LINEAR REGRESSION-checkpoint.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "45de829d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sn\n",
    "import statsmodels.formula.api as smf\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22ada68b",
   "metadata": {},
   "source": [
    "# Question 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "d423d4fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "d_1=pd.read_csv(\"delivery_time.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51d2039a",
   "metadata": {},
   "source": [
    "### EDA AND VISUALISATION OF DATA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "2900416f",
   "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>Delivery Time</th>\n",
       "      <th>Sorting Time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>21.00</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.50</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.75</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>24.00</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>29.00</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Delivery Time  Sorting Time\n",
       "0          21.00            10\n",
       "1          13.50             4\n",
       "2          19.75             6\n",
       "3          24.00             9\n",
       "4          29.00            10"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "ced39492",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 21 entries, 0 to 20\n",
      "Data columns (total 2 columns):\n",
      " #   Column         Non-Null Count  Dtype  \n",
      "---  ------         --------------  -----  \n",
      " 0   Delivery Time  21 non-null     float64\n",
      " 1   Sorting Time   21 non-null     int64  \n",
      "dtypes: float64(1), int64(1)\n",
      "memory usage: 464.0 bytes\n"
     ]
    }
   ],
   "source": [
    "d_1.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "c868b7f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Delivery Time    0\n",
       "Sorting Time     0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#checking null values\n",
    "d_1.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b4b86a9",
   "metadata": {},
   "source": [
    "#### NO null values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "d99b0122",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    21.000000\n",
       "mean      6.190476\n",
       "std       2.542028\n",
       "min       2.000000\n",
       "25%       4.000000\n",
       "50%       6.000000\n",
       "75%       8.000000\n",
       "max      10.000000\n",
       "Name: Sorting Time, dtype: float64"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Checking statatics of data\n",
    "d_1[\"Sorting Time\"].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "726a5530",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Sorting time')"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Checking for outliers\n",
    "sn.boxplot(d_1[\"Sorting Time\"])\n",
    "plt.xlabel(\"Sorting time\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3332c244",
   "metadata": {},
   "source": [
    "There are no outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "0c8c58c3",
   "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>Delivery Time</th>\n",
       "      <th>Sorting Time</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [Delivery Time, Sorting Time]\n",
       "Index: []"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Checking for Duplicate values\n",
    "d_1[d_1.duplicated()]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec0110ce",
   "metadata": {},
   "source": [
    "There are no duplicate Values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "id": "bbdfbf30",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Delivery Time', ylabel='Sorting Time'>"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting Dependent and Independent variables\n",
    "sn.scatterplot(d_1.iloc[:,0],d_1.iloc[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "id": "71be33e3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Renaming the columns\n",
    "d_1=d_1.rename({\"Delivery Time\":\"d_t\",\"Sorting Time\":\"s_t\"},axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "id": "ec72fdd7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16cddd3be80>"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#checking distribution of variables\n",
    "sn.distplot(d_1.s_t)\n",
    "sn.distplot(d_1.d_t)\n",
    "labels=(\"Sorting Time\",\"Delivery Time\")\n",
    "plt.legend(labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6dbcb4f6",
   "metadata": {},
   "source": [
    "### Observations:\n",
    "1.Delivery Time is almost normally distributed\n",
    "\n",
    "2.Sorting Time is normally distributed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "222b5980",
   "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>d_t</th>\n",
       "      <th>s_t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>d_t</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.825997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>s_t</th>\n",
       "      <td>0.825997</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          d_t       s_t\n",
       "d_t  1.000000  0.825997\n",
       "s_t  0.825997  1.000000"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ckecking co relation.\n",
    "d_1.corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea269126",
   "metadata": {},
   "source": [
    "## Model Building"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c3e00f2d",
   "metadata": {},
   "source": [
    "## 1.Without Transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "927c4b02",
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Building model \n",
    "model_1=smf.ols(\"d_t~s_t\",data=d_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "36c46162",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Intercept    6.582734\n",
       "s_t          1.649020\n",
       "dtype: float64"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# checking the cpoefficients of the equation of cost function\n",
    "model_1.params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "id": "dbe21b2e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tvalue= \n",
      " Intercept    3.823349\n",
      "s_t          6.387447\n",
      "dtype: float64 \n",
      " pvalue: \n",
      " Intercept    0.001147\n",
      "s_t          0.000004\n",
      "dtype: float64\n"
     ]
    }
   ],
   "source": [
    "print(\"tvalue=\",\"\\n\",model_1.tvalues,\"\\n\",\"pvalue:\",\"\\n\",model_1.pvalues)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f71a2f76",
   "metadata": {},
   "source": [
    "p values for intercept and sorting time coefficient is also less than 0.05."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "id": "a709ac13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>d_t</td>       <th>  R-squared:         </th> <td>   0.682</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.666</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   40.80</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>3.98e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:07:54</td>     <th>  Log-Likelihood:    </th> <td> -51.357</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>   106.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>   108.8</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>    6.5827</td> <td>    1.722</td> <td>    3.823</td> <td> 0.001</td> <td>    2.979</td> <td>   10.186</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>s_t</th>       <td>    1.6490</td> <td>    0.258</td> <td>    6.387</td> <td> 0.000</td> <td>    1.109</td> <td>    2.189</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 3.649</td> <th>  Durbin-Watson:     </th> <td>   1.248</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.161</td> <th>  Jarque-Bera (JB):  </th> <td>   2.086</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.750</td> <th>  Prob(JB):          </th> <td>   0.352</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.367</td> <th>  Cond. No.          </th> <td>    18.3</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                    d_t   R-squared:                       0.682\n",
       "Model:                            OLS   Adj. R-squared:                  0.666\n",
       "Method:                 Least Squares   F-statistic:                     40.80\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           3.98e-06\n",
       "Time:                        15:07:54   Log-Likelihood:                -51.357\n",
       "No. Observations:                  21   AIC:                             106.7\n",
       "Df Residuals:                      19   BIC:                             108.8\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      6.5827      1.722      3.823      0.001       2.979      10.186\n",
       "s_t            1.6490      0.258      6.387      0.000       1.109       2.189\n",
       "==============================================================================\n",
       "Omnibus:                        3.649   Durbin-Watson:                   1.248\n",
       "Prob(Omnibus):                  0.161   Jarque-Bera (JB):                2.086\n",
       "Skew:                           0.750   Prob(JB):                        0.352\n",
       "Kurtosis:                       3.367   Cond. No.                         18.3\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_1.summary()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "555beb59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'r square:0.6822714748417231,adj r square:0.6655489208860244'"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'r square:{model_1.rsquared},adj r square:{model_1.rsquared_adj}'"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd58c7fc",
   "metadata": {},
   "source": [
    "### The Accuracy is only around 66%. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "id": "94b51e6d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='s_t', ylabel='d_t'>"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line in the No Transformation case\n",
    "plt.plot(d_1.s_t,model_1.params[0]+model_1.params[1]*(d_1.s_t),\"r\")\n",
    "sn.scatterplot(d_1.s_t,d_1.d_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7c2f917",
   "metadata": {},
   "source": [
    "## 2.With log Transformation to X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "2291430f",
   "metadata": {},
   "outputs": [],
   "source": [
    "x=d_1.s_t\n",
    "y=d_1.d_t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "id": "d6a55127",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Applying Log Transformation to only X\n",
    "log_x=np.log(d_1.s_t)\n",
    "d_1[\"log_x\"]=log_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "id": "744720a3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16cddd7b910>"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting original and Log Transformed Data\n",
    "sn.distplot(x)\n",
    "sn.distplot(log_x)\n",
    "labels=(\"Original\",\"Log Transformed\")\n",
    "plt.legend(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "73739720",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model_2=smf.ols(\"d_t~log_x\",data=d_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "id": "868af518",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='s_t', ylabel='d_t'>"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line in the LOG Transformation case\n",
    "plt.plot(log_x,model_2.params[0]+model_2.params[1]*(log_x),\"r\")\n",
