Chapter_3/3.3.2_Non linear fits.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(397, 9)\n"
     ]
    },
    {
     "data": {
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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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>307.0</td>\n",
       "      <td>130</td>\n",
       "      <td>3504</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>chevrolet chevelle malibu</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>15.0</td>\n",
       "      <td>8</td>\n",
       "      <td>350.0</td>\n",
       "      <td>165</td>\n",
       "      <td>3693</td>\n",
       "      <td>11.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>buick skylark 320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>18.0</td>\n",
       "      <td>8</td>\n",
       "      <td>318.0</td>\n",
       "      <td>150</td>\n",
       "      <td>3436</td>\n",
       "      <td>11.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>plymouth satellite</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16.0</td>\n",
       "      <td>8</td>\n",
       "      <td>304.0</td>\n",
       "      <td>150</td>\n",
       "      <td>3433</td>\n",
       "      <td>12.0</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>amc rebel sst</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>17.0</td>\n",
       "      <td>8</td>\n",
       "      <td>302.0</td>\n",
       "      <td>140</td>\n",
       "      <td>3449</td>\n",
       "      <td>10.5</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "      <td>ford torino</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mpg  cylinders  displacement horsepower  weight  acceleration  year  \\\n",
       "0  18.0          8         307.0        130    3504          12.0    70   \n",
       "1  15.0          8         350.0        165    3693          11.5    70   \n",
       "2  18.0          8         318.0        150    3436          11.0    70   \n",
       "3  16.0          8         304.0        150    3433          12.0    70   \n",
       "4  17.0          8         302.0        140    3449          10.5    70   \n",
       "\n",
       "   origin                       name  \n",
       "0       1  chevrolet chevelle malibu  \n",
       "1       1          buick skylark 320  \n",
       "2       1         plymouth satellite  \n",
       "3       1              amc rebel sst  \n",
       "4       1                ford torino  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto = pd.read_csv(r'E:\\programming\\dataset\\Into_to_statstical_learning\\Auto.csv')\n",
    "print(auto.shape)\n",
    "auto.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "auto['horsepower'] = auto['horsepower'].replace('?',np.nan)\n",
    "auto  = auto.dropna()\n",
    "auto['horsepower'] = auto['horsepower'].astype('int')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "auto = auto.dropna()\n",
    "auto = auto.sort_values(by = ['horsepower'],ascending = True,axis = 0)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>mpg</th>\n",
       "      <th>cylinders</th>\n",
       "      <th>displacement</th>\n",
       "      <th>horsepower</th>\n",
       "      <th>weight</th>\n",
       "      <th>acceleration</th>\n",
       "      <th>year</th>\n",
       "      <th>origin</th>\n",
       "      <th>name</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>26.0</td>\n",
       "      <td>4</td>\n",
       "      <td>97.0</td>\n",
       "      <td>46</td>\n",
       "      <td>1835</td>\n",
       "      <td>20.5</td>\n",
       "      <td>70</td>\n",
       "      <td>2</td>\n",
       "      <td>volkswagen 1131 deluxe sedan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>102</th>\n",
       "      <td>26.0</td>\n",
       "      <td>4</td>\n",
       "      <td>97.0</td>\n",
       "      <td>46</td>\n",
       "      <td>1950</td>\n",
       "      <td>21.0</td>\n",
       "      <td>73</td>\n",
       "      <td>2</td>\n",
       "      <td>volkswagen super beetle</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>326</th>\n",
       "      <td>43.4</td>\n",
       "      <td>4</td>\n",
       "      <td>90.0</td>\n",
       "      <td>48</td>\n",
       "      <td>2335</td>\n",
       "      <td>23.7</td>\n",
       "      <td>80</td>\n",
       "      <td>2</td>\n",
       "      <td>vw dasher (diesel)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>325</th>\n",
       "      <td>44.3</td>\n",
