True, cmap = \"YlGnBu\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>Premium</td>     <th>  R-squared:         </th> <td>   0.586</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.517</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   8.507</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sun, 17 Jan 2021</td> <th>  Prob (F-statistic):</th>  <td>0.00501</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>08:26:23</td>     <th>  Log-Likelihood:    </th> <td> -86.127</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    15</td>      <th>  AIC:               </th> <td>   178.3</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    12</td>      <th>  BIC:               </th> <td>   180.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>   <td>  -45.1692</td> <td>  163.594</td> <td>   -0.276</td> <td> 0.787</td> <td> -401.610</td> <td>  311.271</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Engine</th>      <td>  234.2719</td> <td>  101.077</td> <td>    2.318</td> <td> 0.039</td> <td>   14.043</td> <td>  454.501</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Int_Eng_Age</th> <td>  -20.8965</td> <td>    7.531</td> <td>   -2.775</td> <td> 0.017</td> <td>  -37.304</td> <td>   -4.489</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.431</td> <th>  Durbin-Watson:     </th> <td>   2.507</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.806</td> <th>  Jarque-Bera (JB):  </th> <td>   0.001</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.013</td> <th>  Prob(JB):          </th> <td>   0.999</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.967</td> <th>  Cond. No.          </th> <td>    60.1</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                Premium   R-squared:                       0.586\n",
       "Model:                            OLS   Adj. R-squared:                  0.517\n",
       "Method:                 Least Squares   F-statistic:                     8.507\n",
       "Date:                Sun, 17 Jan 2021   Prob (F-statistic):            0.00501\n",
       "Time:                        08:26:23   Log-Likelihood:                -86.127\n",
       "No. Observations:                  15   AIC:                             178.3\n",
       "Df Residuals:                      12   BIC:                             180.4\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================\n",
       "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "Intercept     -45.1692    163.594     -0.276      0.787    -401.610     311.271\n",
       "Engine        234.2719    101.077      2.318      0.039      14.043     454.501\n",
       "Int_Eng_Age   -20.8965      7.531     -2.775      0.017     -37.304      -4.489\n",
       "==============================================================================\n",
       "Omnibus:                        0.431   Durbin-Watson:                   2.507\n",
       "Prob(Omnibus):                  0.806   Jarque-Bera (JB):                0.001\n",
       "Skew:                          -0.013   Prob(JB):                        0.999\n",
       "Kurtosis:                       2.967   Cond. No.                         60.1\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Model \n",
    "finalmodel = ols(\"Premium~Engine+Int_Eng_Age\", data = premium).fit()\n",
    "finalmodel.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "\n",
    "* Clearly the Interaction effect has improved the R2score."
   ]
  }
 ],
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