    "sn.scatterplot(log_x,d_1.d_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "id": "c05ab3d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>           <td>d_t</td>       <th>  R-squared:         </th> <td>   0.695</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.679</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   43.39</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>2.64e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:07:56</td>     <th>  Log-Likelihood:    </th> <td> -50.912</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>   105.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>   107.9</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>    1.1597</td> <td>    2.455</td> <td>    0.472</td> <td> 0.642</td> <td>   -3.978</td> <td>    6.297</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_x</th>     <td>    9.0434</td> <td>    1.373</td> <td>    6.587</td> <td> 0.000</td> <td>    6.170</td> <td>   11.917</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 5.552</td> <th>  Durbin-Watson:     </th> <td>   1.427</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.062</td> <th>  Jarque-Bera (JB):  </th> <td>   3.481</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.946</td> <th>  Prob(JB):          </th> <td>   0.175</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.628</td> <th>  Cond. No.          </th> <td>    9.08</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                    d_t   R-squared:                       0.695\n",
       "Model:                            OLS   Adj. R-squared:                  0.679\n",
       "Method:                 Least Squares   F-statistic:                     43.39\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           2.64e-06\n",
       "Time:                        15:07:56   Log-Likelihood:                -50.912\n",
       "No. Observations:                  21   AIC:                             105.8\n",
       "Df Residuals:                      19   BIC:                             107.9\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      1.1597      2.455      0.472      0.642      -3.978       6.297\n",
       "log_x          9.0434      1.373      6.587      0.000       6.170      11.917\n",
       "==============================================================================\n",
       "Omnibus:                        5.552   Durbin-Watson:                   1.427\n",
       "Prob(Omnibus):                  0.062   Jarque-Bera (JB):                3.481\n",
       "Skew:                           0.946   Prob(JB):                        0.175\n",
       "Kurtosis:                       3.628   Cond. No.                         9.08\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc3f6e2c",
   "metadata": {},
   "source": [
    "### The accuracy has increased to 67%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf809daf",
   "metadata": {},
   "source": [
    "## 3.With log Transformation to Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "cc322ac0",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Applying Log Transformation to only y\n",
    "log_y=np.log(d_1.d_t)\n",
    "d_1[\"log_y\"]=log_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "id": "b6ce00ab",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16cdc4b4550>"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting original and Log Transformed Data\n",
    "sn.distplot(y)\n",
    "sn.distplot(log_y)\n",
    "labels=(\"Original\",\"Log Transformed\")\n",
    "plt.legend(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "id": "00c8ee93",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model_3=smf.ols(\"log_y~s_t\",data=d_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "f98d0bee",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='s_t', ylabel='d_t'>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line in the LOG Transformation case\n",
    "plt.plot(d_1.s_t,model_3.params[0]+model_3.params[1]*(d_1.s_t),\"r\")\n",
    "sn.scatterplot(d_1.s_t,log_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "51540f6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>log_y</td>      <th>  R-squared:         </th> <td>   0.711</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.696</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   46.73</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>1.59e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:07:58</td>     <th>  Log-Likelihood:    </th> <td>  7.7920</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>  -11.58</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>  -9.495</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>    2.1214</td> <td>    0.103</td> <td>   20.601</td> <td> 0.000</td> <td>    1.906</td> <td>    2.337</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>s_t</th>       <td>    0.1056</td> <td>    0.015</td> <td>    6.836</td> <td> 0.000</td> <td>    0.073</td> <td>    0.138</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.238</td> <th>  Durbin-Watson:     </th> <td>   1.325</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.538</td> <th>  Jarque-Bera (JB):  </th> <td>   0.544</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.393</td> <th>  Prob(JB):          </th> <td>   0.762</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.067</td> <th>  Cond. No.          </th> <td>    18.3</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                  log_y   R-squared:                       0.711\n",
       "Model:                            OLS   Adj. R-squared:                  0.696\n",
       "Method:                 Least Squares   F-statistic:                     46.73\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           1.59e-06\n",
       "Time:                        15:07:58   Log-Likelihood:                 7.7920\n",
       "No. Observations:                  21   AIC:                            -11.58\n",
       "Df Residuals:                      19   BIC:                            -9.495\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      2.1214      0.103     20.601      0.000       1.906       2.337\n",
       "s_t            0.1056      0.015      6.836      0.000       0.073       0.138\n",
       "==============================================================================\n",
       "Omnibus:                        1.238   Durbin-Watson:                   1.325\n",
       "Prob(Omnibus):                  0.538   Jarque-Bera (JB):                0.544\n",
       "Skew:                           0.393   Prob(JB):                        0.762\n",
       "Kurtosis:                       3.067   Cond. No.                         18.3\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_3.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5c3d57d9",
   "metadata": {},
   "source": [
    "#### The accuracy Has increased to 69%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca601828",
   "metadata": {},
   "source": [
    "## 4. With log Transformation to X and Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "2527d7cd",
   "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>d_t</th>\n",
       "      <th>s_t</th>\n",
       "      <th>log_x</th>\n",
       "      <th>log_y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>21.00</td>\n",
       "      <td>10</td>\n",
       "      <td>2.302585</td>\n",
       "      <td>3.044522</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.50</td>\n",
       "      <td>4</td>\n",
       "      <td>1.386294</td>\n",
       "      <td>2.602690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>19.75</td>\n",
       "      <td>6</td>\n",
       "      <td>1.791759</td>\n",
       "      <td>2.983153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>24.00</td>\n",
       "      <td>9</td>\n",
       "      <td>2.197225</td>\n",
       "      <td>3.178054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>29.00</td>\n",
       "      <td>10</td>\n",
       "      <td>2.302585</td>\n",
       "      <td>3.367296</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     d_t  s_t     log_x     log_y\n",
       "0  21.00   10  2.302585  3.044522\n",
       "1  13.50    4  1.386294  2.602690\n",
       "2  19.75    6  1.791759  2.983153\n",
       "3  24.00    9  2.197225  3.178054\n",
       "4  29.00   10  2.302585  3.367296"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "3086dcf3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model_4=smf.ols(\"log_y~log_x\",data=d_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "207e1ee9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='s_t', ylabel='d_t'>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line in the LOG Transformation case\n",
    "plt.plot(log_x,model_4.params[0]+model_4.params[1]*(log_x),\"r\")\n",
    "sn.scatterplot(log_x,log_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "d283cef3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>log_y</td>      <th>  R-squared:         </th> <td>   0.772</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.760</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   64.39</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>1.60e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:08:00</td>     <th>  Log-Likelihood:    </th> <td>  10.291</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>  -16.58</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>  -14.49</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>    1.7420</td> <td>    0.133</td> <td>   13.086</td> <td> 0.000</td> <td>    1.463</td> <td>    2.021</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_x</th>     <td>    0.5975</td> <td>    0.074</td> <td>    8.024</td> <td> 0.000</td> <td>    0.442</td> <td>    0.753</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.871</td> <th>  Durbin-Watson:     </th> <td>   1.322</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.392</td> <th>  Jarque-Bera (JB):  </th> <td>   1.170</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.577</td> <th>  Prob(JB):          </th> <td>   0.557</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.916</td> <th>  Cond. No.          </th> <td>    9.08</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                  log_y   R-squared:                       0.772\n",
       "Model:                            OLS   Adj. R-squared:                  0.760\n",
       "Method:                 Least Squares   F-statistic:                     64.39\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           1.60e-07\n",
       "Time:                        15:08:00   Log-Likelihood:                 10.291\n",
       "No. Observations:                  21   AIC:                            -16.58\n",
       "Df Residuals:                      19   BIC:                            -14.49\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      1.7420      0.133     13.086      0.000       1.463       2.021\n",
       "log_x          0.5975      0.074      8.024      0.000       0.442       0.753\n",
       "==============================================================================\n",
       "Omnibus:                        1.871   Durbin-Watson:                   1.322\n",
       "Prob(Omnibus):                  0.392   Jarque-Bera (JB):                1.170\n",
       "Skew:                           0.577   Prob(JB):                        0.557\n",
       "Kurtosis:                       2.916   Cond. No.                         9.08\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_4.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e69cc7e",
   "metadata": {},
   "source": [
    "### Accuracy has increased to 76%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9ab812c5",
   "metadata": {},
   "source": [
    "## 5.With Square Root Transformation "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "479f4ada",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Applying SQUAREROOT TRANSFORMATION\n",
    "sq_x=np.sqrt(x)\n",
    "d_1[\"sq_x\"]=sq_x\n",
    "sq_y=np.sqrt(y)\n",