       "      <td>4</td>\n",
       "      <td>90.0</td>\n",
       "      <td>48</td>\n",
       "      <td>2085</td>\n",
       "      <td>21.7</td>\n",
       "      <td>80</td>\n",
       "      <td>2</td>\n",
       "      <td>vw rabbit c (diesel)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244</th>\n",
       "      <td>43.1</td>\n",
       "      <td>4</td>\n",
       "      <td>90.0</td>\n",
       "      <td>48</td>\n",
       "      <td>1985</td>\n",
       "      <td>21.5</td>\n",
       "      <td>78</td>\n",
       "      <td>2</td>\n",
       "      <td>volkswagen rabbit custom diesel</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      mpg  cylinders  displacement  horsepower  weight  acceleration  year  \\\n",
       "19   26.0          4          97.0          46    1835          20.5    70   \n",
       "102  26.0          4          97.0          46    1950          21.0    73   \n",
       "326  43.4          4          90.0          48    2335          23.7    80   \n",
       "325  44.3          4          90.0          48    2085          21.7    80   \n",
       "244  43.1          4          90.0          48    1985          21.5    78   \n",
       "\n",
       "     origin                             name  \n",
       "19        2     volkswagen 1131 deluxe sedan  \n",
       "102       2          volkswagen super beetle  \n",
       "326       2               vw dasher (diesel)  \n",
       "325       2             vw rabbit c (diesel)  \n",
       "244       2  volkswagen rabbit custom diesel  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "auto.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fit_degree(data,var,target,degree):\n",
    "    poly = PolynomialFeatures(degree)\n",
    "    poly_data = poly.fit_transform(data[var].to_frame())\n",
    "    lin_model = LinearRegression(fit_intercept=False)\n",
    "    lin_model.fit(poly_data,data[target])\n",
    "    pred = lin_model.predict(poly_data)\n",
    "    \n",
    "    return pred\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_1 = fit_degree(auto,'horsepower','mpg',1)\n",
    "pred_2 = fit_degree(auto,'horsepower','mpg',2)\n",
    "pred_5 = fit_degree(auto,'horsepower','mpg',5)\n",
    "\n",
    "plt.figure(figsize = (14,8))\n",
    "plt.scatter(auto['horsepower'],auto['mpg'])\n",
    "plt.plot(auto['horsepower'],pred_1,color = 'orange')\n",
    "plt.plot(auto['horsepower'],pred_2,color = 'green')\n",
    "plt.plot(auto['horsepower'],pred_5,color = 'black')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Poly fit with degree 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(2)\n",
    "poly_data = poly.fit_transform(auto['horsepower'].to_frame())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    mpg   R-squared:                       0.688\n",
      "Model:                            OLS   Adj. R-squared:                  0.686\n",
      "Method:                 Least Squares   F-statistic:                     428.0\n",
      "Date:                Thu, 18 Jun 2020   Prob (F-statistic):           5.40e-99\n",
      "Time:                        08:16:57   Log-Likelihood:                -1133.2\n",
      "No. Observations:                 392   AIC:                             2272.\n",
      "Df Residuals:                     389   BIC:                             2284.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         56.9001      1.800     31.604      0.000      53.360      60.440\n",
      "x1            -0.4662      0.031    -14.978      0.000      -0.527      -0.405\n",
      "x2             0.0012      0.000     10.080      0.000       0.001       0.001\n",
      "==============================================================================\n",
      "Omnibus:                       16.158   Durbin-Watson:                   1.663\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               30.662\n",
      "Skew:                           0.218   Prob(JB):                     2.20e-07\n",
      "Kurtosis:                       4.299   Cond. No.                     1.29e+05\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.29e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "est = sm.OLS(auto['mpg'], poly_data)\n",
    "est2 = est.fit()\n",
    "print(est2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# linear fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(1)\n",
    "poly_data = poly.fit_transform(auto['horsepower'].to_frame())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    mpg   R-squared:                       0.606\n",
      "Model:                            OLS   Adj. R-squared:                  0.605\n",
      "Method:                 Least Squares   F-statistic:                     599.7\n",
      "Date:                Thu, 18 Jun 2020   Prob (F-statistic):           7.03e-81\n",
      "Time:                        08:16:58   Log-Likelihood:                -1178.7\n",
      "No. Observations:                 392   AIC:                             2361.\n",
      "Df Residuals:                     390   BIC:                             2369.\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         39.9359      0.717     55.660      0.000      38.525      41.347\n",
      "x1            -0.1578      0.006    -24.489      0.000      -0.171      -0.145\n",
      "==============================================================================\n",
      "Omnibus:                       16.432   Durbin-Watson:                   1.319\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               17.305\n",
      "Skew:                           0.492   Prob(JB):                     0.000175\n",
      "Kurtosis:                       3.299   Cond. No.                         322.\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
     ]
    }
   ],
   "source": [
    "est = sm.OLS(auto['mpg'], poly_data)\n",
    "est2 = est.fit()\n",
    "print(est2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# poly fit with degree 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(2)\n",
    "poly_data = poly.fit_transform(auto['horsepower'].to_frame())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:                    mpg   R-squared:                       0.688\n",
      "Model:                            OLS   Adj. R-squared:                  0.686\n",
      "Method:                 Least Squares   F-statistic:                     428.0\n",
      "Date:                Thu, 18 Jun 2020   Prob (F-statistic):           5.40e-99\n",
      "Time:                        08:16:58   Log-Likelihood:                -1133.2\n",
      "No. Observations:                 392   AIC:                             2272.\n",
      "Df Residuals:                     389   BIC:                             2284.\n",
      "Df Model:                           2                                         \n",
      "Covariance Type:            nonrobust                                         \n",
      "==============================================================================\n",
      "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
      "------------------------------------------------------------------------------\n",
      "const         56.9001      1.800     31.604      0.000      53.360      60.440\n",
      "x1            -0.4662      0.031    -14.978      0.000      -0.527      -0.405\n",
      "x2             0.0012      0.000     10.080      0.000       0.001       0.001\n",
      "==============================================================================\n",
      "Omnibus:                       16.158   Durbin-Watson:                   1.663\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               30.662\n",
      "Skew:                           0.218   Prob(JB):                     2.20e-07\n",
      "Kurtosis:                       4.299   Cond. No.                     1.29e+05\n",
      "==============================================================================\n",
      "\n",
      "Warnings:\n",
      "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
      "[2] The condition number is large, 1.29e+05. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    }
   ],
   "source": [
    "est = sm.OLS(auto['mpg'], poly_data)\n",
    "est2 = est.fit()\n",
    "print(est2.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# residual plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For degree 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x2cf10abbf28>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "error_1 = auto['mpg'] - pred_1\n",
    "plt.figure(figsize = (12,6))\n",
    "sns.scatterplot(x = auto['mpg'],y = error_1)\n",