    "d_1[\"sq_y\"]=sq_y\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "3c6a9fb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16cddfaeb80>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEkCAYAAAAivzZ6AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAA490lEQVR4nO3deXxcZb348c83k2Wy713SNE1Xujd0BSlStlIWKYgICAIqVOSC6E+9oHK9/NCLcPUnei9ILYKAIFVWK1TZdwp0odB939KUZmmTNvv2/f1xJmGaJu0kzZkzzXzfr9e8zsw5z5zznWl6vvM8z3meI6qKMcaY6BXjdQDGGGO8ZYnAGGOinCUCY4yJcpYIjDEmylkiMMaYKGeJwBhjopwlAhP1RORKEXnZg+OuEZFZ4T6uMR2JjSMwkU5EZgL/DYwDWoB1wPdUdWkP9lUIbAPiVLW5N+Ps5FjVQS+TgAac+AG+rapPuHl8Y0IV63UAxhyJiKQBLwDfAf4GxAOn4pxUu7uvsP69q2pK0LG3A9ep6qvhjMGYUFjTkIl0owBU9UlVbVHVOlV9WVU/BRCRGBG5XUR2iEipiDwmIumBbYUioiLyLRHZCbwOvB3Yb6WIVIvIySJyrYi823bAwHtuEJFNIrJfRO4XEQls84nI/xORchHZJiI3Bcp3O8mIyHYROSvw/A4ReUpEHheRgyKySkRGiciPA59rl4jMDnpvuog8JCJ7RGS3iPxCRHw9/I5NlLNEYCLdRqBFRB4VkXNFJLPD9msDj9OBYUAKcF+HMqcBY4BzgC8G1mWoaoqqLuniuBcA04BJwFcD7wW4HjgXKAImAxf15EN14UvAn4FM4GPgJZz/o4OAO4E/BJV9FGgGRgAnArOB63oxFhNFLBGYiKaqB4CZgAIPAmUiskhE+geKXAn8RlW3qmo18GPg8g6/0O9Q1RpVrevGoe9W1UpV3Qm8gXPiBycp/E5Vi1V1P3B3zz/dYd5R1ZcCfRdPAbmBOJqAhUChiGQEPvu5OP0kNapaCtwLXN6LsZgoYn0EJuKp6jqcX/2IyGjgceC3wBVAHrAjqPgOnL/r/kHrdvXgsJ8FPa/FqWkQOF7w/nqy767sDXpeB5SrakvQawJx5AFxwJ5AixU4P+p6MxYTRSwRmOOKqq4XkUeAbwdWlQBDgooU4DSZ7AXy294WvItjDGFP0H4BBh/j/npiF05neY7bVz6Z6GBNQyaiichoEfmBiOQHXg/GqQl8ECjyJPB9ERkqIinAXcBfj3CCLANacfoTeuJvwC0iMkhEMoBbe7ifHlPVPcDLwP8TkbRAh/lwETkt3LGYvsESgYl0B4EZwIciUoOTAFYDPwhsfxing/VtnPEB9cDNXe1MVWuB/wLeE5FKETmpm/E8iHMS/hSnQ3cxTg2k5UhvcsHVOJfSrgX2A08DA8Mcg+kjbECZMcdARM4F5qvqkKMWNiZCWY3AmG4QkUQROU9EYkVkEPCfwHNex2XMsbAagTHdICJJwFvAaJwreV4Ebglc5mrMcckSgTHGRDlrGjLGmChnicAYY6KcJQJjjIlylgiMMSbKWSIwxpgoZ4nAGGOinCUCY4yJcpYIjDEmylkiMMaYKGeJwBhjopwlAmOMiXKWCIwxJspZIjDGmChnicAYY6KcJQJjjIlysV4H0F05OTlaWFjodRjGGHNcWb58ebmq5na27bhLBIWFhSxbtszrMIwx5rgiIju62mZNQ8YYE+UsERhjTJSzRGCMMVHuuOsjMOZ40dTURHFxMfX19V6HYqKI3+8nPz+fuLi4kN9jicAYlxQXF5OamkphYSEi4nU4JgqoKhUVFRQXFzN06NCQ32dNQ8a4pL6+nuzsbEsCJmxEhOzs7G7XQi0RGOMiSwIm3HryN2eJwJg+rLi4mLlz5zJy5EiGDx/OLbfcQmNj42HlSkpK+MpXvnLU/Z133nlUVlb2KJY77riDX//61z16r3GX9RGY3rXsT6GXnfoN9+IwqCpf/vKX+c53vsPf//53WlpamDdvHj/96U/51a9+1V6uubmZvLw8nn766aPuc/HixW6GbDziao1AROaIyAYR2Swit3WyPV1E/iEin4jIGhGxM4MxveT111/H7/fzjW84/618Ph/33nsvDz/8ML///e+59NJL+dKXvsTs2bPZvn0748ePB6C2tpavfvWrTJw4kcsuu4wZM2a0j+YvLCykvLyc7du3M2bMGK6//nrGjRvH7NmzqaurA+DBBx9k2rRpTJo0iUsuuYTa2lpvvgATMtdqBCLiA+4HzgaKgaUiskhV1wYV+zdgrap+SURygQ0i8oSqHl53NeY49n//sYa1JQd6dZ9j89L4zy+N63L7mjVrmDJlyiHr0tLSKCgooLm5mSVLlvDpp5+SlZXF9u3b28v8/ve/JzMzk08//ZTVq1dTVFTU6f43bdrEk08+yYMPPshXv/pVnnnmGa666iq+/OUvc/311wNw++2389BDD3HzzTcf8+c17nGzRjAd2KyqWwMn9oXA3A5lFEgVp3cjBdgHNLsYkzFRQ1U77ThsW3/22WeTlZV12PZ3332Xyy+/HIDx48czceLETvc/dOjQ9iQxZcqU9mSyevVqTj31VCZMmMATTzzBmjVreucDGde42UcwCNgV9LoYmNGhzH3AIqAESAUuU9VWF2MyxhNH+uXulnHjxvHMM88csu7AgQPs2rULn89HcnJyp+9T1ZD2n5CQ0P7c5/O1Nw1de+21PP/880yaNIlHHnmEN998s2cfwISNmzWCzq5h6vgXdg6wEsgDioD7RCTtsB2JzBORZSKyrKysrLfjNKZPOvPMM6mtreWxxx4DoKWlhR/84Adce+21JCUldfm+mTNn8re//Q2AtWvXsmrVqm4d9+DBgwwcOJCmpiaeeOKJnn8AEzZuJoJiYHDQ63ycX/7BvgE8q47NwDZgdMcdqeoCVZ2qqlNzczudTtsY04GI8Nxzz/HUU08xcuRIRo0ahd/v56677jri+2688UbKysqYOHEi99xzDxMnTiQ9PT3k4/785z9nxowZnH322Ywefdh/ZxOBJNRqYLd3LBILbATOBHYDS4GvqeqaoDIPAHtV9Q4R6Q+sACapanlX+506dara/QgimF0+2m7dunWMGTPG6zC6raWlhaamJvx+P1u2bOHMM89k48aNxMfHex2aCVFnf3sislxVp3ZW3rU+AlVtFpGbgJcAH/Cwqq4RkRsC2+cDPwceEZFVOE1Jtx4pCRhj3FdbW8vpp59OU1MTqsoDDzxgSaCPc3VAmaouBhZ3WDc/6HkJMNvNGIwx3ZOammp3AYwyNsWEMcZEOUsExhgT5SwRGGNMlLNEYIwxUc4SgTF92H/9138xbtw4Jk6cSFFRER9++KHXIfWKrsZCzJgxg6KiIgoKCsjNzaWoqIiioqJD5lLqLWVlZcyYMYMTTzyRd955p9f3H4prr702pFljj8amoTamj1qyZAkvvPACK1asICEhgfLy8k7vRdCbWlpa8Pl8rr/nrrvu4ic/+clh69sS3SOPPMKyZcu47777Dtne3NxMbGzvnPZee+01Ro8ezaOPPhrye3ryWcPBagTG9FF79uwhJyenfU6gnJwc8vLyAPjXv/7F6NGjmTlzJt/97ne54IILgMNvHjN+/Pj2X9MXXXQRU6ZMYdy4cSxYsKC9TEpKCj/72c+YMWMGS5Ys4fHHH2f69OkUFRXx7W9/m5aWlsNiKyws5M4772TmzJk89dRTPPnkk0yYMIHx48dz6623tpfrbP1tt91GXV0dRUVFXHnllUf9Hu644w7mzZvH7Nmzufrqq9m+fTunnnoqkydPZvLkybz//vsAvPnmm8yaNYuvfOUrjB49miuvvLJ93qXbbruNsWPHMnHiRH74wx+ycuVK/v3f/53FixdTVFREXV1dl5+h4/eTkpLCrbfeypQpUzjrrLP46KOPmDVrFsOGDWPRokWAkzB+9KMfMW3aNCZOnMgf/vAHwJkH6qabbmLs2LGcf/75lJaWHvXzh8JqBMaEwz9vg8+6N2fPUQ2YAOfe3eXm2bNnc+eddzJq1CjOOussLrvsMk477TTq6+u5/vrref311xkxYgSXXXZZSId7+OGHycrKoq6ujmnTpnHJJZeQnZ1NTU0N48eP584772TdunXcc889vPfee8TFxXHjjTfyxBNPcPXVVx+2P7/fz7vvvktJSQknnXQSy5cvJzMzk9mzZ/P8888zffp0br311sPW33333dx3332sXLky5K9q+fLlvPvuuyQmJlJbW8srr7yC3+9n06ZNXHHFFe3jJj7++GPWrFlDXl4ep5xyCu+99x5jx47lueeeY/369YgIlZWVZGRkcOedd7bXOkpKSjqN9aKLLjrk+wGoqalh1qxZ3HPPPVx88cXcfvvtvPLKK6xdu5ZrrrmGCy+8kIceeoj09HSWLl1KQ0MDp5xyCrNnz+bjjz9mw4YNrFq1ir179zJ27Fi++c1vhvw9dMVqBMb0USkpKSxfvpwFCxaQm5vLZZddxiOPPML69esZOnQoI0eORES46qqrQtrf//zP/zBp0iROOukkdu3axaZNmwBn5tFLLrkEcJpLli9fzrRp0ygqKuK1115j69atne6vLQEtXbqUWbNmkZubS2xsLFdeeSVvv/12l+t74sILLyQxMRGApqYmrr/+eiZMmMCll17K2rWf3yJl+vTp5OfnExMT0963kJaWht/v57rrruPZZ5/tdMK+I8Ua/P0AxMfHM2fOHAAmTJjAaaedRlxcHBMmTGivfb388ss89thjFBUVMWPGDCoqKti0aRNvv/02V1xxBT6fj7y8PM4444wefR8dWY3AmHA4wi93N/l8PmbNmsWsWbOYMGECjz76KEVFRV3e4Dw2NpbW1s9ngq+vrwecZpNXX32VJUuWkJSUxKxZs9q3+f3+9nZvVeWaa67hl7/85VFja5sGu6v5znpzHrTgKbfvvfde+vfvzyeffEJrayt+v799W8eptdv6FD766CNee+01Fi5cyH333cfrr78ecqzB3w9AXFxc+/cfExPTfsyYmBiam5vb9/e///u/nHPOOYfsa/HixT26Of3RWI3AmD5qw4YN7b/aAVauXMmQIUMYPXo027ZtY8uWLYDTDt+msLCQFStWALBixQq2bdsGQFVVFZmZmSQlJbF+/Xo++OCDTo955pln8vTTT7e3Xe/bt48dO3YcMc4ZM2bw1ltvUV5eTktLC08++SSnnXZal+vBOZk2NTX16Hupqqpi4MCBxMTE8Oc//7nTPoxg1dXVVFVVcd555/Hb3/620yapI8XaE+eccw4PPPBA+2fcuHEjNTU1fPGLX2ThwoW0tLSwZ88e3njjjR4fI5jVCIzpo6qrq7n55puprKwkNjaWESNGsGDBAvx+PwsWLOD8888nJyeHmTNnsnr1agAuueSS9iaJadOmMWrUKADmzJnD/PnzmThxIieccAInnXRSp8ccO3Ysv/jFL5g9ezatra3ExcVx//33M2TIkC7jHDhwIL/85S85/fTTUVXOO+885s51bmbY1fp58+YxceJEJk+e3O17Htx4441ccsklPPXUU5x++uld3qCnzcGDB5k7dy719fWoKvfee2+3PkNPXHfddWzfvp3JkyejquTm5vL8889z8cUX8/rrrzNhwgRGjRp1TMkmmGvTULvFpqGOcDYNdbvjZRrqN998k1//+te88MILXodiekl3p6G2piFjjIly1jRkTJRr60w20ctqBMYYE+VcTQQiMkdENojIZhG5rZPtPxKRlYHHahFpEZEsN2MyJpyOtz44c/zryd+ca4lARHzA/cC5wFjgChEZG1xGVX+lqkWqWgT8GHhLVfe5FZMx4eT3+6moqLBkYMJGVamoqDhkbEQo3OwjmA5sVtWtACKyEJgLrO2i/BXAk11sM+a4k5+fT3FxMWVlZV6HYqKI3+8nPz+/W+9xMxEMAnYFvS4GZnRWUESSgDnATS7GY0xYxcXFMXToUK/DMOao3Owj6GwcdFd15C8B73XVLCQi80RkmYgss19XxhjTu9xMBMXA4KDX+UBJF2Uv5wjNQqq6QFWnqurU3NzcXgzRGGOMm4lgKTBSRIaKSDzOyX5Rx0Iikg6cBvzdxViMMcZ0wbU+AlVtFpGbgJcAH/Cwqq4RkRsC2+cHil4MvKyqNW7FYowxpmuujixW1cXA4g7r5nd4/QjwiJtxGGOM6ZqNLDbGmChnicAYY6KcJQJjjIlylgiMMSbKWSIwxpgoZ4nAGGOinCUCY4yJcpYIjDEmylkiMMaYKGeJwBhjopwlAmOMiXKWCIwxJspZIjDGmChnicAYY6KcJQJjjIlylghM72luhO3vwI4l0NridTTGmBC5mghEZI6IbBCRzSJyWxdlZonIShFZIyJvuRmPcdmL34fVz8Cqv8K6w+5KaoyJUK7doUxEfMD9wNk4N7JfKiKLVHVtUJkM4PfAHFXdKSL93IrHuGzXUvj4cRhxFjTVw7a3oOAkSB3odWTGmKNws0YwHdisqltVtRFYCMztUOZrwLOquhNAVUtdjMe46YP7wZ8BI86GE86FmDjYahU8Y44HbiaCQcCuoNfFgXXBRgGZIvKmiCwXkatdjMe4pbEGNvwLJlwKsQkQnwx5RbBnJbQ0ex2dMeYo3EwE0sk67fA6FpgCnA+cA/yHiIw6bEci80RkmYgsKysr6/1IzbHZ/Bo018HYCz9fN/BEaK6H8g3exWWMCYmbiaAYGBz0Oh8o6aTMv1S1RlXLgbeBSR13pKoLVHWqqk7Nzc11LWDTQ+tfhMQsKPjC5+tyRjnNQ+UbvYvLGBMSNxPBUmCkiAwVkXjgcqDjpSR/B04VkVgRSQJmAOtcjMm4Ycd7MPSL4Au69sAXC1lDoWKTd3EZY0LiWiJQ1WbgJuAlnJP731R1jYjcICI3BMqsA/4FfAp8BPxRVVe7FZNxwYE9ULULBk8/fFv2CDhQAo3V4Y/LGBMy1y4fBVDVxcDiDuvmd3j9K+BXbsZhXFT8kbPM7ywRjHSWFVtg4GEtfsaYCGEji82x2fUR+OJh4MTDt6UPBvFB5c7wx2WMCZklAnNsipfCwCLnstGOfLGQNhCqisMeljEmdK42DZk+YtmfOl/f2gy7l0PhzK7LpA+GPZ+AKkhnVxQbY7xmNQLTc1W7nWSQUdh1mfQCaKqF2oqwhWWM6R5LBKbn9m93lpmFXZfJyHeW1jxkTMSyRGB6rnK7M79QYkbXZVIGAAIH94QnJmNMt1kiMD23f/uRawMAvjhIzoGDn4UjImNMD1giMD1TXwV1+4+eCMCpFVRbjcCYSGWJwPRMKP0DbVIHQE25zURqTISyRGB6Zv92iImF9Pyjl00dANoKNXa7CWMikSUC0zP7tztjBGJCGIqSOsBZVls/gTGRyBKB6b7WZmeiuVCahQCScpxlTblrIRljes4Sgem+qmInGYSaCGITICHdEoExEcoSgem+/ducZaiJAJxLSGstERgTiSwRmO6r2Oo09/jTQ39Pco7VCIyJUJYITPeowv6tkDWse+9LzoGGA9Dc4E5cxpges0RguqemFBprup8IkgL3mq4p6/2YjDHHxNVEICJzRGSDiGwWkds62T5LRKpEZGXg8TM34zG9oGKrs+xJjQCseciYCOTa/QhExAfcD5wNFANLRWSRqq7tUPQdVb3ArThML9u3GRJSITm3e+9rSwTWYWxMxHGzRjAd2KyqW1W1EVgIzHXxeMZt2gpl6yHnhO7fZCbW7yQQqxEYE3HcTASDgF1Br4sD6zo6WUQ+EZF/isg4F+Mxx6qq2Okf6DemZ+9PzIS6fb0bkzHmmLmZCDr7yagdXq8AhqjqJOB/gec73ZHIPBFZJiLLysqss9EzpWsBgdwTevb+xCxnxlJjTEQJKRGIyDMicr6IdCdxFAODg17nAyXBBVT1gKpWB54vBuJEJKfjjlR1gapOVdWpubndbJs2vWfPJ84gsviUnr0/MRPqKp1LUI0xESPUE/sDwNeATSJyt4iMDuE9S4GRIjJUROKBy4FFwQVEZICI09gsItMD8djNbSPRwT3OI29yz/eRmAmtTdBY3XtxGWOOWUhXDanqq8CrIpIOXAG8IiK7gAeBx1W1qZP3NIvITcBLgA94WFXXiMgNge3zga8A3xGRZqAOuFzVfi5GpN0rAIGBk3q+j8RMZ1m33+k4NsZEhJAvHxWRbOAq4OvAx8ATwEzgGmBWZ+8JNPcs7rBuftDz+4D7uhu0CbOWZti5xOkk9qf1fD/BiSCjoHdiM8Ycs5ASgYg8C4wG/gx8SVXb7jv4VxFZ5lZwJkLs+dhpzhn6xWPbT3AiMMZEjFBrBH8M/LpvJyIJqtqgqlNdiMtEClXY9jak9HfGDxyLuCTwxdslpMZEmFA7i3/RybolvRmIiVC7PnJuQlN4avcHkXUkEriEtLJXQjPG9I4j1ghEZADOILBEETmRz8cGpAFJLsdmIsGH851RwfnTemd/iRlWIzAmwhytaegc4FqcMQC/CVp/EPiJSzGZSHFgD6xbBENOce4y1hsSs5wahjEmYhwxEajqo8CjInKJqj4TpphMpFj+J2htcZqFeos/3ZmmoqW59/ZpjDkmR2saukpVHwcKReT/dNyuqr/p5G2mL2htgRWPwcizP585tDe03dWs4UDv7dMYc0yO1lmcHFimAKmdPExfteN9ZyTxpCt6d79t4xAaqnp3v8aYHjta09AfAsv/G55wTMRY/QzEJcOoc+DTv/XefttqBPVWIzAmUoQ66dx/i0iaiMSJyGsiUi4iV7kdnPFIayusf8FJAvHJRy/fHQlticBqBMZEilDHEcxW1QPABTizio4CfuRaVMZbpWucewuPPLv39x2fBOKzRGBMBAk1EcQFlucBT6qqXQjel215w1kOm9X7+5YYp5/AOouNiRihTjHxDxFZjzND6I0ikgvUuxeW8dTWNyB3NKTlubP/hDSrERgTQUKqEajqbcDJwNTAlNM12P2H+6bWFmdaicKZ7h3Dn241AmMiSMjTUANjcMYTBL/nsV6Ox3itbL0z02hvTSnRGX86VGx2b//GmG4JdRrqPwPDgZVAS2C1Yomg7ykOzCo+yMVJZf1p0FQLTXUQl+jecYwxIQm1RjAVGNvdu4eJyBzgdzh3KPujqt7dRblpwAfAZar6dHeOYXrZ7mXgz4Ds4e4do+0S0oOfQdZQ945jjAlJqFcNrQYGdGfHIuID7gfOBcYCV4jI2C7K3YNzS0vjtd0fw6Apxz7l9JH4gxKBMcZzodYIcoC1IvIR0NC2UlUvPMJ7pgObVXUrgIgsxOlgXtuh3M3AM4CLjdImJC1NUL4BRpzh7nESAtNMHNxz5HLGmLAINRHc0YN9DwKC5xsuBmYEFxCRQcDFwBlYIvDevq3Q0gj9Dqu49a62+YasRmBMRAgpEajqWyIyBBipqq+KSBJOu/+RdNa20LGP4bfAraraIkdoihCRecA8gIICu+m5a0oDlbV+Y9w9TlwSxMTCwRJ3j2OMCUmocw1dDzwN/CGwahDw/FHeVgwMDnqdD3T8nz8VWCgi24GvAL8XkYs67khVF6jqVFWdmpubG0rIpidK1zkjf3NGuXscEUhIheoyd49jjAlJqE1D/4bT5v8hgKpuEpF+R3nPUmCkiAwFdgOXA18LLqCq7ZeMiMgjwAuq+nyIMZneVroWsoaH55LOhFSoKXX/OMaYowo1ETSoamNb801gUNkRLyVV1WYRuQnnaiAf8LCqrhGRGwLb5/c8bOOK0nXu9w+0sRqBMREj1ETwloj8BOcm9mcDNwL/ONqbVHUxsLjDuk4TgKpeG2Isxg1NdU5n8fivhOd48amwf1t4jmWMOaJQxxHcBpQBq4Bv45zcb3crKOOBfdtAWyFnZHiOl5AKNeXOvQ+MMZ4K9aqhVhF5HnheVa0+3xdV7nSWmYXhOV5CCmgL1O3r3XsiG2O67Yg1AnHcISLlwHpgg4iUicjPwhOeCZu2RJARpstzEwK3vK62DmNjvHa0pqHvAacA01Q1W1WzcAaFnSIi33c7OBNGlTsg1g/JYbo8Nz6QCOzKIWM8d7REcDVwhaq29+oFpoy4KrDN9BVVuyB9sLtzDAVrqxHUlIfneMaYLh0tEcSp6mH/UwP9BHGdlDfHq8qd4WsWAmsaMiaCHC0RNPZwmznehDsRxCVBTJw1DRkTAY521dAkEensnoIC+F2Ix3ihoRpqK8KbCESc/ggbVGaM546YCFT1aBPLmb6gKjBJbDgTAUBKrtUIjIkAoQ4oM31Z+6WjQ8J73ORc6yMwJgJYIjDhH0PQJrkf1FjTkDFes0RgPh9DkHK0CWV7WUqukwi6dytsY0wvs0RgnBpBOMcQtEnu59wRrb4yvMc1xhzCEoEJ/6WjbdpqIHblkDGeCnUaatPXLPvT58/LN8KASYeuC4e26SxqSiHX5buiGWO6ZDWCaNfcAI01kJQV/mO31wjsyiFjvORqIhCROSKyQUQ2i8htnWyfKyKfishKEVkmIjPdjMd0om6fs0z0IBEkBxKBXTlkjKdcaxoSER9wP3A2zo3sl4rIIlVdG1TsNWCRqqqITAT+Box2KybTidpAIvCiRpCUBRJjicAYj7lZI5gObFbVraraCCwE5gYXUNVq1fZrB5M5yn2QjQu8rBHE+CAp25qGjPGYm4lgELAr6HVxYN0hRORiEVkPvAh808V4TGdq9zmTv7XNBhpuNqjMGM+5mQg6uyj9sF/8qvqcqo4GLgJ+3umOROYF+hCWlZXZSaNX1e2DxMzwjyFok2LTTBjjNTcTQTEwOOh1PlDSVWFVfRsYLiKH3cBWVReo6lRVnZqbG6Y7aEWL2n3e9A+0Se5nE88Z4zE3E8FSYKSIDBWReOByYFFwAREZIeL8FBWRyUA8UOFiTKajun3e9A+0SennDCizaSaM8YxrVw2parOI3AS8BPiAh1V1jYjcENg+H7gEuFpEmoA64LKgzmPjNi/HELRJ6QfNddBwEPxp3sVhTBRzdWSxqi4GFndYNz/o+T3APW7GYI7AyyuG2gSPJbBEYIwnbGRxNPNyDEGblECfj3UYG+MZSwTRLKJqBJYIjPGKJYJo5vUYArD5hoyJAJYIopnXYwgAknIAsUFlxnjIEkE083oMAYAvNjDNxF5v4zAmilkiiGZejyFo0zaWwBjjCUsE0SoSxhC0Sc61zmJjPGSJIFpFwhVDbVL6WWexMR6yRBCtImEMQZuU/k5nsQ0qN8YTlgiiVSTVCJJzoakWGqu9jsSYqGSJIFrV7oOYWEhI8ToSG0tgjMcsEUSruv2BMQQR8Cdg9y42xlMRcBYwnoiEMQRtrEZgjKcsEUSrSBlDAJ8nAruE1BhPWCKIRo01TsdspNQI2qaZsEFlxnjCEkE0qtzlLCOlRuCLdZKSTTNhjCcsEUSjyp3OMlJqBBC4d7HVCIzxgquJQETmiMgGEdksIrd1sv1KEfk08HhfRCa5GY8JqNzhLCOlRgA2utgYD7mWCETEB9wPnAuMBa4QkbEdim0DTlPVicDPgQVuxWOCVO4MjCHw8D4EHaX0s85iYzziZo1gOrBZVbeqaiOwEJgbXEBV31fV/YGXHwD5LsZj2lTujJwxBG2SbQZSY7zi5plgELAr6HVxYF1XvgX808V4TJvKnZHVPwDOvYubaqDBppkwJtzcTASd3faq01nFROR0nERwaxfb54nIMhFZVlZmvxqPWeXOyOofALt3sTEecjMRFAODg17nAyUdC4nIROCPwFxVrehsR6q6QFWnqurU3NxcV4KNGo01UFsegTWC/s7SmoeMCTs3E8FSYKSIDBWReOByYFFwAREpAJ4Fvq6qG12MxbTZH7hiKCnb2zg6SgkkeKsRGBN2sW7tWFWbReQm4CXABzysqmtE5IbA9vnAz4Bs4Pfi3EC9WVWnuhWTAfZvd5aJEZYIkm2+IWO84loiAFDVxcDiDuvmBz2/DrjOzRhMB22JIDnSEkEuzjQTNrrYmHCLoOsHTVhU7oD4FIhL9jqSQ/linbEEBw7rRjLGuMwSQbTZvx0yC0E6u6jLY6kD4eAer6MwJupYIog2+3dAxhCvo+hcWh4csERgTLhZIogmqp/XCCJRWh4ctKYhY8LNEkE0qS6F5jrIjNAaQepA5xaaTXVeR2JMVLFEEE3aZh2N5BoBWIexMWFmiSCatF06GqmJIHWgs7QOY2PCyhJBNGlLBBkFnobRpfYagSUCY8LJEkE02b/DmdMnLtHrSDrXXiOwpiFjwsnVkcUmwlRshqzhXkfRNX+aM9jNpRrBXz7c6cp+w+1rMyK0RmeOW1YjiCYVmyFnhNdRHJldQmpM2FkiiBZ1+53pp7MjPBGkDrSrhowJM0sE0aJ8s7PMHultHEeTMdi5cY4xJmysjyBaVAQSQU6kJ4JCZwbSprrI7dQ+gubWVhqbgx4tzrKppRWl7bZ9ggjEiJAQG+M84nztzyUS54EyfZolgmhRsQnE16N5hj7cts+FgGBLy+G//AsrkvkC8MLbH3IgZZgrx+2OVlVqG1uoaWimprGZmoYWquubqG5w1lUHHm3PG5pbj+l4vhghNSGWVH8sqf440hJjyU5OIDs5nuyUBDKT43rpkxnzOUsE0aJiszOQLDbe60iOqDopH4Dkut2uJILm1lZqG1raT+qfn+CbqWk74bdvb6ausaXTG20LkJQQS0qCj+SEWAZlJpKSEEtSfGz7L/u42BgSfDHEx8YQ54tBxJnu6fNYlIbmFhqaW2lsaqW+2Tn+wXrnUV7dwJay6kOSiwAPvrOVoTkpjBmQyuiBqYwZmMawnBTiY62l1/SMq4lAROYAv8O5Q9kfVfXuDttHA38CJgM/VdVfuxlPVCvfHPnNQkBNojOoLKV2d0jlW1q1/eRZHXxSb2ihtuMJvrGZ+qbOf7ELkBTvnNST4mPpl5pAck4yyfGxJAdO9snxsaT4YwMnfB8xYWjCUVVqGluoqG6goqaRiuoGUvxxbCmt5k9bKmhscT5PnE8Y0S+VMQOcxDA2L43xeemkJ1kNwhyda4lARHzA/cDZODeyXyoii1R1bVCxfcB3gYvcisMArS2wbwsMP93rSI6qLiGHlph4kuucRFDf1MK+msb2k+C+mkYO1DdxsL6ZA/XN1DY0d/qLPUZoP3knJ/gYlJl42EndWTqvE8N0Yu8uESElwUk+Q7Kdmwm1jSNoamllW3kN6/YcYN2eg6zbc4D3tpTz7MefJ9Eh2UmMH5TOhMDDkoPpjJs1gunAZlXdCiAiC4G5QHsiUNVSoFREzncxDrNvKzTXQ/9xXkfSJVVlf20TJZV1nB7Tn/Jdm7h72zoO1DcfUi4lIZa0xFjS/HEMykgk1R9Hqj+WNH/gxB44yfvj+m6na2cD4wqykijISuKccQOoaWimpKqOkv11FFfW8f7mcl789PNBelnJ8QzKSGRQRiJ5gWVivC+cH8EGxUUYNxPBIGBX0OtiYIaLxzNd2bvaWfYb620cQVShvLqBbWU1bC2vZlt5TftJf3Z8Fv19nzEsN4X+af5AR2k8WcnxJMSG94R1PEpOiGVkv1RG9kttX1fb0Mzuqjp2769jd2UdxftrWbW7qn17JCQH4x03E0FnP8c6q8UffUci84B5AAUF9kui2/auAYmB3NGehtGssP5gEksrU1hWlUp540YAUhNiGZqbTGF2MvmZiQwsHkXh3pf56tTBnsbblyR1lRwq69ofR0oO+ZmJ5GcmWYd0H+VmIigGgv8n5wM9GjKqqguABQBTp07tUTKJanvXOAPJ4vxhP3SLwqcHknlvXxorqlKoafERJ61MSqvhC2OGMCw3mdyUhEOacWr355PQVEVc00Ga4lKPsHdzLJISYhnZP5WR/UNLDjECA9MT25uhCrKTyEiM67NNcNHEzUSwFBgpIkOB3cDlwNdcPJ7pyt41MGhKWA+5sy6etyvSeacincrmWJJ9LUxJr2ZaxkEmptXg9ylbCr7Q6XsPJjljHVJrd7IvPXL7NfqizpJDTUMzu/bXsnNfLTsralm2Yx9LtlYAkOaPpSAriWG5KYzol0J2crwlhuOQa4lAVZtF5CbgJZzLRx9W1TUickNg+3wRGQAsA9KAVhH5HjBWVQ+4FVfUqT/g3Jls8tWuH6qxVXhvXxovl2WwtTYRH8qJ6dWcll3F5PRqQm1VOJAyFIC06q2WCCJAckIsowekMXpAGuBcsrv3QD079tWys6KG7RW1rC5x/stmJMUxIpAUhuWmkJJgQ5WOB67+K6nqYmBxh3Xzg55/htNkZNxSGrhIy8Urhkob4nilLIPXyzOobvGR72/gmvy9zMw6QFpcS7f3dzBpMK0SS3r1VheiNcfKFyPkBTqVTx6WjapSUdPI5tJqNpdWs7qkimU79gMwODORsQPTGJOXRr/U8DdNmtBYuu7rdq9wlgOLen3XG6v9LNqbzbLKFASYlnGQOf32MyaljmNpHdCYOA4mDSatZluvxWrcIyLkpCSQk5LAScOyaWlVSirr2FR6kHV7DvLS2r28tHYvOSkJjMtLY1J+htchmw4sEfR1u5dB2iBIG9gru1OFlQeS+ftn2ayrTiLZ18JFAyo4O7eS7Pjmo+8gRAdShpFmNYLjki9GGJyVxOCsJM4Y3Z/K2kbWfXaQdSUHeGdTGW9tLOPltZ8xt2gQc4vyyMs4/iYX7GssEfR1xct6paO4WWHJvjQW7c1iZ52f7Lgmrs7fy5k5lfh9vX8h14HkoQwqfYuY1iZaY2wk7PEsIymek4dlc/KwbKobmllVXElxZR33/Gs9//3SeqYXZnHxiYO4YFKe9Sl4xL71vqym3OkonvatHu+irhn+WZrJi3uzKGuMI9/fwI2FJZySdYBYFy8OqUwdQYw2k1a9lcq0E9w7kAmrlIRYTh6ew9dmFLCjooa/ryzh+ZW7ue3ZVdz5wlrmFuVx+bQCJuan29VHYWSJoC/b9ZGzHDS122+tahQe25LInzYlsa8xhtEptXxj8GecmF5DTBj+f7ZdLZRVtdYSQR81JDuZ7545kpvPGMHHuypZ+NFOnv+4hCc/2sXYgWlcMaOAuUV5pPmtRug2SwR92ba3IdYP+aEngtK6GB7alMgTWxOpbo7hjAENnJb+GaNT6lwM9HAHkwpo8iWTdWANW7k4rMc24SUiTC7IZHJBJrdfMJa/ryzhLx/u5D+eX81dL67jwkl5XHXSECbkp3sdap9liaAv2/4ODJ4BsQlHLbqzOoY/bEziqe2JNLfCBYMb+M4JNYzJaOHDbeFNAgBIDPvSx5BVtS78xzaeSfPH8fWThnDVjAI+La7iLx/uZNEnJfx12S4m5qdz5YwCvjQpj6R4O3X1Jvs2+6qacmeyuTP+44jF1lf5eGB9Mv/YlUBsDHylsJ5vj6plSEr3r//vbfvSxjJy51+R1ibUOoyjiogwaXAGkwZn8JPzx/D8x7t5/IMd3PrMKn7x4joumZzPlTMKDhkBbXrOEkFftfk1Zzls1mGbVJW3P4vnT5sTefOzBJJjW7luVC3fGllH/8Rju9VibyrPmMSY7Y+RXbWG8swir8MxHklPjOOaLxRy9clDWLp9P098uIO/fLiTR97fzvShWVw5o4A54wfYzLTHwBJBX7X+H5AyAPImt6+qbWzm2RW7eeT97WwuzSDX38IPxlXz9eF1ZMRH3lx+pdnTAOhf8ZElAoOIMH1oFtOHZvGzCxp4ankxf/lwJ7csXEl2cjyXTh3MlTMKGJyV5HWoxx1LBH1RU51TI5h0BcTEULy/lsc/2MmTH+2kqq6JCYPSuXdaFecPbiA+gmcVbojPZH/qCfTf9xFrnFnIjQEgOyWBG04bzrxTh/HO5nKe+GAHC97ewh/e3sIXR+Zy5YwCzhjdj1hfBP+BRxBLBH3RhsXQVMuShFP4/UMf8u7mcgSYM34A3zxlKFOGZCLLN3kdZUj2Zk9n5M6/4muupSXWfumZQ8XECKeNyuW0Ubnsqapj4Ue7WLh0J/P+vJyB6X4un1bA5dMH0z/N5jk6EksEfYiq8klxFWkv3U8CuXzttXjyMmq45cyRXDp1MIOOw6H8xf1OZ/T2P5Nf+hY78s71OhwTwQamJ/L9s0dx8xkjeG19KY9/sIN7X93I717byCkjcvjSpDzmjB9g4xI6YYngOKeqrCk5wAuf7uHFVSXE7d/C6wnLWZT9LR495yROGZGDLxwjwFxSmjWF2oR+DNmz2BKBCUmsL4Zzxg3gnHED2FFRw9PLi1n0SQn//vSn3P78as44oR/nTRzIaaNySU+0pACWCI5L9U0tfLC1gjc3lPHGhlJ2VNTiixFmjsjhzow30LIkLvzGbZCS63Wox05i2JF3LqO2P0Fi/V7q/P29jsgcR4ZkJ/OD2Sfwf84exSfFVfx95W7+8cke/rXmM2JjhJOGZXPWmH6cOaZ/VHcyWyI4DjQ2tzpzvG/fx5ItFSzZWkF9Uyv+uBhOGZ7Dt784nDnjB5BVuRoeXAwzvwcp/bwOu9dsLLicE7Y/zpitj7Bi7K1eh2OOQyJC0eAMigZncPv5Y1m5az8vr93Lq2v3csc/1nLHP9YyNCeZk4dn84XhzgR52SlHH4jZV7iaCERkDvA7nDuU/VFV7+6wXQLbzwNqgWtVdYWbMUU6VWXXvjrWlFSxpuQAy3fs5+Nd+6lvcq7vH5aTzOXTCjh9dD9mDM3CHxe4drqxBp67AVIHwinf8+4DuKAmKZ9teRcwYtdTbC64lAMpw7wOyRzHfDHClCFZTBmSxY/PHcPWsmpeX1/Kki0VLApMbwEwol8KRYFBbUX5GZwwIJX4UG+zd5xxLRGIiA+4Hzgb50b2S0VkkaquDSp2LjAy8JgBPBBY9nlNLa0U769jW3k1W8tq2FZew6bSataVHOBggzOvf4zA2Lw0rphewLTCLKYWZnZ+l6eGavjrVVCxCa56BhIzwvthwuCTUbcwqPQtvrDyVl6b8RBNcWleh2T6iGG5zm01rzt1GM0trazaXcX7WypYvmM/b6wv5enlxQDE+2IY3i+FkW2P/ikMz01hUGbicT/lhZvRTwc2q+pWABFZCMwFghPBXOAxVVXgAxHJEJGBqrrHxbhc09jcSlVdE1V1jVTVNVFZ28T+2ib2Hqhn74F6PqsKLA/UU3awgdagMVxp/lhG9Eth7ol5jMtLZ+zANE4YkPr5L/7OtDTD5lfh5dth3xa48D4Yfob7H9QD9f5clky6iy8u/y5nfXgtH42/g4qMiV6HZfqYWF8MJxZkcmJBJuDU0HdX1vHJrio+La5k496DrNi5n0WflBzyvsykuPbbdw7KSGRgup+s5HiykuPJTI4nMymerKR4Uv2xxETgxRtuJoJBwK6g18Uc/mu/szKDgF5PBDsqanh7UzmtrUpzq9LaqrSo0tLqPNrWNbcqrao0tzjLllalqaWVuqYW6ptaqGtqpb6xJei1s6xtdB5dSfPHMiDdT/80P6P6pzIg3c+Q7GSG5jiPzKS40OZfr6+Cd34DZeudm87UlkPGEPj68zDstN77wiLQntxTeXvKfZy06nbOWXIlmwZfytLxP/M6LNOHiQj5mUnkZyZx/sTP7/JX29jMltIatpZXs7uyjpLKOnbvr2NnRS1LtlRQ3dD53fpiBJLiY0mK95EU7yMxPpbkeB+J8T6S42Pxx8UQ54sh1hdDvE8OeR7ri2HqkEy+MCKn1z+nm4mgs7Nax3kMQimDiMyD9qGl1SKy4RhjA8gBynthPyFbFVqxHsS1Cr4/q5vRdItL39UPj+XNOfBQOTzUW8H0lrD/XYUg4mK6MgJjCojEuHorpiFdbXAzERQDg4Ne5wMlPSiDqi4AFvRmcCKyTFW7f8cWl0ViXBZT6CIxLospdJEYVzhicrMLfCkwUkSGikg8cDmwqEOZRcDV4jgJqDpe+weMMeZ45VqNQFWbReQm4CWcy0cfVtU1InJDYPt8YDHOpaObcS4f/YZb8RhjjOmcq9c8qepinJN98Lr5Qc8V+Dc3YziCXm1q6kWRGJfFFLpIjMtiCl0kxuV6TOKci40xxkSrvjlMzhhjTMiiOhGIyK9EZL2IfCoiz4lIhoexzBGRDSKyWURu8yqOoHgGi8gbIrJORNaIyC1ex9RGRHwi8rGIvOB1LG0CgyGfDvw9rRORkyMgpu8H/u1Wi8iTIuLJpPwi8rCIlIrI6qB1WSLyiohsCiwzIyAmz88HncUVtO2HIqIi0usDCaI6EQCvAONVdSKwEfixF0EETcdxLjAWuEJExnoRS5Bm4AeqOgY4Cfi3CIipzS3AOq+D6OB3wL9UdTQwCY/jE5FBwHeBqao6HueCjcs9CucRYE6HdbcBr6nqSOC1wGuvY4qE88EjHB4XIjIYZ7qenW4cNKoTgaq+rKptQwA/wBnH4IX26ThUtRFom47DM6q6p20CQFU9iHNiG+RlTAAikg+cD/zR61jaiEga8EUCo9tUtVFVKz0NyhELJIpILJBEJ2N0wkFV3wb2dVg9F3g08PxR4CKvY4qE80EX3xXAvcC/08mA294Q1Ymgg28C//To2F1NtRERRKQQOBH40ONQAH6L8x+i1eM4gg0DyoA/BZqs/igiyV4GpKq7gV/j/ILcgzNG52UvY+qgf9uYocAy0uZN9/J8cAgRuRDYraqfuHWMPp8IROTVQBtpx8fcoDI/xWkKecKrMDtZFxGXc4lICvAM8D1VPeBxLBcApaq63Ms4OhELTAYeUNUTgRrC39RxiECb+1xgKJAHJIvIVV7GdLyIgPNBcCxJwE8BVyfVOr7nTg2Bqp51pO0icg1wAXCmenctbUhTbYSbiMThJIEnVPVZr+MBTgEuFJHzAD+QJiKPq6rXJ7hioFhV22pMT+NxIgDOArapahmAiDwLfAF43NOoPre3baZhERkIlHodEETM+SDYcJxk/klgUsp8YIWITFfVz3rrIH2+RnAkgRvn3ApcqKq1HoYSynQcYRW4adBDwDpV/Y2XsbRR1R+rar6qFuJ8R69HQBIg8B9yl4icEFh1JodOt+6FncBJIpIU+Lc8k8jqYF8EXBN4fg3wdw9jASLqfNBOVVepaj9VLQz83RcDk3szCUCUJwLgPiAVeEVEVorI/KO9wQ2BDqq26TjWAX9T1TVexBLkFODrwBmB72Zl4Je46dzNwBMi8ilQBNzlZTCB2snTwAqciW9j8GjUrIg8CSwBThCRYhH5FnA3cLaIbMK5GubuI+0jTDF5fj7oIi73jxsZtR9jjDFeifYagTHGRD1LBMYYE+UsERhjTJSzRGCMMVHOEoExxkQ5SwTGuEREvhcYGWpMRLPLR41xiYhsx5n9s9zrWIw5EqsRGNNNIpIsIi+KyCeBeasu66TMd3Hm+HlDRN4If5TGhM5qBMZ0k4hcAsxR1esDr9NVtaqTctuxGoE5DliNwJjuWwWcJSL3iMipnSUBY44nlgiM6SZV3QhMwUkIvxQRV6cINsZtfX4aamN6m4jkAftU9XERqQau7aLoQZxJzKxpyEQ0SwTGdN8E4Fci0go0Ad/potwC4J8iskdVTw9bdMZ0k3UWG2NMlLM+AmOMiXLWNGTMMRKR53BuJxjsVlV9yYt4jOkuaxoyxpgoZ01DxhgT5SwRGGNMlLNEYIwxUc4SgTHGRDlLBMYYE+UsERhjTJT7/3jQNxB3KHpKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting original and Log Transformed Data\n",
    "plt.subplots(1,1)\n",
    "plt.suptitle(\"Sorting Time\")\n",
    "sn.distplot(x)\n",
    "sn.distplot(sq_x)\n",
    "labels=(\"Original\",\"Square root Transformed\")\n",
    "plt.legend(labels)\n",
    "\n",
    "plt.subplots(1,1)\n",
    "plt.suptitle(\"Dlivery Time\")\n",
    "sn.distplot(y)\n",
    "sn.distplot(sq_y)\n",
    "\n",
    "labels=(\"Original\",\"Square root Transformed\")\n",
    "plt.legend(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "2c6899d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model_5=smf.ols(\"sq_y~sq_x\",data=d_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "7468e9cd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='s_t', ylabel='d_t'>"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line in the LOG Transformation case\n",
    "plt.plot(sq_x,model_5.params[0]+model_5.params[1]*(sq_x),\"r\")\n",
    "sn.scatterplot(sq_x,sq_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "e1ded391",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>sq_y</td>       <th>  R-squared:         </th> <td>   0.729</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.715</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   51.16</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>8.48e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:08:01</td>     <th>  Log-Likelihood:    </th> <td> -5.7320</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>   15.46</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>   17.55</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>    1.6135</td> <td>    0.349</td> <td>    4.628</td> <td> 0.000</td> <td>    0.884</td> <td>    2.343</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sq_x</th>      <td>    1.0022</td> <td>    0.140</td> <td>    7.153</td> <td> 0.000</td> <td>    0.709</td> <td>    1.295</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.869</td> <th>  Durbin-Watson:     </th> <td>   1.279</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.238</td> <th>  Jarque-Bera (JB):  </th> <td>   1.685</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.690</td> <th>  Prob(JB):          </th> <td>   0.431</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.150</td> <th>  Cond. No.          </th> <td>    13.7</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                   sq_y   R-squared:                       0.729\n",
       "Model:                            OLS   Adj. R-squared:                  0.715\n",
       "Method:                 Least Squares   F-statistic:                     51.16\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           8.48e-07\n",
       "Time:                        15:08:01   Log-Likelihood:                -5.7320\n",
       "No. Observations:                  21   AIC:                             15.46\n",
       "Df Residuals:                      19   BIC:                             17.55\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      1.6135      0.349      4.628      0.000       0.884       2.343\n",
       "sq_x           1.0022      0.140      7.153      0.000       0.709       1.295\n",
       "==============================================================================\n",
       "Omnibus:                        2.869   Durbin-Watson:                   1.279\n",
       "Prob(Omnibus):                  0.238   Jarque-Bera (JB):                1.685\n",
       "Skew:                           0.690   Prob(JB):                        0.431\n",
       "Kurtosis:                       3.150   Cond. No.                         13.7\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_5.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "51f8f950",
   "metadata": {},
   "source": [
    "#### Accuracy is  71%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dcc0b8dc",
   "metadata": {},
   "source": [
    "## 6.Boxcox Trandformation yo X and Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "4f914bb1",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "755704de",
   "metadata": {},
   "outputs": [],
   "source": [
    "#BOXCOX TRANSFORMATION of X and Y\n",
    "bc_x=stats.boxcox(x)\n",
    "bc_x=list(bc_x)\n",
    "bc_x.pop()\n",
    "bc_x=bc_x[0]\n",
    "d_1[\"bc_x\"]=bc_x\n",
    "\n",
    "bc_y=stats.boxcox(y)\n",
    "bc_y=list(bc_y)\n",
    "bc_y.pop()\n",
    "bc_y=bc_y[0]\n",
    "d_1[\"bc_y\"]=bc_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "id": "3f3a0310",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16cdf142e50>"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting original and Log Transformed Data\n",
    "plt.subplots(1,1)\n",
    "plt.suptitle(\"Sorting Time\")\n",
    "sn.distplot(x)\n",
    "sn.distplot(bc_x)\n",
    "labels=(\"Original\",\"BOXCOX Transformed\")\n",
    "plt.legend(labels)\n",
    "\n",
    "plt.subplots(1,1)\n",
    "plt.suptitle(\"Dlivery Time\")\n",
    "sn.distplot(y)\n",
    "sn.distplot(bc_y)\n",
    "\n",
    "labels=(\"Original\",\"BOXCOX Transformed\")\n",
    "plt.legend(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "id": "ca3c1306",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model_6=smf.ols(\"bc_y~bc_x\",data=d_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "id": "bf56b089",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line in the box cox Transformation case\n",
    "plt.plot(bc_x,model_6.params[0]+model_6.params[1]*(bc_x),\"r\")\n",