    "plt.axhline(y = 0,linestyle = 'dashed',color = 'black',linewidth = 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### for degree 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.lines.Line2D at 0x2cf131d5518>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bKPtYW2uPTPy31xizQ9I5knIG1gDqT1Bmv1fjtH5QXqsXvF7GPWyn/4M63kJBqZf92At1AHFbJlJLnxOEVyADa2NMq6SItXZw4v//TNI/+zwsAAHj9+Iq1cyQ+f1aveJ1ezuvA/VKq9R43R7gVbL2OVuh4NeLg45a+ZwgvAIZWEuaL2mHMUYaH+Nd1toH/R0SUNvCMqEqSKoVjNQSr7OKYetDXYnxenGAV81Mer7gN2wHSUAugQysrbW/kfRWv8cBeCnIgSu1ieUJ6mn9oPMyqxi20//ljrfQ94cXB3hBCGrDdpAE5BLIwBqoNdUIXN0E7mReyxOEYAThU+qBRbHvDy8O8IIQ1IbtIAnIhcAaqIJKB65uA3cyr+UJQjCSLchnRSqlHs62FPv+8OIALyhBLTXSCDsCa6AKyg1cnQZKbgN3Mq/lCUowItVHgJlLEM62eH1AM/XxUqlUwe8Prw7wCGoB9wisgSooJ3AtJVBym3EOWuY1TIISjOQLMO+76h0yMr4H/pXi99kWrw9ocj3e5kuX6c+WzNND+3ozt8v+/gjSAR5Q74K88iLgKzcrgE3ldAWzbKWsUJdvxTFJjsae/cO8+9rzteOqFTWf6aw1+QLMkVgyFKv8lcvv1fa8WEky+7vmd6+9Pu3xVt/Rrc++f0nB749qrAAKoDgy1kAOXmehyskolZKJy5VxXn/xUl191x71DcUcjT0omVeUJ99ZkedfHi5YJhGEumw3Y6j02ZZiY3ObMZ/6XXPPlefmfLyGiCEjDYQAgTWQQyXqNksNXEspH8kO3EfHkjrQO6R1D/Zoz8FjkkSHjwKCEFh6IVeAufmSZfrsd/ZOul120FfsALIa28btQWwlyyCcjM3t/ISp3zX9w/G8j8fnFwg+SkGAHKpVt1mo3KTU8pF04N5gpMu3PpEJqis19lqQDpxqoVQiVznPiXNmqG8oNul22UFfoTKGam0bL0opvCyDmFqW8aUf9RQcWzllXtmmftds2nVAN1y0tOzHA+AvMtZADtXoklEsG1ZuJo4OH84FoaOEl6aeFUmlbMEyiUIHkNXaNn5PPsyW6zN5w0VL1TcYzxyoTh2bk89pocz/1M/rnoPHdNsjz2vbquWZ68N6FgWoR2SsUbe8zBaXw0mmrpxMXDXGXiuCFNRVQrFJqYUm/lVr2/g9+TBbrs/ktfc+pSvPO63g2Ap9Totl/nN9Xj/1jlN13fd+pddeTxBUAyFDxhp1qVLZ4lJUKnCh9dZkpWQLpdrL7heq7W9vbdItl3bqijuyPgeXjh+EFar19VKQWj3m+0ymx1LO2Ipl/tOf1+2rz9WRY6PqH47rxh+Oz4/Y99JgaM+eAPWKwBp1yclp7kp3yahkUEeHj3HFDqCCFNT5IZlMKRo1uv7CszSzqUEj8aSiUaNkMlW1bROkA8F8n8kFc1q0+9rzyxqbkwPoSMTIWquLNz1a8HYAgo/AGnUpCCUA9R7UVYPTbGEQgjo/9A7FdPk3n5gWSG5btVwntc2s2rYJyoFgvs/km06YUfbrdnoAXQ9nT4B6QGCNmlWoBKAxGsn5I9YYdTbtwIs2ZPUe1FWD02xhEII6PyRSNuf2SUzU/9bbtsn1mWxraXT1WXd6AB2EA+1aaT0J+InAGjWpWAlANGK0/uKluuaepyYtqBJ18CPi5eIx9Ra4VBtZwMKiEZNz+zj5HGSrpYAs+zPpxWc93wG0NL4qavZlTm9XiW3r9aJYQL0y1oavX+tUnZ2dtqury+9hIED6BmNauWH3tIAhXQJweGBEV9+1R1eed5rmtDTq2OiYNu06oJs/8Tad1DbT1WMjOAgWCovHE+rpG9Zf3dmd2T4bL1mmxR2tampylnfxYhsXC8z9Ctwr9Vl3us2quf/yvQY4Z4zpttZ25rqOjDVqUrESgKZog/qGYlp9R3fmeqeZzCDUZ8MZym0KezWWVPfzL+uuK5bLWitjjH6y7yW96YQZ6nAYWLvtd+1k9cdygstcwXh6vE73hUp91p1us2r2Wed7DfAGgTVqUrESADf1jPkee2p9di2dHg8zym3yiyeSWrvzWa3d+eyky9/zlhNLegw3AVmx4LGc4DJfMN4cjeiyWx93HKBXqpSo0DbLLvtwejsvvlsomwK8wQIxCK1CC7y0tTRq0yXLJi26sOmSZWpraZRUfOGMQnIt6LD+4qUaej2RGUMpy0EXeh1AJXmxOEt6IvDUx3A6EbhYYF5O4J4vGH+xf6SkpdMrtdhSvu2eTNlJ3xnJlHV0Oy+WmmdhKcAbZKwRSqmU1Qv9w3qxfyTTf/fN7TO1qL1VkYjRwOiYvvrwfq25YEmmhvqrD+/XF1Yudd2nOhIxmn9Cc6b377HRMa17sEd9Q7GSs2zUAMOtRCKl3qGYxpIpNTZENG9Ws6IOg1ovOlG4mQgsFc+U5rteGq8LzpWtzReMz2xqmHZZoQC9UqVEubb75kuX6fMP7Jv0nfH5B/Zp86XLtPqO7oK386I8hLIpwBsE1gilY6NxHX3tda25f++kH/M5Mxv1xtZmxRNJPbSvVw/t6510v899wJt6wdF4UpdvfWLa5aVm2apZQ+mnei6LqeRrTyRSevbooK7Mmny46ZJlOnP+bMfBdXM0MmmBmGaH90sbjSe17sGeSQex6x7s0c2feJvUWvz+xYL7XNevv3iprr5rj/qGYtp86TLNbW1SJBLJbNt8wfhIfPLnz0l2vhKlRLmC2FQqNe376qF9vbr+wrOK3s6LWuh6/owCXiKwRiiNxpOZDJk0/sNyzT1Paduq5VJr5esFy82yTX3+Wp8wlEpZvTwc00gsqedfHtZXH35OfUOxTFZeyj+ZrBZ+6Ct9RqJ3KJYJqqXxfefKO7u1ffW5WjCnpci9x7d9uuY4rdROEG4mAkvFM6XZ14+OJXWgd0jrHhxf8luSVt/RrTUXLNH1O/dltm2+YL05q399+rKGiHR4YKTq+9jUgL1vMJbzOyMSiTi6nZvvNs6cAd6hxhqhlLS5F7ZITpQZVrpesNjjO33+fLWWxpjQ11qnf6w/tOERnXfjLq25f6/+/r2L1TGrWVfc3qWXh2N569BLqVEPsnxnJLLret3U2I8lU7kXeEmmHN3fiwM7Lz5r6SDzpLaZmRUxc13fYKTLtz6RCarT453T0jhp2+abQ7GovTVz2X1XvUPN0Yg+ePPkfeyVYX/mOzjdjpX4bnOynwJwhow1QmlGnozwjInT2JWuF3SSZfu9ua3atmq5EimraMRo3qzpAUOuzNoNFy3V2u/u1Wfes7jiGaNKZoVz/Vhfe+9TWnPBEq2+o1uvj6XylsFIKqtEJmhZ7mKBq9tMYWND7hVEow3OciZenNmpZm1uvvEeGx2TNHnb5ivhSF/WNxiblK1P72PXX3iWLt/6RNWztk63Y6Hblbv/1/qZM6CayFgjlKINRl/6yFsnZW2+9JG3Ktpw/EekWBbMrUKPn0ik1NM7pI9ueUzvXL9LH93ymHp6h5RIpKY9xuL5s7V99bm658pzteaCJbrxhz16aF9vxTNGlc4K5/uxntPSqIVtLWowyvtjXs4PfRCz3MW6brjNFM6b1Zyz+828Wc7KOLzKflb6s5aWa7w3XLRUm3YdyPzt9KCg2ARHP7K2Trdjrtu52f+96A4DYBwZa4TSaDypf/n+s5MmTP3L9591PGGq0kqpfY1EjKy1unjTo5Mur3TGqNITJwtNILvlsk61NBXOlpaaSQ3iRNBiE/PcZgpTqZRmt0S19fJzFDFSykqNUaNUKiUneZOwdYKYOt5kyurzD+zTnoPHCh4U5MrkFst+S+HK2rrZ/73oDgNgHIE1QqkxGsk5Ycpp71xJGhtLqncoNqlUo7HRmwxNqbWvXpySL/U0cKVP/+ZsKXbJMp04Z4bmtIz/YBf6MS/1hz6Ip7PzBa7SeCmClPsAwhhngW3fcFyfvOUX0+6/bdVyneRw5cQgLKBTyr6bPd5UyuoLK5fqcx/If7985Tand8zK2W1k3YM9mfuGKWvrZv8P2wEWEGQE1gglt71zx8aSerZ3SH+V1aZs4yXLdOa8WY6D60LBQKm1r24zRuXU6la6c4qTH+tC15f6Q+/XynHF+khPDVyz36uNn3y7brhoqa699/h+fMNFS9XgMJ5JpHJP4k2EaJKnmzpzJwcFhTK56TKsI8dG9fpYUi1N4x1OpPAtkOJ2/w/CARZQC4y1xb+AjTEfynHxq5Kettb25riuqjo7O21XV5ffw0AVHR4Y0dV37dGV552WKQXZtOuAbv7E23RS20xH97/ue7/SRctOztz/3u6D+twH3uLo/sWCgXL6C7uZeNc3GNPKDbtLaptWay22/Hg95bzP2e/V5kuX6d7ug9P2w+yFjAo5PDCij255LHfG2sF+HATl7LulODwwohU3/HTa5buvPV8ntc2ctN90zGrW/3jX6Tp1bqtmNjdobmvl6sW9VmufZyDIjDHd1trOXNc5zVh/WtK5ktLfTudJekzSGcaYf7bW3uF6lEAJ3PbONUb61DtOnZYpdHgGvmg9YzQa0ZkT2bBEMqWogxXx3GSMyjkNXGunf528Hq+7hpTTRzr7vdq064D+/r2LJ+2HpWRJO1qbtPGSZdPOvHSEJMsqVb6Ep1gmt1C5TpA6zBRTa59nIKycBtYpSb9vrT0qScaY+ZI2SvojST+XRGCNkvm5FLO1ygQz0vFWcNtWLXd0fyfBQDQacbRIhxfKPQ1c6dO/bt7jchR6PZXI6JXTRzr7vdpz8Jhu/GGPrr/wLJ38xhYdfGU0s/Khk4OAaLRB809o0t2rliuZsmqIGDVFjaJVrgt2c8BS6RIeJ98Vhcp1wpT9pZwD8J/TwHpROqie0CvpDGvtK8aYsXx3AvJxuxSz2+xMKs8CM05LU70KBrzKoAZxVr8Xy217qRJdQ8rpIz31veobiqkpGtE1334q093ivqveof6heNHArn84rg9teLRiZRROuA1CK73vlvNdEcQOMwDCwWlg/e/GmJ2Svj3x98WSfm6MaZV0LP/dgNzcLsUsucvONDfmDoybG6uTMZe8zYoF8TSwF++xlwqdZThybLSsrHq6j/TUg4dCfaQnLdEdT+iZ3w3qxh8eX6L70MBowcVzsvf5fK9pNJ5Q36Cqsg+4DUKrse8W+66YeoAbxA4zAMLBaWD915I+JOmPJRlJt0m6147PfDy/QmNDDXO7FLNbc1ubcwbGc1udBepeBANeZ8WCdhrY7/d4qnxnGRIpq09+/bGysurl1NJLx9+rvkHp+p37po2p0OI5Tl7TM78b1PU795V0oObnqn1+7ru5DnDv+ss/8qXDDIDwc5SWmQigd0vaJelhSf9hnbQTAfJIn0LPVspSzG5lB8a7rz0/03qrlMDY7WpztZ4V8/s9nirXqn0bPvl2feGBfZMObq68s1u9Ey3XnIhEjBobImqY+G8p+0G+lQ/Ti+dkyxXYFVqJMH2gVmzlwFTK6pXhmJ556bWaXbUvlbLqG4zp8MCI+gZjk15XrgPczz+wT5svXTbtfQlL6z0A/nHabu8vJf1/kn6i8Yz1OyX9s7X21soOzxna7YXP2FhSLwyM6NAr40sIj8STWvjGFi1qm+nZIi1ued1BYqpKtxmrhkLbyEmNdaW3cb7xjo4ldaB3SHNnNekDN++edrufX3OeTmkvvoSnF+U8ubaBJMePm3lNE2Ulm3YdyJSVSMfbyhUa/+9efV1r7t9b1r4Y9Il+xcaXrx3fL/7pTxWJRAJTWgUgOLxot3eNpLdZa/snHrBd0iOSAhFYI3wG4wm9NjqW+TFf2Nair3zsbA22JvRGh4F1LJbQyyPxzMqJc2c2qbn5+C7tJmjzMljIN44gTjgsRbFtVKxMwo+ALH2W4fDAiC7f+kQmKzmtFMPh8zsp5ym2H+Yrgyi11KghYnKWlThZBv6mD7+1ZlftK/Ye5SuniUQioTnABRAcTs/JHpI0mPX3oKSD3g8HYVLo9Goxo/Gk/vbuJyf92P3t3U9qNO6sDCIWS2j/y8P66JbH9M71u/TRLY9p/8vDisUSmbH1HB0seGq71NPDTk6rT1VoHF6Uo/jJyTZKtxw8pb1VC+a0TKo99moblyMdTG3adUA3XLR0WnlIs8PJi8XKeZzsh/k4KbG+ObYAACAASURBVDXKfvyr79qj9RcvLal8IT3+Y6Njrso53JZFVVKx9yhfOU5YDnABBIvTjPVhSb8wxtw/8fcHJT1ujPlfkmSt/WIlBofgcpttTFqrjlnNWnPBkkkrJyYdxuYvj8Qzi2JI4z+Uf3Vn9/iKc83RolmqYuP3qv652DiCNuGwFG63kZ815tlnC9J9pBfNnSlrpW2Pv6hP/5fTHD1OsbaLXk5QzZX5zn78QwOjWvfg+Gs5bd4stTQWzxw3RiOTDjDKXaim2iU9pTy/k9aYzdGIrr/wrExZmtMDKwCYymlgfWDiXzrsuX/i/2dXYlCSZIx5n6SvSGqQ9HVr7b9W6rlQOrcBQ2tTg/7hfYt1zT3Hf8jXX7xUrU3Hf9AK1u+mcvehTkxkAosFbeWeHi51QlatTFDM9V643UaVXhikkPTZgu2rz9XrY0m92D+i/7Xtl+obimn9xUsdP06xch6v3v98B4JvnNk46fH3HDymy7c+od3Xnu/ocxiNGK2/eKmuueepzAHGm9tnqqWxQfNPmOG4m4ifNdbFnj/fe9TW0qi+wZhGxxJ6sX9EX334uUxtetjmOgAIDqeH5d+XdLaklZI+rPE+1hdba6+z1l7n9aCMMQ2S/o+kP5e0RNLHjTFLvH4elC+WJ2CIOc5W2kxQnb7vNfc8pXhiPDAudgo9GjG5O05MyVJNvT4dtHlxethJKUwYOiYUk++9aGtpdHUK3e9T8JGI0Vgypb/b/kvFkyn945+fqTUXLNG6B3v0+piz/bhYOY9X73++A8GkVcHHL7aPjsaTWvdgj9ZcsET/+OdnKj6xPVLWOg6K/SzpcfL8ud6j0ztm6bm+Ia3csFt/sm6X1ty/V3//3sV628lzMo8RtoNfAMHgNGN9p6S/l7RX48ubV9o5kn5trf2NJBlj7pZ0oaR9VXhuOGCknNlGp/mpeJ4ex2MTPY6LZZTnzmzSxkuWZcpBFra1aOMlyzR35nhQ1tbSmHPhjraWRknFs6XFJmQ5zdKFfYKilP+9uO+qd7g6hR6ESW+NDRH1DcW0+o7uzGWltgQsVM7j1fuf70DQWpv38Z3so03Rhpyvv5TA3++zMk6ef+p71DcYm7ZPX3vvU1pzwRKtvqM7dAe/AIKjYe3atUVvdN11133MWvuPa9euPbZ27dpX0/8qNajrrrtuuaR5a9eu/e7E36dK+v21a9d+P30bY8yq6667bvN11123KpVKLRgaGlJ7e7u2b9+uH/zgBzrjjDN00003qb+/XwcPHtSdd96pE088Ubfddpt27dqlk08+WV/+8pc1ODio/fv361vf+pYWLVqkDRs26PHHH1d7e7tuvvlmxWIx/fKXv9T27dszj/n0009r5syZ2rhxoyTpkUce0b333pu5vqenR8YYbdmyRU1NTXr44Yf1ne98J3P9Cy+8oJGREX3jG9/Q7Nmz9b3vfU87d+7MXH/kyBH19/dr69atgX1ND/34R0o+/4SGZnToyL9/W7PHBnTlioV64J5/09y2OY5e06s9v9DXrny/kr/8nj6weLaaX39FT/1spxadvFBf/8at2vnDhxU9Ya5e67pfqfio+o+8oNf27tLi00/Tpk0b9czT3fr0n/6B7K8e1IV/0KFDB/bpuzvu0+LFi/X5f12nDff9RJf+8Rma8esf6x2nzdXXvrVT+x79sc5acqY2fu3LOq3pNb3w8oh+9/hOzZszSyvnD+jRn/xAixcv1k033aQXX3xRJhnXt++6XW+a26adO4+/puv//3W6btt/6KWjfRp6+scaMi3avm27Dj/9iM5acmbmfTp06KB+sGO7rvqLP1TrC/+uU2Iv6A/fcrq++tWvhGbf+97OB7S7r0mvPbFDydFBJV/r00vdD+lP375YF33mX3Tbfd/Xjude1x1f36DvdR3QnES/7vv2Nkev6Ytf/KJ+s/8ZzX/jG3TbN7bIGFPSa7rxxhu1t+fX+t3Lr+ob3/iG2t5wwqT3qdjnadPXvqK3z49q7/7fqG/Pj7RgwQL9iX6lZ7of0ymnnOL487Rnz5Paeuddal/wZn3pi1/Us/v2aubMmdq0aaPaW5t0Uvyg5vU/qc9+4l3a/s2Neu65/SW/T4/t+pGSs980/j4MvaL2hphe3vOQ3nLqSTK/eVRvHunJPP7AwCvau/83uuyfbtQrtlXDe3+s3v17tOtQSr/+6XbFRoe1f/9+feeebfrUn/2h7v/WNzX422d04vwOdQ4/rllRq6eecrbvnXra7+nfbvk/Gur9rSSjoSd/oHlzZmnmy8/oBzu/52jfu/HGG9Xzm9/q+cO/09atWzW/Y66+/W1n33vzTzxJd39zk0ZHhjT2ymEN7/uZFp78Zr3yxE49+Z9dOfe9N518qm686SbF+16UaWzW4J4H9NrrY1oQ+626dz2om//q/dp26wbt31/6+xS273JeE6+J11T6a/rZz3720tq1a7fkimGd9rF+l6SPa3xxmMzKCdba+4qHyaUzxnxY0nuttX858felks6x1v5NrtvTx7r6Dg+M6Lrv/UoXLTs5M/nw3u6D+twH3pK3Z262eDyhnr7haRnnxR2tamqKFu3xfOTYqD6y+dFp16eXy87Xmza7p6+bCVdOHr9W5Hsvtq1a7us28Kq2N5FIqXcoVtLKiZUYh9fP4XQfdTvx0O3rd3v/3tde14G+oWnzNU7rmKV5J8zIeZ9C+3TQ2gUCCB4v+lhfLulMSY06XgpiJVUksNZ4e7+Ts/5eKOlIhZ4LZZjRGNHfvOuMaYHxjEZnAcnLI2M5u3psX32uFjRFi55CL7ZctpOJcdmnh0