    "sn.scatterplot(bc_x,bc_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "id": "94c87723",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>bc_y</td>       <th>  R-squared:         </th> <td>   0.719</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.704</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   48.50</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>1.23e-06</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:08:03</td>     <th>  Log-Likelihood:    </th> <td> -23.352</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>   50.70</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>   52.79</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>    3.7288</td> <td>    0.447</td> <td>    8.334</td> <td> 0.000</td> <td>    2.792</td> <td>    4.665</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>bc_x</th>      <td>    0.8038</td> <td>    0.115</td> <td>    6.965</td> <td> 0.000</td> <td>    0.562</td> <td>    1.045</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.775</td> <th>  Durbin-Watson:     </th> <td>   1.263</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.250</td> <th>  Jarque-Bera (JB):  </th> <td>   1.589</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.668</td> <th>  Prob(JB):          </th> <td>   0.452</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.170</td> <th>  Cond. No.          </th> <td>    10.9</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                   bc_y   R-squared:                       0.719\n",
       "Model:                            OLS   Adj. R-squared:                  0.704\n",
       "Method:                 Least Squares   F-statistic:                     48.50\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           1.23e-06\n",
       "Time:                        15:08:03   Log-Likelihood:                -23.352\n",
       "No. Observations:                  21   AIC:                             50.70\n",
       "Df Residuals:                      19   BIC:                             52.79\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      3.7288      0.447      8.334      0.000       2.792       4.665\n",
       "bc_x           0.8038      0.115      6.965      0.000       0.562       1.045\n",
       "==============================================================================\n",
       "Omnibus:                        2.775   Durbin-Watson:                   1.263\n",
       "Prob(Omnibus):                  0.250   Jarque-Bera (JB):                1.589\n",
       "Skew:                           0.668   Prob(JB):                        0.452\n",
       "Kurtosis:                       3.170   Cond. No.                         10.9\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_6.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b09426f3",
   "metadata": {},
   "source": [
    "#### The ACcuracy is 70%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c232624",
   "metadata": {},
   "source": [
    "## 7.Cuberoot Transformation to X and Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "43c76b27",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Applying CUBEROOT TRANSFORMATION\n",
    "cr_x=np.cbrt(x)\n",
    "d_1[\"cr_x\"]=cr_x\n",
    "cr_y=np.cbrt(y)\n",
    "d_1[\"cr_y\"]=cr_y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "id": "4d8c09c8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model_7=smf.ols(\"cr_y~cr_x\",data=d_1).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "id": "f804fa0c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='s_t', ylabel='d_t'>"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line in the cuberoot Transformation case\n",
    "plt.plot(cr_x,model_7.params[0]+model_7.params[1]*(cr_x),\"r\")\n",
    "sn.scatterplot(cr_x,cr_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "id": "668d6516",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>cr_y</td>       <th>  R-squared:         </th> <td>   0.744</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.731</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   55.25</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>4.90e-07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:08:05</td>     <th>  Log-Likelihood:    </th> <td>  13.035</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    21</td>      <th>  AIC:               </th> <td>  -22.07</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    19</td>      <th>  BIC:               </th> <td>  -19.98</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>    1.0136</td> <td>    0.207</td> <td>    4.900</td> <td> 0.000</td> <td>    0.581</td> <td>    1.447</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>cr_x</th>      <td>    0.8456</td> <td>    0.114</td> <td>    7.433</td> <td> 0.000</td> <td>    0.607</td> <td>    1.084</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.570</td> <th>  Durbin-Watson:     </th> <td>   1.292</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.277</td> <th>  Jarque-Bera (JB):  </th> <td>   1.532</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.661</td> <th>  Prob(JB):          </th> <td>   0.465</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.075</td> <th>  Cond. No.          </th> <td>    16.4</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                   cr_y   R-squared:                       0.744\n",
       "Model:                            OLS   Adj. R-squared:                  0.731\n",
       "Method:                 Least Squares   F-statistic:                     55.25\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           4.90e-07\n",
       "Time:                        15:08:05   Log-Likelihood:                 13.035\n",
       "No. Observations:                  21   AIC:                            -22.07\n",
       "Df Residuals:                      19   BIC:                            -19.98\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept      1.0136      0.207      4.900      0.000       0.581       1.447\n",
       "cr_x           0.8456      0.114      7.433      0.000       0.607       1.084\n",
       "==============================================================================\n",
       "Omnibus:                        2.570   Durbin-Watson:                   1.292\n",
       "Prob(Omnibus):                  0.277   Jarque-Bera (JB):                1.532\n",
       "Skew:                           0.661   Prob(JB):                        0.465\n",
       "Kurtosis:                       3.075   Cond. No.                         16.4\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_7.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3250017d",
   "metadata": {},
   "source": [
    "# Among all Model The Log Transformed to X and Y Model Has most accuracy of 76%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fcfc9fde",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "434829d3",
   "metadata": {},
   "source": [
    "# Question2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "id": "24bcd6bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "d_2=pd.read_csv(\"Salary_Data.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "id": "6f74aacb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(30, 2)"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9380fcd8",
   "metadata": {},
   "source": [
    "# EDA and Visualization Of Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "id": "909c3694",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 30 entries, 0 to 29\n",
      "Data columns (total 2 columns):\n",
      " #   Column           Non-Null Count  Dtype  \n",
      "---  ------           --------------  -----  \n",
      " 0   YearsExperience  30 non-null     float64\n",
      " 1   Salary           30 non-null     float64\n",
      "dtypes: float64(2)\n",
      "memory usage: 608.0 bytes\n"
     ]
    }
   ],
   "source": [
    "d_2.info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "9a93f49f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>YearsExperience</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.1</td>\n",
       "      <td>39343.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.3</td>\n",
       "      <td>46205.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.5</td>\n",
       "      <td>37731.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2.0</td>\n",
       "      <td>43525.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.2</td>\n",
       "      <td>39891.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   YearsExperience   Salary\n",
       "0              1.1  39343.0\n",
       "1              1.3  46205.0\n",
       "2              1.5  37731.0\n",
       "3              2.0  43525.0\n",
       "4              2.2  39891.0"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d_2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "de02970b",
   "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>y_e</th>\n",
       "      <th>salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>30.000000</td>\n",
       "      <td>30.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>5.313333</td>\n",
       "      <td>76003.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>2.837888</td>\n",
       "      <td>27414.429785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.100000</td>\n",
       "      <td>37731.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>3.200000</td>\n",
       "      <td>56720.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>4.700000</td>\n",
       "      <td>65237.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>7.700000</td>\n",
       "      <td>100544.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>10.500000</td>\n",
       "      <td>122391.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             y_e         salary\n",
       "count  30.000000      30.000000\n",
       "mean    5.313333   76003.000000\n",
       "std     2.837888   27414.429785\n",
       "min     1.100000   37731.000000\n",
       "25%     3.200000   56720.750000\n",
       "50%     4.700000   65237.000000\n",
       "75%     7.700000  100544.750000\n",
       "max    10.500000  122391.000000"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Checking Statistics of data\n",
    "d_2.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "d62abbd9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAASgAAACaCAYAAAAactXTAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAJH0lEQVR4nO3dXYycVR3H8e+fXaULBNtSbOqWuJAlGDUGoUbQRBQMChKICRcQUUANJiZNoxdK08RIYkxQL8QlCJWIb4gVfCMEA0aDF14A24hQpZWRF+ny1tqASCtSOF48Z2G62d2+zMzOv8P3k2zmmTPPy/mnM7+e58zMM1FKQZIyOqTfHZCkuRhQktIyoCSlZUBJSsuAkpSWASUpreH9WXnZsmVlbGysR12R9Hq1cePG7aWUo2e271dAjY2NMTk52b1eSRIQEY/N1u4pnqS0DChJaRlQktIyoCSlZUBJSsuAkpSWASUpLQNKUlr79UFN7WliYoJWq9Xz40xNTQEwOjra82OpM+Pj46xevbrf3RgYBlQHWq0W9216kJcPW9rT4wztfA6Ap170nyuzoZ07+t2FgeMzvkMvH7aUXW87u6fHGNl8O0DPj6POTP87qXucg5KUlgElKS0DSlJaBpSktAwoSWkZUJLSMqAkpWVASUrLgJKUlgElKS0DSlJaBpSktAwoSWkZUJLSMqAkpWVASUrLgJKUlgElKS0DSlJaPQuoiYkJJiYmerV7SQl1+3Xfsx9NWIifY5KUS7df957iSUrLgJKUlgElKS0DSlJaBpSktAwoSWkZUJLSMqAkpWVASUrLgJKUlgElKS0DSlJaBpSktAwoSWkZUJLSMqAkpWVASUrLgJKUlgElKa2eXZN8amqKXbt2sWbNml4dou9arRaH/K/0uxtK4pD//ptW6/mBfs7vTavVYmRkpGv72+sIKiIui4jJiJjctm1b1w4sSXuz1xFUKWU9sB5g1apV+zxcGB0dBeCqq6460L6lt2bNGjY+/HS/u6EkXll0JOPHLR/o5/zedHv06ByUpLQMKElpGVCS0jKgJKVlQElKy4CSlJYBJSktA0pSWgaUpLQMKElpGVCS0jKgJKVlQElKy4CSlJYBJSktA0pSWgaUpLQMKElpGVCS0jKgJKXVs5+dGh8f79WuJSXV7dd9zwJq9erVvdq1pKS6/br3FE9SWgaUpLQMKElpGVCS0jKgJKVlQElKy4CSlJYBJSktA0pSWgaUpLQMKElpGVCS0jKgJKVlQElKy4CSlJYBJSktA0pSWgaUpLQMKElp9eya5K8XQzt3MLL59h4f418APT+OOjO0cwewvN/dGCgGVAcW6pdrpqZ2AzA66pM/t+X+mlGXGVAd8JdrpN5yDkpSWgaUpLQMKElpGVCS0jKgJKVlQElKy4CSlJYBJSktA0pSWlFK2feVI7YBj3Xp2MuA7V3a18HAegeb9XbmraWUo2c27ldAdVNETJZSVvXl4H1gvYPNenvDUzxJaRlQktLqZ0Ct7+Ox+8F6B5v19kDf5qAkaW88xZOUVlcCKiKGIuLPEXFbvb80In4XEQ/V2yVt666NiFZEbImIj7S1nxwRD9THvhMRUdsPjYgNtf3uiBjrRp8PVEQsjohbImJzRDwYEacOeL1fiIi/RsSmiLgpIhYNUr0R8f2IeCYiNrW1LUh9EXFxPcZDEXFxH+v9Zn0+3x8Rv4qIxWnqLaV0/Ad8EfgpcFu9/w3g8rp8OXBlXX478BfgUOBY4B/AUH3sHuBUIIDfAmfV9s8D19blC4AN3ehzB7X+EPhsXX4jsHhQ6wVGgUeAkXr/58Alg1Qv8AHgJGBTW1vP6wOWAg/X2yV1eUmf6j0TGK7LV2aqtxsFrwR+D5zOawG1BVhRl1cAW+ryWmBt27Z31CJXAJvb2i8Ermtfpy4P03w4LBbySdzWryNpXrAxo31Q6x0FHq9PqmHgtvpkHqh6gbEZL9ie19e+Tn3sOuDCftQ747GPAzdmqbcbp3jfBr4EvNLWtryU8iRAvX1zbZ9+wk/bWttG6/LM9j22KaXsBp4DjupCvw/EccA24IZ6Snt9RBzOgNZbSpkCvgX8E3gSeK6UcicDWm+bhahvrn3126dpRkSQoN6OAioizgGeKaVs3NdNZmkr87TPt00/DNMMj79bSnk38ALNKcBcDup669zLeTTD+7cAh0fERfNtMkvbQVPvPuhmfenqjoh1wG7gxummWVZb0Ho7HUG9Hzg3Ih4FfgacHhE/AZ6OiBUA9faZuv5W4Ji27VcCT9T2lbO077FNRAwDbwJ2dNjvA7UV2FpKubvev4UmsAa13g8Dj5RStpVSXgJ+CbyPwa132kLUN9e++qJOWp8DfKLUczAS1NtRQJVS1pZSVpZSxmgmxP5QSrkIuBWYnqW/GPhNXb4VuKDO9B8LHA/cU4fRz0fEKfXdgE/N2GZ6X+fXY/Tlf5pSylPA4xFxQm06A/gbA1ovzandKRFxWO3nGcCDDG690xaivjuAMyNiSR2pnlnbFlxEfBT4MnBuKWVn20P9r7eLE28f5LVJ8qNoJs4fqrdL29ZbR/NuwBbqzH9tXwVsqo9dzWsfIl0E3Ay0aN45OG4hJhLnqfNEYBK4H/g1zTsSg1zvFcDm2tcf07yjMzD1AjfRzK+9RPO//GcWqj6a+Z5W/bu0j/W2aOaH7qt/12ap10+SS0rLT5JLSsuAkpSWASUpLQNKUloGlKS0DCjNKyLWRXM1g/sj4r6IeO886/4gIs5fyP5psA33uwPKKyJOpfl08UmllBcjYhnNFRy6tf/h0nxfS5qVIyjNZwWwvZTyIkApZXsp5YmI+EpE3BvNNaLWT18LqN1c60TEXRHx9Yj4I7AuIh6JiDfUx46MiEen70sGlOZzJ3BMRPw9Iq6JiNNq+9WllPeUUt4JjNCMsmaab53FpZTTSilXAHcBH6vtFwC/KM33/iQDSnMrpfwHOBm4jOYyMxsi4hLgQ/VqiQ/QXAfsHbNsPt86G9qWrwcurcuXAjd0twodzJyD0rxKKS/TjHLuqmHzOeBdwKpSyuMR8VWa71+9KiIWAdfMs84Lbfv/U0SM1dHZUCllE1LlCEpziogTIuL4tqYTab40CrA9Io6g+cb6TIv2YZ12P6L5EqujJ+3BEZTmcwQwEc1F9HfTfAv9MuBZ4AHgUeDemRuVUp6NiO/Nt84MNwJfowkp6VVezUB9Vz87dV4p5ZP97otycQSlvoqICeAs4Ox+90X5OIKSlJaT5JLSMqAkpWVASUrLgJKUlgElKS0DSlJa/wdmYH2odXz9uQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#checking for outliers\n",
    "for i in d_2.columns:\n",
    "    plt.figure(figsize=(5,2))\n",
    "    sn.boxplot(d_2[i])\n",
    "    plt.xlabel(i)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75932dbe",
   "metadata": {},
   "source": [
    "#### There are no outliers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "d80d843e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "YearsExperience    0\n",
       "Salary             0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking for null values\n",
    "d_2.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e2cdf42",
   "metadata": {},
   "source": [
    "#### There are no null values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "790be834",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='YearsExperience', ylabel='Salary'>"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting dependent and Independent Variables\n",
    "sn.scatterplot(d_2.iloc[:,0],d_2.iloc[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "ec5946ca",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>YearsExperience</th>\n",
       "      <th>Salary</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [YearsExperience, Salary]\n",
       "Index: []"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Checking Duplicate Datad\n",
    "d_2[d_2.duplicated()]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aaa999fe",
   "metadata": {},
   "source": [
    "#### No duplicate Datas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "0ef4cf4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "# REnaming columns\n",
    "d_2=d_2.rename({\"YearsExperience\":\"y_e\",\"Salary\":\"salary\"},axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "id": "75ce61f4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in d_2.columns:\n",
    "    sn.distplot(d_2[i])\n",
    "    plt.suptitle(i)\n",
    "    plt.xlabel(i)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52a4f4b3",
   "metadata": {},
   "source": [
    "#### Both Years Experienced and Salary looks like normal Distribution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "id": "9dd3de62",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             y_e    salary\n",
      "y_e     1.000000  0.978242\n",
      "salary  0.978242  1.000000\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.PairGrid at 0x16cdf7b4610>"
      ]
     },
     "execution_count": 140,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# checking correlation\n",
    "print(d_2.corr())\n",
    "sn.pairplot(d_2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2bdfea78",
   "metadata": {},
   "source": [
    "# Model fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "b812b374",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Separating Independent and dependent Variable\n",
    "X=d_2.y_e\n",
    "Y=d_2.salary"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "283172f1",
   "metadata": {},
   "source": [
    "## 1. Without Transformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "a65129d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model1=smf.ols(\"salary~y_e\",data=d_2).fit()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "4489849f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='y_e', ylabel='salary'>"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZgAAAEGCAYAAABYV4NmAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAqqElEQVR4nO3de5zWc/7/8cdrEtGBdEJhpKzKOs5GVtZh0WLl59BmLS3ZHNpyXrEH1inH2BAi5LAlOYRvRWLlUFEKHRw6SaRGkoqhul6/P96f4WrMTHO4Ptfnmpnn/Xab23XN+/q8P9frmlvNa95nc3dEREQyLS/pAEREpHZSghERkVgowYiISCyUYEREJBZKMCIiEovNkg4gVzRv3tzz8/OTDkNEpEaZPn36l+7eorTXlGAi+fn5TJs2LekwRERqFDP7pKzX1EUmIiKxUIIREZFYKMGIiEgslGBERCQWSjAiIhILJRgREYmFEoyIiMRCCUZEpC579lkYNiyWWyvBiIjURcuXQ8+e0L17SDCpVMbfQglGRKQucYdHH4UOHeDpp+Haa+HVVyEv8+lAW8WIiNQVixfDOefAuHHQpUtouXToENvbqQUjIlLLpdZvoPCm29nQsSOpV18ldfvt8NprsSYXUIIREanVUh98yNf7/5oWl13IGy1244gz7mT8YT1IWR6plLOgcA2T53/JgsI1pFKe0fdWF5mISG20fj0MGgRXXkk9NuPS3/XniV8eAWZcNGomHc/vypylq7lo1EyK1qVoUD+PQT32plun7cjLs4yEoAQjIlLbvPsunHkmvPMOK488hm7t/0Bho21/fLloXYpl33z/Y3IpLrto1Ex279+Vti0aZSQMdZGJiNQWRUXwj39AQQF89hmMHs2qR0eyumnzjS5rUD+PtT+s/zG5/Fh9XYrlq4syFk5sCcbMHjCz5WY2K63sZjP7wMzeM7OnzWybtNcuN7N5ZvahmR2VVr6fmb0fvTbYzCwq38LMHo/Kp5pZflqdXmb2cfTVK67PKCKSM958E/bZB667Dk49FebMgRNPJL9ZQwb12JsG9cOv++KusJ23bfhjWbEG9fNo2bhBxkKKswXzENCtRNkEYA933xP4CLgcwMw6Aj2BTlGdIWZWL6pzN9AHaB99Fd+zN7DS3dsBtwE3RvfaFrgS2B/oDFxpZk1j+HwiIslbswbOPx8OOgi+/RbGj4eHHoJtQ5dYXp7RrdN2jO3flZF99mds/65067QduzQvPfHkN2uYsdBiG4Nx90nprYqo7MW0b6cAJ0XPuwMj3f17YKGZzQM6m9kioIm7TwYws4eB44FxUZ2rovqjgTuj1s1RwAR3/yqqM4GQlEZk+COKiCRrwgTo0wc++QT69oXrr4fGjX92WV6e0bZFo5+NrXTrtB279+/K8tVFtGzcgPxmDTM2wA/JDvKfCTwePW9NSDjFlkRl66LnJcuL63wK4O7rzWwV0Cy9vJQ6GzGzPoTWETvttFM1PoqISBatXAkXXwwPPgi/+AVMmhRaMJVUVuLJlEQG+c3s78B64LHiolIu83LKq1pn40L3oe5e4O4FLVq0KD9oEZFc8NRT0LEjPPwwXH45zJxZpeSSDVlPMNGg+7HAqe5e/It/CbBj2mVtgM+j8jallG9Ux8w2A7YGvirnXiIiNdcXX8BJJ8GJJ8J228Hbb4cusQaZG5TPtKwmGDPrBlwGHOfu36a99CzQM5oZtgthMP8td18KrDazA6LxldOBMWl1imeInQS8HCWsF4AjzaxpNLh/ZFQmIlLzuMPw4aHV8vzzMHAgvPVWmDGW42IbgzGzEcAhQHMzW0KY2XU5sAUwIZptPMXdz3H32WY2CphD6Drr6+4boludS5iRtiVhcH9cVD4MeCSaEPAVYRYa7v6VmV0DvB1dd3XxgL+ISC5JpZxFK9ay7JsiWjUpZZD9k0/g7LPhhRdCN9j994cxlxrCfuqlqtsKCgp82rRpSYchInVEKuWMn/1F6Vu14DBkCAwYAGZwww1w7rmxbKlfXWY23d0LSnst96IVEakDFq1YW+pWLZ9NeQcOPhj69QutllmzwhTkHEwum6K9yEREErDsm6KNtmrZbMN6zpz8FK1vGgkNG4Zxl9NOCy2YGkoJRkQkAa2aNKBB/TyK1qXotGw+N439D52WL2DN74+n0X33QKtWSYdYbUowIiIJyG/WkNu7784n5w+g9+TRfNVwa6YPup99zj8TMriaPklKMCIiCch78w2O6t0b++gjlp90Ct9efyP77Nomo1u1JE0JRkRqnU1O/03S6tVhBf5dd2H5+fDii7Q84oiko4qFEoyI1CrlTv9NOsmMGxfWtSxZEnZAvvZaaBTPPmC5oObNexMRKUdZ038XrVibXFArVsDpp8PRR4eE8sYbcPvttTq5gBKMiNQyJaf/QuZPaqwwd3jiibDNy4gR4bTJGTOgS5efXZpKOQsK1zB5/pcsKFxDKlXzF8Gri0xEapX06b/FMn1SY4UsXQrnnQfPPAP77Qcvvgh77VXqpTndrVcNasGISK1S1hHBmTypsVzu8MAD0KFDOF3yxhthypQykwvkaLdeBqgFIyK1SvERwXGe1FimBQvCIP5LL0HXrmFzyt1222S18rr14joMLBuUYESk1on7pMaf2bAB7rgD/v73sGfYkCEh0VRw/7Cc6dbLMHWRiYhUx5w5YVPKCy+E3/wGZs+u9M7HiXfrxUQtGBGRqvjhB7jpJrjmGmjcGB59FP74xyptTplot16MlGBERErY5E4A06ZB797w3nvQo0foHmvZslrvmfVuvSxQghERSVPulOHvi+DKK+HWW8Nux888A927Jx1yzlKCERFJU9aU4b0LjB0u6Qfz5sFZZ8HNN8M22yQbbI5TghERSVNyynCj779lwAsPssO146Bt2zAF+fDDE4yw5lCCERFJkz5l+JD5b3P9C3fRas1XfH3OX9nmlhvCaZNSIUowIiJp8ps15I4jduS7vv05btYrfNx8J6bc/RBdTjm61hwEli1KMCIixdzJe2IUv+3XD1auZEm/S6j3twF02WHbGj9lOAlKMCIiAJ9/HhZIPvss9qtfwcSJtPnlL5OOqkbTSn4Rqdvcw55hHTvChAlwyy0weTJsIrnUxu31M00tGBGpu+bPh7/8BV55BQ45BO67D9q122S12rq9fqapBSMidc+GDTBoUGilTJ8O994LEydWKLlA7d1eP9OUYESkbpk1Cw48EC6+OKxnmT0b+vSp1OaUOXVqZg5TghGRuuGHH+Df/4Z99w3ntowYAc8+C23aVPpWxWtl0tWG7fUzTQlGRGq/t94KxxZfdRWcfDLMnQs9e1Zp52OovdvrZ5oG+UWk9vr2W/jXv+C222D77eG55+DYY6t929q6vX6mKcGISO30yithU8riY4xvvBG23jpjt6+N2+tnmrrIRKR2WbUqJJTDDgsD96+8Avfck9HkIhWjBCMitcdzz4UFk/ffD5dcAu++G9a3SCLURSYiNUaZJ00WFkL//jByZFjbMmYMFBQkHW6dpwQjIjVCqavnT96Lbu+9Qt4F58M338DVV8Nll8HmmycdrqAEIyI1RMnV801XLGOrE48nb97bsP/+MGwYdOqUcJSSLrYxGDN7wMyWm9mstLJtzWyCmX0cPTZNe+1yM5tnZh+a2VFp5fuZ2fvRa4PNwsR1M9vCzB6PyqeaWX5anV7Re3xsZr3i+owikj3Fq+fNU5w6YywvDjuPzp+8x6J/XANvvKHkkoPiHOR/COhWomwAMNHd2wMTo+8xs45AT6BTVGeImdWL6twN9AHaR1/F9+wNrHT3dsBtwI3RvbYFrgT2BzoDV6YnMhGpmVo1acAvVi9lxIgruO7FIby7/W4c12cIqf4XQL16m6wv2RdbgnH3ScBXJYq7A8Oj58OB49PKR7r79+6+EJgHdDaz7YEm7j7Z3R14uESd4nuNBg6PWjdHARPc/St3XwlM4OeJTkRqkvXryX9wCGOH9aPj8oX8rVt/zvrT9Vx09u+0ej6HZXsMppW7LwVw96Vm1jIqbw1MSbtuSVS2Lnpesry4zqfRvdab2SqgWXp5KXU2YmZ9CK0jdtppp6p/KhGJz3vvQe/e5E2bhh/XnZXX3swJDZtyjlbP57xcGeQv7V+Il1Ne1TobF7oPBYYCFBQU6LQgkSoqc/pwdXz/PVx3HQwcCNtuC6NGYSedxM5m7JyZsCVm2U4wy8xs+6j1sj2wPCpfAuyYdl0b4POovE0p5el1lpjZZsDWhC65JcAhJer8L7MfQ0SKxXL41pQp0Ls3zJkDp50W9hJr1iyzgUvssr2S/1mgeFZXL2BMWnnPaGbYLoTB/Lei7rTVZnZANL5yeok6xfc6CXg5Gqd5ATjSzJpGg/tHRmUiEoOMHr61di1ceGE4r2X1ahg7Fh5+WMmlhoqtBWNmIwgtieZmtoQws+sGYJSZ9QYWAycDuPtsMxsFzAHWA33dfUN0q3MJM9K2BMZFXwDDgEfMbB6h5dIzutdXZnYN8HZ03dXuXnKygYhkSHmHb1VqI8iXXgoHfy1cCH37hq6xxo0zHK1kU2wJxt1PKeOlw8u4/jrgulLKpwF7lFJeRJSgSnntAeCBCgcrIlVWfPhWepKp1OFbX38dTpd84AFo3x4mTYKuXeMJVrJKm12KSLVU6/CtZ54Jm1MOHw4DBoTNKZVcao1cmUUmIjVUlQ7fWrYM+vWDJ56AvfYKuyDvt1/2gpasUIIRkWqr8OFb7vDoo3DBBbBmTZiGfOmlUL9+VuKU7FKCEZHsWLwYzjkHxo2DLl3C5pQdOiQdlcRIYzAiNVAq5SwoXMPk+V+yoHANqVQOrxNOpWDIkLAZ5aRJMHgwvPaakksdoBaMSA0Ty8LGuHz0EZx1VkgoRxwBQ4dCfn7SUUmWqAUjUsNkdGFjXNavhxtvhD33hPffhwcfhBdeUHKpY5RgRGqY8hY25oSZM8MBYAMGwDHHwNy58Oc/g+VY60pipwQjUsMUL2xMV6mFjXEpKoK//x0KCuCzz2D0aHjySdhuu2TjksQowYjUMNVa2FhJFZ5M8OabsM8+cP318Kc/hU0qTzwx4/FIzaJBfpEapkoLG6ugQpMJ1qyBK66AO++EHXeE8ePhqKPKv7HUGWrBiNRAxQsbD2jbnLYtGsUye2yTkwlefBH22CMkl7/+FWbNUnKRjSjBiEipyppMsOLTpXDGGSGZNGgQpiAPHqydj+Vn1EUmIqUqbZfk4+a9yT7dzoSvVoSusX/+MyQZkVIowYhIqYonE1w0aiaNV67g2on3cNQHb+D77AMvvgB77510iJLjlGBEpFR5eUa3jq0oaLmYbe8YQF7Rd6QGDiTv4ou1OaVUiBKMiJRu0SLyzj6bli++CAcdBPffD7/4RdJRSQ2iQX4R2VgqBXfcEWaIvfkm3HUXvPqqkotUmlowIvKTuXPD5pRvvgndusE998DOOycdldRQasGICKxbF1bh7703fPABPPwwjB2r5CLVohaMSF33zjvQu3fYpPLkk0P3WKtWSUcltYBaMCJ11XffweWXQ+fO8MUX8NRTMGqUkotkjFowInXR66+HVstHH4XHm2+Gpk2TjkpqGbVgROqS1avDvmFdu8IPP8CECWH6sZKLxKBCCcbM6sUdiIjEbNw46NQJhgyBCy4Im1P+9rdJRyW1WEVbMPPM7GYz6xhrNCKSeStWwOmnw9FHQ6NG8MYbcNtt0DDz58eIpKtogtkT+Ai438ymmFkfM2sSY1wiUl3u8MQT0LEjjBgRNqacMQO6dEk6MqkjKpRg3H21u9/n7gcCfwOuBJaa2XAzaxdrhCJSeUuXwgknQI8e4SCwadPg6qthiy2SjkzqkAqPwZjZcWb2NPAf4FagLfAcMDbG+ESkMtzhgQegQ4dwuuRNN8GUKbDXXklHJnVQRacpfwy8Atzs7m+mlY82s4MzH5ZI7ZBKOYtWrGXZN0W0ahLP0cY/WrgQ+vSBl16Cgw+G++6D3XaL571EKmCTCSaaQfaQu19d2uvu3j/jUYnUAhU60z4TNmwIxxZfcQXUqwd33x0STZ5WIUiyNvkv0N03AIdmIRaRWmWTZ9pnwpw5YSv9Cy6AQw6B2bPhnHOUXCQnVLSL7E0zuxN4HPjxf4e7vxNLVCK1QFln2i9fXUTbFo0qfb+Nutsa5JH/wF3kXXstNG4Mjz4Kf/wjWEzdbyJVUNEEc2D0mN5N5sBhmQ1HpPYo7Uz7BvXzaNm48mfYp3e3tV/8ITePH0ze8oV4jz9gdwyGli0zGbpIRlQowbi7ushEKin9TPv0MZj8ZpVf4LhoxVqueGwKF7zyKH95+xkKG27DuT3+xaV3Xlql1pBINlR4s0szOwboBPz451dZA/8VuNeFwFmEVtD7wBnAVoQuuHxgEdDD3VdG118O9AY2AP3d/YWofD/gIWBLwnTp893dzWwL4GFgP2AF8Ad3X1SVWEWqKi/P6NZpO3bv35Xlq4to2bjqs8i+mzCRp4f2ZZeVS/nvXkcx8NAzWb1FQ3pVsbtNJBsqug7mHuAPQD/AgJOBKp1EZGatgf5AgbvvAdQDegIDgInu3h6YGH1PtD1NT0Jy6wYMSdsb7W6gD9A++uoWlfcGVrp7O+A24MaqxCpSXXl5RtsWjTigbXPatmhU+eTyzTdw7rl0OvV46rlzSs/ruKJbP1Zv0bDK3W0i2VLRqSYHuvvphF/a/wa6ADtW4303A7Y0s80ILZfPge7A8Oj14cDx0fPuwEh3/97dFwLzgM5mtj3QxN0nu7sTWizpdYrvNRo43Eyjn1LD/N//hc0phw7FL7yQOS+8zox2+wBUq7tNJFsq2kX2XfT4rZntQOh22qUqb+jun5nZLcDi6L4vuvuLZtbK3ZdG1yw1s+JRy9bAlLRbLInK1kXPS5YX1/k0utd6M1sFNAO+TI/FzPoQWkDstNNOVfk4IplXWBimHf/3vyHBjB6N7b8/R6acsbu0qnZ3m0i2VLQF87yZbQPcDLxDGCMZWZU3NLOmhBbGLsAOQEMz+1N5VUop83LKy6uzcYH7UHcvcPeCFi1alB+4SNzcYeTIsDnlE0/AVVeF44z33x/IQHebSJZVdBbZNdHTJ83seaCBu6+q4nv+Fljo7oUAZvYUYRr0MjPbPmq9bA8sj65fwsbdcW0IXWpLoucly9PrLIm64bYGvqpivCLx++wzOPdceO65cITxsGGwxx5JRyVSLeUmGDM7oZzXcPenqvCei4EDzGwrQhfZ4cA0wgLOXsAN0eOY6Ppngf+a2SBCi6c98Ja7bzCz1WZ2ADAVOB24I61OL2AycBLwcjROI5Jb3MOJkpdcAuvWwa23wvnnhy1fRGq4TbVgfl/Oaw5UOsG4+1QzG03oalsPzACGAo2AUWbWm5CETo6un21mo4A50fV9o+1rAM7lp2nK46IvgGHAI2Y2j9By6VnZOEViN38+/OUv8MorcOihYXPKXXdNOiqRjDH9YR8UFBT4tGnTkg5D6oING+D228MBYPXrwy23wFlnaZsXqZHMbLq7F5T2WiILLUXqrFmz4Mwz4e234fe/Dzsft2696XoiNVDWF1qK1Ek//BBmhe27bzi3ZcQIGDNGyUVqtaQWWorUHW+9FRLLv/8djjCeOxd69lSXmNR6FU0wRdFj8ULL9VRxoaVInfHtt3DxxdClC6xaBc8/H7bVb9486chEsqKiYzDPlVho6cB9cQUlUuO98koYuF+wIBwAdsMNsPXWSUclklUVTTAfABvc/clo88l9gWdii0qkplq1Ci69NEw5btcO/vc/+M1vko5KJBEV7SL7p7uvNrODgCMIa0/uji0qkZrouefCNi/DhoUk8+67Si5Sp1U0wRQvbDwGuMfdxwCbxxOSSA1TWAinnALHHQfNmsHUqXDTTbDVVklHJpKoiiaYz8zsXqAHMDY60KuidUVqJ/ew43GHDvDkk3D11TBtGhSUuuZMpM6paJLoAbwAdHP3r4FtgUvjCkok5336aVgoeeqpYaxlxoywMn9zNexFilV0N+VvSdt3LDq3ZWlcQYnkrFQKhg6Fv/0tbPly223Qr582pxQpRYW3ihGp8z7+OGxO+eqrcPjhIdG0bZt0VCI5S+MoIpuyfj3cfDPsuSfMnBlmiU2YoOQisglqwYiU5733oHfvMHh//PFw112www5JRyVSI6gFI1Ka77+Hf/0L9tsPFi+GUaPgqaeUXEQqQS0YkZImTw6tlrlz4fTTYdCgsL5FRCpFLRiRYmvXwgUXwK9/HZ6PGwfDhyu5iFSRWjAiAC+9FGaILVoEffvCwIHQuHHSUYnUaGrBSN329dehO+yII8IiyUmT4M47S00uqZSzoHANk+d/yYLCNaRSOm5cpDxqwUjd9cwzcN55sHw5DBgAV14JDRqUemkq5Yyf/QUXjZpJ0boUDernMajH3nTrtB15eTo4TKQ0asFI3bNsWThZ8v/9P2jVKpw4OXBgmckFYNGKtT8mF4CidSkuGjWTRSvWZitqkRpHCUbqDnd4+OGwOeWYMXDddT8dZ7wJy74p+jG5FCtal2L56qIyaoiIusikbli8GM4+G8aPhwMPDKvxd9+9wtVbNWlAg/p5GyWZBvXzaNm47FaPSF2nFozUbqlUWH3fqRO89hoMHhweK5FcAPKbNWRQj71pUD/8lykeg8lv1lCD/yJlUAtGaq8PP4SzzoLXXw+zxIYOhfz8Kt0qL8/o1mk7du/fleWri2jZuAH5zRoCaPBfpAxqwUjts24d3HAD7LUXzJ4NDz0EL7xQ5eRSLC/PaNuiEQe0bU7bFo3IyzMN/ouUQy0YyahUylm0Yi3LvimiVZPwV35W/5KfORPOPDMcAHbiiWFNy3bbxfZ25Q3+t23RKLb3FakJlGAkYxJdK1JUBNdcAzfeCM2bw+jRIcHETIP/ImVTF5lkTGLdRW+8AXvvDddfD6edBnPmZCW5QPmD/yJ1nVowkjFxdheV2vX27Vq44orQDbbTTmGc5cgjq/U+lVXW4L8G+EWUYCSD4uouKq3r7eE2X/OrgZdjixfDX/8aWi+NkhnzKB7815iLyMbURSYZE1d3UXrX29bfreaaZwbR+Zw/sq7+5j+tbUkouYhI2dSCkYyJq7uouOvtqA/f5NoJQ2j67Tfc2aUHvxp2K/t3aJOh6EUk05RgJKPi6C7a4btV3DtmIEd98AazWu1Kr5OvZkGbdoxtvk2V75n4dGqROkAJRnKXOwwfzk4XXkibb7/jlsPO4O79jqf+FvWr1fWmrfdFskMJRnLTokXQpw9MmIAddBA29D5OaN6GgzLQ9VbWdOrd+3fVQL1IBiUyyG9m25jZaDP7wMzmmlkXM9vWzCaY2cfRY9O06y83s3lm9qGZHZVWvp+ZvR+9NtjMLCrfwswej8qnmll+Ah+z1op1c8dUCu64A/bYAyZPDlOQX32VvA67/2yblqrS1vsi2ZHULLL/AOPdfXdgL2AuMACY6O7tgYnR95hZR6An0AnoBgwxs3rRfe4G+gDto69uUXlvYKW7twNuA27MxoeqC4q7l44e/Bqn3DeVowe/xvjZX2QmycydC127Qv/+4XHWLOjbF/Iy+8+0eDp1Oq2+F8m8rCcYM2sCHAwMA3D3H9z9a6A7MDy6bDhwfPS8OzDS3b9394XAPKCzmW0PNHH3ye7uwMMl6hTfazRweHHrRqonltX669aFdSx77w0ffBAOBRs7FnbeOTNBl6DV9yLZkcQYTFugEHjQzPYCpgPnA63cfSmAuy81s5bR9a2BKWn1l0Rl66LnJcuL63wa3Wu9ma0CmgFfpgdiZn0ILSB22mmnTH2+Wi3jq/XfeSdsTvnuu+EY48GDwzHGMdLqe5HsSKKLbDNgX+Bud98HWEvUHVaG0v7Xeznl5dXZuMB9qLsXuHtBixYtyo9agAx2L333HQwYAJ07w7Jl8PTT8PjjsSeXYqVtvS8imZVEglkCLHH3qdH3owkJZ1nU7UX0uDzt+h3T6rcBPo/K25RSvlEdM9sM2Br4KuOfpA7KSPfSa6+F7rAbb4Q//zlsTnn88XGEKyIJynoXmbt/YWafmtkv3P1D4HBgTvTVC7ghehwTVXkW+K+ZDQJ2IAzmv+XuG8xstZkdAEwFTgfuSKvTC5gMnAS8HI3TSDVVq3tp9erQahkyJBz+NWEC/Pa3G11SlQWQWjQpkpuSWgfTD3jMzDYHFgBnEFpTo8ysN7AYOBnA3Web2ShCAloP9HX3DdF9zgUeArYExkVfECYQPGJm8wgtl57Z+FC1WWm/xCs15jJuHJx9NixZAhdcANdeCw03bvVUZgFkcTwr1n7P518XcdmT72nRpEiOMf1hHxQUFPi0adOSDiMnVWvl+4oVcOGF8Mgj0LEjDBsGBxxQ6qULCtdw9ODXfrYb89gSCyDT4+l9UFuGvb5gk3VEJB5mNt3dC0p7TbspyyZVaWqyO4waBR06wIgR8M9/hhljZSQXqPgCyPR4zNCiSZEcpQQjm1Tple+ffw4nnAB/+EM4CGz6dLj6athii3Lfp6Iz1ErGo0WTIrlJCUY2qcJTk91DF1jHjjB+PNx8M0yZAnvuWaH3qegMta023+zHa56cvoT+h7XXokmRHKQxmIjGYMpWoTGYBQvC5pQTJ/LdgQfxwdW3sPWenSo9o6t48L68GWpvL1rB2wtXMvjljylal2LnZltyWbcObJZntGvZSLPIRLKovDEYJZiIEkz5yvzFv2FD2Jzy73/H69Vj1gX/oEeqE9+tJ7YZXQsK13DGQ29x7J6tMQsNp+ff+4wH/9xZA/siWaYEUwFKMFUwZw707h26wY45hk+uu5WjRsc/o0vnuYjkjvISjM6Dkcr74YewCv+aa6BJE3jsMTjlFD5fsIKidfM2urRa+5SVQXuJidQMSjBSOW+/HVot778PPXuGzSmjfdyKJwOUbMHEMaMrjqOZRSSzNItMKubbb+HSS8M6lhUrYMyYsL4lbZNQbYMvIunUgpFN+9//4C9/gXnzwkyxm26Crbf+2WXquhKRdEowUrZVq+Cyy+Dee2HXXeHll+HQQ8utoq4rESmmLjIp3f/9H3TqBPfdBxdfDO+9t8nkIiKSTglGNlZYCKeeCsceC02bwuTJcMstsNVWSUcmIjWMEowE7jByZNjm5Ykn4Kqrwh5inTsnHZmI1FAag5FwRst558Fzz4WEMmwY7LFH0lGJSA2nFkxdlkrB0KFhrOWll2DQIHjzTSUXEckItWDqqvnz4ayzwhTkQw8Ng/m77pp0VCJSi6gFU9ds2AC33gq//GU4AOy++2DiRCUXEck4tWDqklmz4Mwzw3Yvv/893H03tG6ddFQiUkupBVMX/PBDmBW2776waFGYLTZmjJKLiMRKLZjaburUsDnl7Nlhfcvtt0Pz5klHJSJ1gFowtdXatXDRRdClS9jy5fnn4dFHlVxEJGvUgolJ8QmQy74polWTLG/6+PLLYXPKBQvgnHPC2S1NmmTnvUVEIkowMUjsxMWvvw5b6t9/P7RrF6Yg/+Y38b2fiEg51EUWg0Ur1v6YXCCc6njRqJksWrE2vjd99tmwYPKBB+CSS+Ddd5VcRCRRSjAxWPZN0UanOsJPRwdn3PLl4WTJ7t2hWbMwqH/zzdqcUkQSpwQTg+Kjg9Nl/Ohg9zBo36EDPP00XHMNTJsGBQWZew8RkWpQgolB7EcHf/pp2E7/tNNgt91gxgz4xz9g880zc38RkQzQIH8MYjs6OJWCe+/FL7sM37CBT/5xLd73r+S3bKK/FEQk5yjBxCTjRwd//HHYnHLSJFYc0JU/7HcG89e1pMFdb2ZnhpqISCXpD99ct3493HQT7LknvPsuhbffxUGHD2B+o5ZAlmaoiYhUgRJMLnv3Xdh/f7jsMujWDebMYd6xPSha7xtdFtsMNRGRalCCyUXffw///GeYEbZkCYwaBU89BTvskJ0ZaiIiGaAEk2smT4Z99oFrr4U//hHmzIGTTwYL4yuxz1ATEckQDfLnijVrwlTjwYNhxx1h3LjQLVZCbDPUREQyLLEWjJnVM7MZZvZ89P22ZjbBzD6OHpumXXu5mc0zsw/N7Ki08v3M7P3otcFm4c98M9vCzB6PyqeaWX7WP2BlTJgQTpj8z3/gvPPCwWClJJdixTPUDmjbnLYtGim5iEhOSrKL7Hxgbtr3A4CJ7t4emBh9j5l1BHoCnYBuwBAzqxfVuRvoA7SPvop/K/cGVrp7O+A24MZ4P0oVrVwZzmo58siwSHLSJLjzTmjcuEq3S6WcBYVrmDz/SxYUriGV8k1XEhGJSSIJxszaAMcA96cVdweGR8+HA8enlY909+/dfSEwD+hsZtsDTdx9srs78HCJOsX3Gg0cXty6ybQq/1J/+mno2BGGD4cBA2DmTOjatVpxjJ/9BUcPfo1T7pvK0YNfY/zsL5RkRCQxSbVgbgf+BqTvCNnK3ZcCRI8to/LWwKdp1y2JylpHz0uWb1TH3dcDq4BmJYMwsz5mNs3MphUWFlb6Q1Tpl/oXX4RB+xNOgO22g7fegoEDYcstK/3+6RLZwVlEpBxZTzBmdiyw3N2nV7RKKWVeTnl5dTYucB/q7gXuXtCiRYsKhvOTSv1Sd4eHHw6tlueeg+uvD8ll330r/b6lyeoOziIiFZBEC+bXwHFmtggYCRxmZo8Cy6JuL6LH5dH1S4Ad0+q3AT6PytuUUr5RHTPbDNga+CrTH6TCv9Q/+QR+9zvo1Qs6dCD1zgwWnNWPyYtXZWysROtjRCTXZD3BuPvl7t7G3fMJg/cvu/ufgGeBXtFlvYAx0fNngZ7RzLBdCIP5b0XdaKvN7IBofOX0EnWK73VS9B4ZH4zY5C/1VAruugv22ANefx3uuIPUq5MYv2GbjI+VaH2MiOSaXFoHcwMwysx6A4uBkwHcfbaZjQLmAOuBvu6+IapzLvAQsCUwLvoCGAY8YmbzCC2XnnEEXPxLveTRyPnNGsKHH4bNKV9/HY46Cu69F3bemUWFa0rtVtu9f9dqbYyp9TEikmsshj/sa6SCggKfNm1apeulUs6iFWt/+qXeZHPybhsEV10VTpW87TY4/fQfV+JPnv8lp9w39Wf3Gdlnfw5o27y6H0NEJKvMbLq7l3rSYS61YGqkjbblnzEjrGuZMQNOOgnuuCPMFEtT3K2WPnajsRIRqY20F1kmFBXBFVfAr34Fn38OTz4JTzzxs+QCGisRkbpDLZjqWrgwzBD78EM44wy49VZo2rTMyzVWIiJ1hRJMdbVuDe3ahU0qjzyyQlUyftqliEgOUoKprs03h+efTzoKEZGcozEYERGJhRKMiIjEQglGRERioQQjIiKxUIIREZFYKMGIiEgslGBERCQWSjAiIhIL7aYcMbNC4JOk46ik5sCXSQeRsLr+M6jrnx/0M4BkfwY7u3upRwIrwdRgZjatrG2y64q6/jOo658f9DOA3P0ZqItMRERioQQjIiKxUIKp2YYmHUAOqOs/g7r++UE/A8jRn4HGYEREJBZqwYiISCyUYEREJBZKMDWMme1oZq+Y2Vwzm21m5ycdU1LMrJ6ZzTCzOnnim5ltY2ajzeyD6N9Dl6RjyjYzuzD6fzDLzEaYWYOkY4qbmT1gZsvNbFZa2bZmNsHMPo4eyz63PYuUYGqe9cDF7t4BOADoa2YdE44pKecDc5MOIkH/Aca7++7AXtSxn4WZtQb6AwXuvgdQD+iZbFRZ8RDQrUTZAGCiu7cHJkbfJ04JpoZx96Xu/k70fDXhl0rrZKPKPjNrAxwD3J90LEkwsybAwcAwAHf/wd2/TjSoZGwGbGlmmwFbAZ8nHE/s3H0S8FWJ4u7A8Oj5cOD4bMZUFiWYGszM8oF9gKkJh5KE24G/AamE40hKW6AQeDDqJrzfzBomHVQ2uftnwC3AYmApsMrdX0w2qsS0cvelEP4IBVomHA+gBFNjmVkj4EngAnf/Jul4ssnMjgWWu/v0pGNJ0GbAvsDd7r4PsJYc6RbJlmicoTuwC7AD0NDM/pRsVJJOCaYGMrP6hOTymLs/lXQ8Cfg1cJyZLQJGAoeZ2aPJhpR1S4Al7l7ceh1NSDh1yW+Bhe5e6O7rgKeAAxOOKSnLzGx7gOhxecLxAEowNY6ZGaHffa67D0o6niS4++Xu3sbd8wmDui+7e536y9XdvwA+NbNfREWHA3MSDCkJi4EDzGyr6P/F4dSxiQ5pngV6Rc97AWMSjOVHmyUdgFTar4HTgPfNbGZUdoW7j00uJElIP+AxM9scWACckXA8WeXuU81sNPAOYXblDHJ0y5RMMrMRwCFAczNbAlwJ3ACMMrPehMR7cnIR/kRbxYiISCzURSYiIrFQghERkVgowYiISCyUYEREJBZKMCIiEgslGBERiYUSjIiIxEIJRiQHmNk16Wf7mNl1Zta/jGsvNbO3zew9M/t39qIUqRwlGJHcMIxoqw8zyyNsgfNYyYvM7EigPdAZ2BvYz8wOzl6YIhWnrWJEcoC7LzKzFWa2D9AKmOHuK0q59Mjoa0b0fSNCwpmUnUhFKk4JRiR33A/8GdgOeKCMawwY6O73ZisokarSXmQiOSLatPJ9oD7Q3t03lHLNkcA1wOHuviY6Nnidu+fE9uwi6dSCEckR7v6Dmb0CfF1acomuedHMOgCTww71rAH+RI6c/yGSTi0YkRwRDe6/A5zs7h8nHY9IdWkWmUgOMLOOwDxgopKL1BZqwYjkIDP7JfBIieLv3X3/JOIRqQolGBERiYW6yEREJBZKMCIiEgslGBERiYUSjIiIxOL/A6PH8wsup3QHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line in the cuberoot Transformation case\n",
    "plt.plot(X,model1.params[0]+model1.params[1]*(X),\"r\")\n",
    "sn.scatterplot(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "f9693774",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>salary</td>      <th>  R-squared:         </th> <td>   0.957</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.955</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   622.5</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>1.14e-20</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:32:40</td>     <th>  Log-Likelihood:    </th> <td> -301.44</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    30</td>      <th>  AIC:               </th> <td>   606.9</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    28</td>      <th>  BIC:               </th> <td>   609.7</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> 2.579e+04</td> <td> 2273.053</td> <td>   11.347</td> <td> 0.000</td> <td> 2.11e+04</td> <td> 3.04e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>y_e</th>       <td> 9449.9623</td> <td>  378.755</td> <td>   24.950</td> <td> 0.000</td> <td> 8674.119</td> <td> 1.02e+04</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.140</td> <th>  Durbin-Watson:     </th> <td>   1.648</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.343</td> <th>  Jarque-Bera (JB):  </th> <td>   1.569</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.363</td> <th>  Prob(JB):          </th> <td>   0.456</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.147</td> <th>  Cond. No.          </th> <td>    13.2</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                 salary   R-squared:                       0.957\n",
       "Model:                            OLS   Adj. R-squared:                  0.955\n",
       "Method:                 Least Squares   F-statistic:                     622.5\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           1.14e-20\n",
       "Time:                        15:32:40   Log-Likelihood:                -301.44\n",
       "No. Observations:                  30   AIC:                             606.9\n",
       "Df Residuals:                      28   BIC:                             609.7\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept   2.579e+04   2273.053     11.347      0.000    2.11e+04    3.04e+04\n",
       "y_e         9449.9623    378.755     24.950      0.000    8674.119    1.02e+04\n",
       "==============================================================================\n",
       "Omnibus:                        2.140   Durbin-Watson:                   1.648\n",
       "Prob(Omnibus):                  0.343   Jarque-Bera (JB):                1.569\n",
       "Skew:                           0.363   Prob(JB):                        0.456\n",
       "Kurtosis:                       2.147   Cond. No.                         13.2\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model1.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40ee649e",
   "metadata": {},
   "source": [
    "### Accuracy is around 95%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e663ba51",
   "metadata": {},
   "source": [
    "## 2.With LOG Transformation to y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "03b27a73",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Aplpying log Transformation to X and Y\n",
    "log_X=np.log(X)\n",
    "log_Y=np.log(Y)\n",
    "d_2[\"log_x\"]=log_X\n",
    "d_2[\"log_Y\"]=log_Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "8cee3ee3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting original and LOG Transformed Data\n",
    "plt.subplots(1,1)\n",
    "plt.suptitle(\"Years Experienced\")\n",
    "sn.distplot(X)\n",
    "sn.distplot(log_X)\n",
    "labels=(\"Original\",\"log Transformed\")\n",
    "plt.legend(labels)\n",
    "\n",
    "plt.subplots(1,1)\n",
    "plt.suptitle(\"Salary\")\n",
    "sn.distplot(Y)\n",
    "sn.distplot(log_Y)\n",
    "\n",
    "labels=(\"Original\",\"log Transformed\")\n",
    "plt.legend(labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "id": "5b399c8b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model2=smf.ols(\"log_Y~y_e\",data=d_2).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 166,
   "id": "6a9ba22e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>log_Y</td>      <th>  R-squared:         </th> <td>   0.932</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.930</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   383.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>7.03e-18</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:50:12</td>     <th>  Log-Likelihood:    </th> <td>  28.183</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    30</td>      <th>  AIC:               </th> <td>  -52.37</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    28</td>      <th>  BIC:               </th> <td>  -49.56</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>   10.5074</td> <td>    0.038</td> <td>  273.327</td> <td> 0.000</td> <td>   10.429</td> <td>   10.586</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>y_e</th>       <td>    0.1255</td> <td>    0.006</td> <td>   19.585</td> <td> 0.000</td> <td>    0.112</td> <td>    0.139</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.826</td> <th>  Durbin-Watson:     </th> <td>   1.438</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.661</td> <th>  Jarque-Bera (JB):  </th> <td>   0.812</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.187</td> <th>  Prob(JB):          </th> <td>   0.666</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.286</td> <th>  Cond. No.          </th> <td>    13.2</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                  log_Y   R-squared:                       0.932\n",