sNLvyceOclJ68733uRXh3Qr23gVceN9MqJ1tqSV070chzFxlhq2YzTfdRtZxonYyu0n7ndfqNjx+vE0wf56x7s0Vc+dnbe++Tbp098QwsBNQBXnAbWb7XW/kFFRzLZE5JON8acqvFWfx+T9IkqPj+KiCWsXuh7TXevWq5kyqohYrTnxX61t851dP98gXG6xrrYj3V6ueypQUO6NraU2tZyMmZe1k770aoslbI6NhrXS8de1+qsg6NcrzvfeyHJ9TZw89q9qO3N997PP6FZo3FnY6pWjXGpAXA16/sLja3SrS3LqZMPQn0/gNrkNLB+zBizxFpblcmD1tqEMeZqST/UeLu9W621v6rGc8OZ1uaIFnWcoI9teWxSxrq12VnGOt3VY1pg7GBFOkmaN6s55+TEebOaM/d1+sNZTsbMqx9mP1qV5VvGutDr9mp1wFzjKPe1e3HWIN97f/2FZ+nyrU84GlO6F3TQzl4EJXisdGvLYt8F+YS5hzyA4HJaSPjHkp40xvQYY54yxjxtjHmqkgOz1n7fWnuGtfY0a+0XKvlcKN3Q68mcpRxDrzvLMs2IRrThk2+ftuLdDIe1rdnLZf/8mvO0ffW5OnP+7Em1sU5Xgys3Y+bFanN+tCpLP+fMpgbXmVY328Dta58zI6qNlyybtA9tvGSZ5sxwmi/I/97PbGpwNKZUymro9UTJKx5WSxBWRKz0yofRaESL583StlXL9bNrztO2Vcu1eN6skurkAcArTn+B3lfRUaDqxsaS4xO2UlbRiNG8Wc1qbHSeYUva3Au0OF050Uo6oSWqrZefo4iRUlaKNhxfgciJ9HLZbpWbMfOihMOPVmVTl7F28rorUa7i9rX3Dcf1tYf3T6qt/drD+7X2g2c53i/yvffHRscmjWl0LKnDAyM564Mvu/XxSauIjsSTmn9CsJb1LiQ9eXMsmVJjGZM3i3HS2vL0jlnavvrcSRNISznz8euXh31boAYAsjn69rTWvpjrX6UHh8oYG0vq2d4hfXTLY3rn+l366JbH9GzvkMYcLoohSTMacy984XTy4nA8qQ0/OaB0VxprrTb85ICG49VflKGcjFmxBWyc8mMBmfRzppexLrYITu/g6/rtKyPae/hVXX3XnrJfa75xZCvltY8lU3poX69W39Gtj255TKvv6NZD+3ozE1iLSaWsIhGrTVOy3hs++XY9vO/opDEd6B3K+T6nDw72HDyWGcflW5/QqA/7cTkSiZSePTqoj2x+VO9cv0sf2fyonj06qETCu+UKin2+Uimr5/qG9JHNj+pPJsbwXN+Q4/3L7wVqACCbo3Z7QUe7vdIcHhjRRydqo9PSraactklL/yBPrWucWo5RyTF4qdSMbLF2gKU8r9tWZaVmkrOfs2NWs/7Hu07XqXNbNbO5QXNbj2cKc43thouW6sYf9qhvKOa664XbfahYy8VSt8Ep7TP10rFR3f7oC/r4OW/O1Fivv3ip1j3Yk3O5a6/2A7+42YalKLSfut2GXrS+9GMCMYDw8qLdHmpIIpW7jCNRQgZyYHRMX51yGv6rD+/XF1YudfRjOLslknPlxNkt/tRFljqRyasSDjcTzMoNyp0+Z65MYPbqdG7LVdzuQ+VOWpv62g4NjGaC6DUXLNFD+3r12Qveot3Xni9JuvquPZmgWspdHxzWlTWLta30SqHPl9vPktvJj35MIAZQuwis65CTjhzFxBNJPbSvVw/t6510+ec+4OzHMDZmNDY2pm2rlmfqvI++OqLY2Awp95oOgeJlH+tyuxO46f/r5DnzBTxzWho9KVdxuw9lT2AtdXGXYq+tpbEhk5HuG4pNut3U+uAgdN4oV7G2lU65qdPON4ZGh2Nwe3BTjT7kAOoH06br0LxZzTm7KTjJ9KUZY3LWxxrjLKBob21SS3PTpDrvluam0GT63HYy8EKlJz7mq4EeiSc9ea3pNnVTH7+xhIlz6Qmsp7S3asGcFsfBnNPX5uR9DkLnjXKls/7Zr89p1j/NSZ12KmXVNxjT4YER9Q3GptVPT+2qsv7ipY6fP/vgZve152vHVStKyjb7MYEYQO2ixroOpVJWRwdHlUhKKWsVMUbRBmn+bOerjh19dVS/7hvWtfceX0b4houW6vc6WjX/Dc5qM8Ne1+j3+Ctd35vrFPnmS5bpxDkzNKfF/Wt9ZTimnt8NTluKevGbZuuNrZXNFJby2ir9Pvu9H7ld0r1YnXaxUosX+4f1P+9+Uleed1qmJGjTrgP6ysfO1intrZV4yZOEvU4eQPVRY41J+ofj+vCm6RMHS/khiUQiuu2R5yfVx972yPP6wsrSMk1h/uHye/yVqu/NDvTmn9Cs+656h8YSKc+DvtF47qWob/7E26QKx1OllHBU8n0OQn2v27aVxeq0i5ValLNyopfCXicPIFgIrOuQF6c+21ub9Jl3n6Er7shaDvvSZVVbzhqVqe+tZqDXFG3IGVBVa8VCvw+MpNqo7y1Wp13s+8bNJFQvhL1OHkCwEFiHlJug1IuJd4lEUtFoRNdfeJZmNjVoJD7+dyKRVFNT8d0qCJm6WuB1cFjNQK+tpTFnQNXW0ujp8wRZLdT3FguMi33fuJmE6pUgHGQBqA0E1iHkNij1IqDpG47r8m8+kbsPtYPAuhYyddVS6CDK66x/NQM9t+32akF6EvDUz5HTScBBUCwwLlRqMXX/fdMJM3Luv5zdAhAWBNYh5DYo9SKgcdsLuxYyddWQSKTU0zuo1dklNxMHUZI8z/p72UawGLft9mpBg5FuuGjptEnADSGLGQvVaecrtZCc7b+c3QIQJrTbC6F4IqmOWc3afOkybVu1XJsvXaaOWc2Og9J0QDN1KehSgtp0L+xspfTC9mIp72ItvMKg0GtIpayOvDqaCaqlycs1e7GU89Tnb2tpnNZebvOly5RKpTzfxm5bNtYCEzGZScDbVi3XmguW6LZHnpepsYAxV0tCp/svS5YDCBMy1iHU0tSgtR9coleGxyRJTQ0Rrf3gErU0OQtKvchKtrc05Vw5sb3F2eRFt+Uo1chiVaPNWqHX0D8cV+9grGBm303WP9/zn94xK5NdTKasPv/APj20r9fzbVwr2Vo3+0k0YnT5ilOntRwsZbGmsHJ61oqzWwDChMA6hKysRuJJrbl/76QfYytn2cT21ibd/t/P0Yv9I5mJh29un1lSR49XXh/TC32v6e5Vy5VMWTVEjPa82K/21iYtmFF8t3JbjlLpGu1qBO7FXkM8kVT/cLzgQVCu66Tx3rzFArxizz+1v6/X29iLlo3l8PKAye1+4mfLQb85PcCvZnkSALhFYB1Cr8dTmQyXNB7wXHPPU9q2arnjH+NYIjUpML/lspx9zvMaS6b0N3c/Ne3yn19znqP7u62vrXQWqxqTK4u9hqZog+7tPjgtq7s5q63h1Elh6y9eqqvv2qO+oVjRAK/Y81d6G7e3Nukz71lcsH9wsSC41CDZ6wMmt/uJ3y0H/eS0fzR9pgGECYF1CCVt7omDSYflr14EjcV61xbjNgtV6SxWNU4/F3sN6cDzSz8az2i2tzZp3uxmLXjD8RUy05PCRseSOtA7pHUP9mjPwWOSVPQ9Lfb8ld7GxfoHFwuCywmSvT5gcruf1HPQ6LR/NH2mAYQJkxdDaEZj7ol/MxqdvZ1eBI3p3rXZk9xKWdQhHVBk37+UgMLt/YvxYnJlMek686nbMF1nng4ovrByqc5acILe3N6qhW0zJ/X3TU8KazDS5VufyATVUvH3dM6MqDZOef6NlyzTnIlSnlK2cbkTSXNNaksrNmmtnEltXh8wuZ2AmR007r72fO24akVddbso9P6Xczu/JBIpHTk2qhf7h3Xk2KgSiZTfQwLgEzLWITS3tTlnlmtuq7Og1otMZDQa0eJ5s7Rt1XIlUlbRiClpUQe3WahKZ7GqkUl0UmfudOGKct7TvuG4vjbl+b/28H6t/eBZWjCnxfE2rlQ9eiVKVbzOwnsxAZPFScItkUjp2aOD0yZinzl/dlUXuQEQDATWPnEzgcptUOlF0JhKWf365WFXwZTbgKKSAUk1Tj972ce5nPd0LJnK+fyfff/xbJuTbVypevRKlKp4fcDkxQTMRCKl3qGYxpIpNbpcdZCFVKqvdyiWCaql8f3/yju7tX31uXl7ewOoXQTWPvAiw+cmqPQiaKyHlRMrnUn0Mntaznvqtk4+rVL16MWC4HKCZK8PmApNwHQS5HqZ7QzTQiq1dAAwlkzl3P8TScpBgHpEYO2DIASlboNGessWVyx48D57Wtp7mq6TnxrUOa2TT/O6vCJ7u80/oVn3XfUOjSVSObdhczSi6y88K9M2stlBMOrlAZPbVQW9zHYG4XvFiTAdADjh1QEqgNpAYO2DWghKw9Bb1s+smJPgwe9uB9FoRGfOn63tq89VIplStMwyBC8PEEoJuvqH47rs1sen7YPVDiRzBep9gzFHQa6X2c6wfK+E5QCgmPT3S1ODmbZYVjkHqABqA4G1D8IQlBYT9DZhfmfFnAYPfk9ci0YjBTOjTg5OvDxAKCXo8iqQrMQBmNOxOcl2Oh1fWL5XwnIAUMjU75fV/2WR7l61XKmULfsAFUBt4JPvg0q3iquGoLcJK6cVm5dqKXhYuWG3VtzwU63csFs9RwdzttLzqh1aKdvNi5aIpbzGUjgdW7G2laWMLyzfK9VoZVlpU79fNv/7C/rYlsfU0hTVgjktBNVAHSNj7QO/SwC84ne2tZBqBLaFujk4zR6OjSXVOxSb1LKwsTEYAYYfp+xLybp6cdakUq/R6diKleOUMr6wfK8E/WyXE7Vw4AygMgisUZMqfVq8WDcHJ8HD2FhSz/YOTarN3HjJMp05b5bj4DoeT6hvOJ4JzDtam9TU5M3H2o/goZSgy4tAslKvsZSxFSrHKXV8QT7YTQvLAUAhYSm7AVB9BNY+8KL+t5baVVVCpbNixbo5OAkeeodimaA6/Rh/dWe3tq1arpPaZhYdQzyeUE/f8LTAfHFHq+PgutB+5EfwUO2gq5Kv0Ysgt1YDuDAcABRSC1l3AJVhrHVXSxgEnZ2dtqurq6rP6Saw7RuMaeWG3WV3M/B7Yl5YVPLg48X+Yb1z/a5pl//8mvN0Snurq8f42TXn6c0OHuPwwIg+uuWxafuR08C82H4U9P3MqwPUWn+NqAySG0D9MsZ0W2s7c11HxroMbn/s3J5+rpV2VZVWyayYF71roxGT+zEc/jgnUjZ3qzaHE++K7UdOssdugws39/fic+BFhrySAVYtlE3UqrBn3QFUBlOXy+C244TbWfFMnPFfsW4OTh9j45TH2FjCY6QD82ylBOZO9qNC3T7cdtRwe3+vPgduOppUqquIV+MDAFQXgXUZ3P6gu22LFZR2VYlESkeOjerF/mEdOTaqRKJ+lvDN7ubw82vO0/bV55a8DHVjY4POnDdL21Yt18+uOU/bVi0vaeJiR2tTzsC8o0r7kdsDTL8PUL3gd1tHAECwUApSBrcTitye3g3CxJliXTHqQbHFVZxobGxwVA+dS1NTVIs7WrVt1fKyuoK43Y/cHmB6dYDq5+eAs0cAgGwE1mXw4gfdTX1eEOoui3XFQHVEow3jB3QT+0G0hGyt2/3I7QGm3weoXvCiaweT4ACgdhBYlyEIP+h+T5wZS6ZyZurGkvVTDuI3LzpGuNmP3B5g+n2A6gW3r4GuHwBQW2i3h7K4bfUWBGHIFBYao9u2jZUeXzXuHwR+tt4EAFQf7fbgudbmBm345Nt11b/9ZybTtuGTb1drczgWrghKprDQkubFxhiE+l63GWO/M85ecPMagvAeAgC8Q2CNspwwo0ltMxPaevk5ihgpZaXmqNEJM8Kx8lgQeoEXW9K82Bi9ru9tjEYUjRiNxp1nXmsh4+ynxmjufuiNdTIBGABqDd/eKEskYnTSnJl6Q0ujmqMRvaGlUSfNmRmaoCoImcJ8S5r3DsUcjbGtpTFnL+22lkZHzz+1B/OHNjyint8N6uq79jjqx1yNHs7V4GfbyGjEaP3FSye9h+svXuq4FzkAIFgCF1gbY9YaYw4bY56c+PcXfo8JuYV54Yog9EAutnJisTEOjI7pqw/v15oLlmjbquVac8ESffXh/RoYHXP0/Lky4tfc85SuPO80R/2Ya6GHc7pt5Ec2P6p3rt+lj2x+VM8eHaxacD0aT2rdgz2T3sN1D/ZoNE4pCACEUVBLQb5krb3R70GgdgWhB3KxJc2LjTGeSOqhfb16aF/vpMf93Afc9ZGeM5HxLpbBD0LW320pihdtI92MoSnaoL6hmFbf0Z25zI/FnsKOkiQAQRHUwBqoqCC0TEwvaT61xjq9pHmxMbqtsTYmd2B/bCLjXeyx8t3fmOpsQy8moOZrG5lw2DbS7RiCcIAXdkGZiAwAUgDb7Rlj1kr6b5Jek9Ql6e+stQOF7kO7PYRVLJbQyyPxTFeQuTOb1Nzs7HjXbUBx9NVR/bpvWNfe+1Tm/usvXqp1D/aobyhW9LFy3f+Gi5bq9zpaNf8NlV8kyItWdUeOjeojmx+d9hhOM9ZejCGRSI13hkmmFG2IaN6s5rpZvdQLtCwEUG2Ba7dnjPmxpDfluOp/S9oo6XpJduK/N0n67zkeY5WkVZJ0yimnVGysQKUkEik99/Jw2cvCu826RyIR3fbI81pzwRLNaWnUWDKlaCSi9R9eqoOvjKo5zxjSp93HUnbS/Y+Njum2R57X2g+eVdJ2KJcXpSjzZjVr0yXLpr0H6bMGlR5DKmX1XN8Q2VYXglCSBABpvgTW1tp3O7mdMeYWSTvzPMYWSVuk8Yy1d6MDqsOL+l63Kyd+5j2LJwV1N334rbrm209pz8FjObN+2VnyjlnN+of3LdY190zOWDdUKR70ot1gNBrRmfNna/vqc8vKGLsdQxDaPoadF/sBAHglcDXWxpgTrbUvTfy5UtJeP8eD4HI7YSl9Cn4smVKjD6fg3db3FuJ02zRHI7r+wrM0s6lBI/GkmhuPv/5cWb/sQPDQwKjWPdij6y88Sye/sUUH+oZ12yPP6wsrl7oevxNe1SdHoxHHBzJej4Fsq3vUqQMIksAF1pLWGWPO1ngpyAuSVvs7HASR2/ridJu1cssw0mNwE9g3NuReHCTa4C64d7pt+ofjuuzWx6c9/5oLlmj1Hd05s35TA8E9B4/p8q1PaNuq5bp+576qBjRBmIDqdgxkW90Lwn4AAGmBmyFjrb3UWvsH1tql1toPZmWvgQy3PZTzlWGkF2cpxovFUdL1vVMXeHFa35uP021TqN1evqxfvt7a6bKRatcGB6GXupsxpLOt2fsA2dbSBWE/AAApmBlroCi3p9DdlmF4URsbiRi9oSU6bVn4UoOCqZnzVCr3a5u6bfJlS9NBcq6sX77T7ie+oYVgpgxkWwGgthBYI5TcnkJ3W4bhRW1s/3BcH7/lF65btR15dVS9gzH1D8d1b/dB/e27z9CfLZk3aeGYXNsmV5C8+dJlBZfTJhD0npsJqACAYCGwRii5nbDkts2aF7WxXrRq6+kd1Oo7jr+GGy5aqq/8eL8++/4l2vfSYMFtMzVITqasPv/APj20r7dgzTqBIAAAuQVugZhysEBMffKqK0g5bda8WO3N7cIW+e6/5oIlOmvBCWqKNjjeNiyyAQCAM4FbIAbwgtvMqZs2a05KIooF/pVq1dbe2qSmaENJ24a2bwAAuEdgDZSpUGDvJKNdqVZt82Y3FwzOcwX8tH0LL7dnbgAA3glcuz2gFjhteeemTdicGVFtzNGu700FHidfm8C2lkbavoWQF20fAQDeIWONulXJlRerUVrRNxzX1x7erzUXLNGclkYdGx3TVx/er7UfPEsLmnJ/tAu1CfSj2wfZVndYEh0AgoXAGnXJi5UXC6lGacVYMqWH9vVOaqsnSZ99f/5e3IUC/mp3+/BiAmi9ozYeAIKFUhDUJbcrLxZTjRX10r24sxXrxZ1v5UQ/aqndrp6JYL2fAAACa9QptysvFpM9MXH3tefnXe47lbLqG4zp8MCI+gZjFV8SPUhLaJNtdS9I7ycAgFIQ1Cm3Ky86Uay0wm0pRDQa0ZnzZ2v76nMd9+IO0sqJdCJxLyjvJ7XyADCOjDXqUjnZXq95UQqR7sV9SnurFsxpcVQf7qYTiZfItnrD7/eTkHz6YQAADblJREFUziQAcBwZa9SlcrK9XvOiFCLMmcKgZFvhDp1JAOA4AmvULTcrL3rBbSlELXTVqHYnEniPWnkAOI5SEMAn7a1NuuXSKaUQlzovhaCrBoKAziQAcBwZa8AnqZRVY9To+gvP0symBo3Ek2qMGqVS1lHGmUwhgiBdKz/1zAm18gDqEYE1QivM9cXSeC/t//bNJ6aVgmxffa6jEhW6aiAIqJUHgOMIrBFKtVBf7LaXdi1kCsN+cIRx1MoDwDgCa4RSLXQicNtLO+yZwlo4OAIAIBuTFxFKtVBf7EUvbb97GLvB5EsAQK0hY41QqoX64iD00vZTLRwcYRwlPQAwrj5+wVFzamXVvnJWTqwVtGmrDay8CADHGWvD/+XX2dlpu7q6/B4GqowsWbhRY10b+gZjWrlh97SzR2Ga7wAApTDGdFtrO3NdRykIQotOBOEW9smXGEdJDwAcR2ANwDccHIVfLcx3AACv1E9BJ+CTVMqqbzCmwwMj6huMUXuKmlIr8x0AwAtkrIEKoo4YtY6SHgA4jow1UEG13quZbDykcPdTBwAvkbEGKqiWJ3bVSzae7jMAAKfIWAMVVMu9mms9Gy/RoxkAUBoCa6CCanliVy1n49Pq4eABAOAdSkGACqrliV310GatHg4eAADeIWMNVFitTuyq5Wx8Wi2X8gAAvMeS5gDKVusT++plgiYAwDmWNAdQEbW+cmItl/IAALxHYA0ABdT6wQMAwDvUWAMAAAAeILAGAAAAPEBgDQAAAHjAl8DaGPNhY8yvjDEpY0znlOv+yRjza2NMjzHmvX6MD6iWVMqqbzCmwwMj6huMsaIfAAAh5tfkxb2SPiRpc/aFxpglkj4m6S2SFkj6sTHmDGstqzGg5tDKDQCA2uJLxtpa+4y1tifHVRdKuttaG7PWPi/p15LOqe7ogOpguWwAAGpL0GqsT5J0MOvvQxOXTWOMWWWM6TLGdPX19VVlcICXWC4bAIDaUrHA2hjzY2PM3hz/Lix0txyX5Sw6tdZusdZ2Wms7Ozo6vBk0UEUslw0AQG2pWI21tfbdZdztkKSTs/5eKOmINyMCgqW9tUm3XNY5rca6vbXJ76EBAIAyBG3lxe9KussY80WNT148XdLj/g4JqAyWywYAoLb4ElgbY1ZK+pqkDkkPGGOetNa+11r7K2PMdkn7JCUk/TUdQVDLWC4bAIDa4Utgba3dIWlHnuu+IOkL1R0RAAAA4E7QuoIAAAAAoURgDQAAAHiAwBoAAADwAIE1AAAA4AECawAAAMADBNYAAACABwisAQAAAA8QWAMAAAAeILAGAAAAPEBgDQAAAHiAwBoAAADwQNTvAQBAPUskUuodimksmVJjQ0TzZjUrGiXnAQBhRGANAD5JJFJ69uigrryzW4cGRrWwrUWbLlmmM+fPJrgGgBDimxsAfNI7FMsE1ZJ0aGBUV97Zrd6hmM8jAwCUg4w1gNBKpaz6h+OKJ5JqijaovbVJkYjxe1iOjSVTmaA67dDAqBLJlE8jAgC4QWANIJRSKaueo4O64vauTBnFLZd1avH82aEJrhsbIlrY1jIpuF7Y1qJoAycTASCM+PYGEEr9w/FMUC2NZ3qvuL1L/cNxn0fm3LxZzdp0yTItbGuRpEyN9bxZzT6PDABQDjLWAEIpnkjmLKOIJ5I+jah00WhEZ86fre2rz1UimVKUriAAEGoE1gBCqSnakLOMoina4OOoSheNRrRgTovfwwAAeIC0CIBQam9t0i2XdU4qo7jlsk61tzb5PDIAQL0iYw0glCIRo8XzZ2vHVStC2xUEAFBbCKwBhFYkYtQxm4l+AIBgoBQEAAAA8ACBNQAAAOABAmsAAADAAwTWAAAAgAcIrAEAAAAPEFgDAAAAHiCwBgAAADxAYA0AAAB4gMAaAAAA8ACBNQAAAOABAmsAAADAAwTWAAAAgAcIrAEAAAAPEFgDAAAAHiCwBgAAADwQ9XsAQLkSiZR6h2IaS6bU2BDRvFnNikY5VgQAAP4gsEYoJRIpPXt0UFfe2a1DA6Na2NaiTZcs05nzZxNcAwAAX/gSgRhjPmyM+ZUxJmWM6cy6fJExZtQY8+TEv01+jA/B1zsUywTVknRoYFRX3tmt3qGYzyMDAAD1yq+M9V5JH5K0Ocd1B6y1Z1d5PAiZsWQqE1SnHRoYVSKZ8mlEAACg3vmSsbbWPmOt7fHjuVEbGhsiWtjWMumyhW0tijZQBgIAAPwRxCjkVGPMHmPMz4wx/8XvwSCY5s1q1qZLlmWC63SN9bxZzT6PDAAA1KuKlYIYY34s6U05rvrf1tr789ztJUmnWGv7jTHLJH3HGPMWa+1rOR5/laRVknTKKad4NWyERDQa0ZnzZ2v76nOVSKYUpSsIAADwWcUCa2vtu8u4T0xSbOL/u40xBySdIakrx223SNoiSZ2dndbdaBFG0WhEC+a0FL8hAABAFQQqvWeM6TDGNEz8//8j6XRJv/F3VAAAAEBxfrXbW2mMOSTpXEkPGGN+OHHVn0h6yhjzS0n3SLrSWvuKH2MEAAAASuFLuz1r7Q5JO3Jcfq+ke6s/IgAAAMCdQJWCAAAAAGFFYA0AAAB4gMAaAAAA8ACBNQAAAOABAmsAAADAAwTWAAAAgAcIrAEAAAAPGGvDvxq4MaZP0ot+j6NMcyW97PcgQo5t6B7b0D22oXtsQ/fYhu6xDd2r9W34ZmttR64raiKwDjNjTJe1ttPvcYQZ29A9tqF7bEP32IbusQ3dYxu6V8/bkFIQAAAAwAME1gAAAIAHCKz9t8XvAdQAtqF7bEP32IbusQ3dYxu6xzZ0r263ITXWAAAAgAfIWAMAAAAeILCuImPMrcaYXmPM3qzL3miM+ZEx5rmJ/7b5Ocagy7MN1xpjDhtjnpz49xd+jjHIjDEnG2N+aox5xhjzK2PM305czn7oUIFtyH7okDFmhjHmcWPMLye24XUTl59qjPnFxH64zRjT5PdYg6rANtxqjHk+az882++xBp0xpsEYs8cYs3Pib/bDEuXYhnW7HxJYV9dWSe+bctk/SnrYWnu6pIcn/kZ+WzV9G0rSl6y1Z0/8+36VxxQmCUl/Z639fUnLJf21MWaJ2A9LkW8bSuyHTsUk/am19q2Szpb0PmPMckk3aHwbni5pQNKnfRxj0OXbhpJ0TdZ++KR/QwyNv5X0TNbf7Ielm7oNpTrdDwmsq8ha+3NJr0y5+EJJt038/22S/mtVBxUyebYhHLLWvmSt/c+J/x/U+BfhSWI/dKzANoRDdtzQxJ+NE/+spD+VdM/E5eyHBRTYhiiBMWahpPdL+vrE30bshyWZug3rHYG1/+Zba1+Sxn+wJc3zeTxhdbUx5qmJUhHKGBwwxiyS9DZJvxD7YVmmbEOJ/dCxiVPHT0rqlfQjSQckHbPWJiZuckgcsBQ0dRtaa9P74Rcm9sMvGWOafRxiGHxZ0j9ISk383S72w1JN3YZpdbkfElijFmyUdJrGT4e+JOkmf4cTfMaYWZLulfQ/rbWv+T2eMMqxDdkPS2CtTVprz5a0UNI5kn4/182qO6pwmboNjTFnSfonSWdK+kNJb5R0rY9DDDRjzAWSeq213dkX57gp+2EeebahVMf7IYG1/44aY06UpIn/9vo8ntCx1h6d+IFJSbpF4z/SyMMY06jxgPDfrLX3TVzMfliCXNuQ/bA81tpjknZpvF59jjEmOnHVQklH/BpXmGRtw/dNlCpZa21M0jfFfljICkkfNMa8IOlujZeAfFnsh6WYtg2NMXfW835IYO2/70r61MT/f0rS/T6OJZTSAeGElZL25rttvZuoH/yGpGestV/Muor90KF825D90DljTIcxZs7E/7dIerfGa9V/KuniiZuxHxaQZxs+m3WAbDReG8x+mIe19p+stQuttYskfUzST6y1nxT7oWN5tuEl9bwfRovfBF4xxnxL0nmS5hpjDkn6nKR/lbTdGPNpSb+V9GH/Rhh8ebbheROtfKykFySt9m2AwbdC0qWSnp6ozZSk/1fsh6XItw0/zn7o2ImSbjPGNGg8wbPdWrvTGLNP0t3GmM9L2qPxAxjklm8b/sQY06HxkoYnJV3p5yBD6lqxH7r1b/W6H7LyIgAAAOABSkEAAAAADxBYAwAAAB4gsAYAAAA8QGANAAAAeIDAGgAAAPAAgTUAAADgAQJrAAAAwAMsEAMANcYYs0jSg5L+Q+NLhf9S48sKXydpnqRPSvoLSadJOknSyZLWWWtvMcZEJN0s6Z2Sntd4AuZWa+091X0VABA+BNYAUJt+T+MraK6S9ISkT0j6Y0kf1PhKkU9KWqrxwLtV0h5jzAOS3iFpkaQ/0HgQ/oykW6s8dgAIJUpBAKA2PW+tfdpam5L0K0kP2/Gldp/WeOAsSfdba0ettS9L+qmkczQefH/bWpuy1v5u4nIAgAME1gBQm2JZ/5/K+jul42cr7ZT7WEmmwuMCgJpFYA0A9etCY8wMY0y7pPM0XjLyH5IuMsZEjDHzJy4HADhAjTUA1K/HJT0g6RRJ11trjxhj7pX0Lkl7Je2X9AtJr/o3RAAIDzNecgcAqCfGmLWShqy1N+a4bpa1dmgik/24pBUT9dYAgALIWAMAptppjJkjqUnjmWyCagBwgIw1AAAA4AEmLwIAAAAeILAGAAAAPEBgDQAAAHiAwBoAAADwAIE1AAAA4AECawAAAMAD/xf5r/OThxackgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "error_2 = auto['mpg'] - pred_2\n",
    "\n",
    "plt.figure(figsize = (12,6))\n",
    "sns.scatterplot(x = auto['mpg'],y = error_2)\n",
    "plt.axhline(y = 0,linestyle = 'dashed',color = 'black',linewidth = 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "# we can see the that the former graph has kind of U pattern, and thus it does not follow a linear relationship,\n",
    "# on the other hand the latter graph has no such kind of definate pattern, and is dispersed quite well"
   ]
  },
  {
   "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
}