       "Model:                            OLS   Adj. R-squared:                  0.930\n",
       "Method:                 Least Squares   F-statistic:                     383.6\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           7.03e-18\n",
       "Time:                        15:50:12   Log-Likelihood:                 28.183\n",
       "No. Observations:                  30   AIC:                            -52.37\n",
       "Df Residuals:                      28   BIC:                            -49.56\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     10.5074      0.038    273.327      0.000      10.429      10.586\n",
       "y_e            0.1255      0.006     19.585      0.000       0.112       0.139\n",
       "==============================================================================\n",
       "Omnibus:                        0.826   Durbin-Watson:                   1.438\n",
       "Prob(Omnibus):                  0.661   Jarque-Bera (JB):                0.812\n",
       "Skew:                           0.187   Prob(JB):                        0.666\n",
       "Kurtosis:                       2.286   Cond. No.                         13.2\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 166,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cf84d4ec",
   "metadata": {},
   "source": [
    "#### The Accuracy is 93%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "id": "d402d655",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='y_e', ylabel='salary'>"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line\n",
    "plt.plot(X,model2.params[0]+model2.params[1]*(X),\"r\")\n",
    "sn.scatterplot(X,log_Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8ce34282",
   "metadata": {},
   "source": [
    "## 3.With Log Transformation to both X and Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "234e559a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model3=smf.ols(\"log_Y~log_X\",data=d_2).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "id": "a4b74174",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='y_e', ylabel='salary'>"
      ]
     },
     "execution_count": 178,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line\n",
    "plt.plot(log_X,model3.params[0]+model3.params[1]*(log_X),\"r\")\n",
    "sn.scatterplot(log_X,log_Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 179,
   "id": "e9db6f58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>log_Y</td>      <th>  R-squared:         </th> <td>   0.905</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.902</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   267.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>7.40e-16</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>15:56:39</td>     <th>  Log-Likelihood:    </th> <td>  23.209</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    30</td>      <th>  AIC:               </th> <td>  -42.42</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    28</td>      <th>  BIC:               </th> <td>  -39.61</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>   10.3280</td> <td>    0.056</td> <td>  184.868</td> <td> 0.000</td> <td>   10.214</td> <td>   10.442</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>log_X</th>     <td>    0.5621</td> <td>    0.034</td> <td>   16.353</td> <td> 0.000</td> <td>    0.492</td> <td>    0.632</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.102</td> <th>  Durbin-Watson:     </th> <td>   0.988</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.950</td> <th>  Jarque-Bera (JB):  </th> <td>   0.297</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.093</td> <th>  Prob(JB):          </th> <td>   0.862</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.549</td> <th>  Cond. No.          </th> <td>    5.76</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                  log_Y   R-squared:                       0.905\n",
       "Model:                            OLS   Adj. R-squared:                  0.902\n",
       "Method:                 Least Squares   F-statistic:                     267.4\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           7.40e-16\n",
       "Time:                        15:56:39   Log-Likelihood:                 23.209\n",
       "No. Observations:                  30   AIC:                            -42.42\n",
       "Df Residuals:                      28   BIC:                            -39.61\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     10.3280      0.056    184.868      0.000      10.214      10.442\n",
       "log_X          0.5621      0.034     16.353      0.000       0.492       0.632\n",
       "==============================================================================\n",
       "Omnibus:                        0.102   Durbin-Watson:                   0.988\n",
       "Prob(Omnibus):                  0.950   Jarque-Bera (JB):                0.297\n",
       "Skew:                           0.093   Prob(JB):                        0.862\n",
       "Kurtosis:                       2.549   Cond. No.                         5.76\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 179,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model3.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75a7e05f",
   "metadata": {},
   "source": [
    "#### The Accuracy is 90%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b666037f",
   "metadata": {},
   "source": [
    "## 4. Square Root Transformation on Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "id": "3679ca42",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Applying square root transformaton\n",
    "sq_X=np.sqrt(X)\n",
    "sq_Y=np.sqrt(Y)\n",
    "d_2[\"sq_X\"]=sq_X\n",
    "d_2[\"sq_Y\"]=sq_Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "id": "88d9bac5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16ce233ee50>"
      ]
     },
     "execution_count": 200,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting original and Square Root Transformed Data\n",
    "plt.suptitle(\"Years Experienced\")\n",
    "sn.distplot(X)\n",
    "sn.distplot(sq_X)\n",
    "labels=(\"Original\",\"square root Transformed\")\n",
    "plt.legend(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "id": "26809168",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model4=smf.ols(\"sq_Y~y_e\",data=d_2).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "effafd70",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='y_e', ylabel='salary'>"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEGCAYAAACKB4k+AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAp3klEQVR4nO3deXhU5fn/8fcdjEYFNwyIoEa+YllcQONW17pSq7W21epPrWvRiuIuon7LF5WqVbFSKShu1LVUUNECFRFRqGADohBwAURFWSKKbIZt7t8fzyQNIQmTZM6cSfJ5XVeuTM6cc+ZOxLnn2e7H3B0RERGAnLgDEBGR7KGkICIi5ZQURESknJKCiIiUU1IQEZFyW8UdQH3suuuuXlBQEHcYIiINyrRp075x9/yqnmvQSaGgoICioqK4wxARaVDM7PPqnlP3kYiIlFNSEBGRckoKIiJSTklBRETKKSmIiEg5JQURESmnpCAiIuWUFEREGpJEAh57DF59NZLbKymIiDQUc+bAccfB734Hzz4byUsoKYiIZLvSUujbFw48EGbNCi2F556L5KUadJkLEZFG76234PLL4ZNP4P/9P3jwQWjVKrKXU0tBRCQbffstXHop/OQnsH49jB0buowiTAigpCAikl3c4ZlnoGNHGDYMevcOXUannJKRl1f3kYhItpg3D37/exg3Dg47DN54Aw44IKMhqKUgIhK39evhnntgv/1gyhR4+GGYPDnjCQHUUhARideUKdCjB8ycCb/8JQwcCG3bxhaOWgoiInH4/nu48kr48Y/hu+/glVdgxIhYEwJEmBTMLM/M3jOzD8ys2Mz6JY//n5l9ZWYzkl+nVrimj5nNNbOPzSwzoyoiIpnkDi++CJ06wSOPQK9eMHs2/Pzn5ackEs78klW8O+8b5pesIpHwjIUXZffRWuB4d19lZrnAJDMbk3zuQXe/v+LJZtYZOAfoAuwOvGFm+7r7xghjFBHJnC++gJ494bXXoGtXGDUKCgs3OSWRcMYWL+b64TMoXZ8gLzeHAWd3pXuX3cjJMRIJZ8Gy1SxZUUrrHfIoaLk9OTmWthAjayl4sCr5Y27yq6Z0dwbwgruvdffPgLnAoVHFJyKSMRs2hEVnnTvDm2/C/ffDf/6zWUIAWLBsdXlCAChdn+D64TNYsGx1ecI4deA7nDt0KqcOfIexxYvT2pKIdEzBzJqZ2QxgKTDO3acmn7rKzD40syfMbOfksbbAlxUuX5g8VvmePcysyMyKSkpKogxfRKT+pk8P00uvvx6OPRaKi+GGG2CrqjtqlqwoLU8IZUrXJ1i6srTGhJEukSYFd9/o7l2BdsChZrYfMBj4H6ArsAh4IHl6Ve2fzdKfuz/q7oXuXpifnx9J3CIi9bZqVUgEhxwCX38Nf/976DYqKKjxstY75JGXu+lbc15uDq1a5NWYMNIlI7OP3H058BbQ3d2XJJNFAhjKf7uIFgJ7VLisHfB1JuITEUmr116DLl1Cl9Hvfheqm559NtiW+/4LWm7PgLO7lieGsjGFgpbb15gw0iWygWYzywfWu/tyM9sWOBG418zauPui5GlnArOSj0cBz5nZAMJAcwfgvajiExFJu0WLwmyiF18M4weTJsGRR9bqFjk5Rvcuu9Gx19EsXVlKqxb/HUwuSxiVB6ELWm6ftl8hytlHbYBhZtaM0CIZ7u6vmdnTZtaV0DW0ALgcwN2LzWw4MBvYAPTUzCMRaRASiTC99JZbYO1auOsuuOkm2HrrOt0uJ8don9+c9vnNNzteXcJIF3PP3PzXdCssLPSioqK4wxCRpmzWrLAi+d134fjjYcgQ6NAh7qhqZGbT3H3zqU+ozIWISK2UrRMoWfod+z42kJ0e/jO2446houkFF6Q0bpDNlBRERFJUtk5g+L1P0Xf0X9j5u0Us/PnZ7D70YXJaNY7ZkEoKIiIp+uLjBaw77zKemvkmn+3chnPP6c/7+3RjtG1L+7iDSxMlBRGRLXGHYcNoe/0N7P79Cv5yxG94+IizWZu7DSTXCVQeFG6olBRERGryySdwxRUwYQIbDz2cX3e7kFk7/XdJVbrXCcRNpbNFRKqydi3ccQfsv38oVTFkCFtPnsSVPc+ocmFZY6GWgojELurKn7X2zjtw+eX/XYn85z9DmzbkQOTrBOKmpCAisdpSqeiM+u476N0bhg6FvfaCf/4TTj11k1OqW1jWWKj7SERilYnKn1vkDi+8EDa+eeKJUMW0uHizhFBZnJvhREUtBRGJVU2VPzPyafyzz8K2mGPHhv0NxoyBbt22eFlWtXDSSC0FEYlVJip/Vmn9evjTn0I100mTwrjBlCkpJQTIkhZOBJQURCRWNZWKjsx774VWQe/ecNJJYY/ka66BZs1SvkUm9jaIg7qPRCRWmaj8WW7FCrjtNhg0CNq0gREj4Mwz61SvqKyFUzExNIY1C2opiEjsymb0HN5+V9rnN48mIbz8ctjjYNCgMIYwezb88pd1LmAXSwsnA9RSEJFGodq1DgsXwtVXh6Sw//5hA5zDD6/362W0hZNBSgoi0uBVORPoV/vT/e2R5Nx+O2zYAPfcE/ZMzs1N2+s2xjULSgoi0uBVngm091dzafuza8n5+hM4+WQYPBjaN5Y6ptFSUhCRBq9sJlDe+lKunfw8l733Esu3bcGnDw6hwzU9GvzGN5mkpCAiDV7rHfI48Yv3+cPoh9nz+yW8cMDJPHjSpTx/3qlKCLWkpCAiDduSJex97XU89sLzzG/Zjt+cezcf/M+BjWImUByUFESkYUokQp2im27C1qwh0bcvXHY1163zRjMTKA6RJQUzywPeBrZJvs6L7t7XzO4DTgfWAfOAi919uZkVAHOAj5O3mOLuV0QVn4g0YHPmhNLW77wDxx4LQ4aQ07Ej7aHGbTGzrkR3FoqypbAWON7dV5lZLjDJzMYA44A+7r7BzO4F+gC9k9fMc/euEcYkIg1ZaSncfXf4at4cHn8cLr44pXGDxlrALt0iW9Hswarkj7nJL3f31919Q/L4FKBdVDGISCMyYQIceGDYDe3ss+Gjj+CSS1IeSG6sBezSLdIyF2bWzMxmAEuBce4+tdIplwBjKvy8t5m9b2YTzezoau7Zw8yKzKyopKQkmsBFJHssWxZaA8cfHxah/etf8Mwz0KpVrW7TWAvYpVukScHdNya7g9oBh5rZfmXPmdltwAbg2eShRcCe7t4NuB54zsx2qOKej7p7obsX5ufnRxm+iMTJHZ5+Gjp2DEnglltg5sywGK0OYivR3cBkpCCeuy8H3gK6A5jZhcBpwHnu7slz1rr7suTjaYRB6H0zEZ+IZJm5c8Ob/29/C/vsA9Onh3GE7bar8y0bawG7dIty9lE+sD45s2hb4ETgXjPrThhYPtbd11Q6/1t332hm7YEOwPyo4hORLLRuHdx/P9x5J2y9dahoevnltdrnoDqNtYBdukU5+6gNMMzMmhFaJMPd/TUzm0uYpjrOwgBR2dTTY4A7zGwDsBG4wt2/jTA+Eckm//53SACzZoWS1gMHQtu2aX2JxljALt0iSwru/iGw2b527r5PNeePAEZEFY+IxGOLawOWL4c+fWDIEGjXDl55BX7+89jibeq0ollEIlPj2gAj7G3QqxcsXRq2w7zzTmjRIu6wmzTtvCYikalubcDCGXPg9NPDeoM2bWDqVPjzn5UQsoBaCiISmcprA5olNnLe5JdoO+D5cOCBB0JLYSu9FWUL/ZcQkchU3Nx+v8VzuXvsX9h/yTzWnHgy2w19BAoK4g5RKlFSEJHIFLTcnodO68Cia27igvdGsWz7HZl+3xC6Xvc7aKbe62ykpCDSRGWiYmjO6H9ycs+e2BdfsOTcC/nhjrvo2r6t1gZkMSUFkSYo8oqhX38dZhO9+CLWuTNMmkTrI4+s/30lcmq/iTRBkVUMTSRg8GDo1AlefRXuugvefx+UEBoMJQWRJiiSiqGzZsFRR8GVV0JhYShed9ttoVyFNBhKCiJNUForhv7wA9x6K3TrBp98AsOGwRtvQIcOaYpWMklJQaQJSlvF0DfegP33DxVMzzsvbHzz29+mvPGNZB8NNIs0QfWuGFpSAtdfH/Y56NABxo8Pm+BIg6ekINJE1aliqDs89RTceCOsXAm33x7GDfK0UU1joaQgkiGZWBcQqU8+CaWt33orzCZ69FHo3DnuqCTNlBREMiDydQFRWrsW7r0X+veHbbeFRx6Byy6DHA1JNkb6ryqSAZGtC4jaO++EWUV9+8KZZ4aB5B49lBAaMf2XFcmASNYFROm778Kb/zHHwJo1MHo0vPAC7LZb3JFJxJQURDIgresCtiCRcOaXrOLded8wv2QViYSnfrF7ePPv1AmeeCIMKBcXw09/mvY4JTtpTEEkA8rWBVQeU6j1uoAtqNfYxWefhdXIY8eGFcljx0LXrmmNT7KfudfiU0SWKSws9KKiorjDEElJ2eyjOq0LSNH8klWcOvCdTbqq8nJzGN3r6Oqnnq5fH3Y969sXmjULA8o9e4bH0iiZ2TR3L6zquci6j8wsz8zeM7MPzKzYzPolj+9iZuPM7NPk950rXNPHzOaa2cdmdkpUsYnEoWxdwOHtd6V9fvNIZh3VeuzivffgkEPg5pvh5JNh9uywE5oSQpMV5ZjCWuB4dz8Q6Ap0N7PDgVuA8e7eARif/Bkz6wycA3QBugN/NTP9yxSphZTHLlasCG/+hx8eViePHAkvvwx77JG5YCUrRZYUPFiV/DE3+eXAGcCw5PFhwC+Sj88AXnD3te7+GTAXODSq+EQao5RqGr38clh09vDDoZtozpww3VSEiAeak5/0pwH7AIPcfaqZtXb3RQDuvsjMWiVPbwtMqXD5wuQxEUlRjTWNFi6Eq68OSeGAA2DECDjssLhDliwTaVJw941AVzPbCXjJzPar4fSqOlg3GwU3sx5AD4A999wzHWGKNCqb1TTauBEGDgo1ijZuDKuTr7sOcnPjDVSyUkbWKbj7cuAtwljBEjNrA5D8vjR52kKgYodmO+DrKu71qLsXunthfn5+lGGLNHwzZsARR4StMY88MmyEc/PNSghSrShnH+UnWwiY2bbAicBHwCjgwuRpFwKvJB+PAs4xs23MbG+gA/BeVPGJNGqrV4c3/8JC+PxzeO45GDMG2rePOzLJclF2H7UBhiXHFXKA4e7+mpm9Cww3s0uBL4CzANy92MyGA7OBDUDPZPeTiNTGmDFhEdqCBaFw3b33wi67xB2VNBCRJQV3/xDoVsXxZcAJ1VzTH+gfVUwijdrixXDttfD3v0PHjjBxYqhdJFILqn0k0tAlEmFvg06d4KWXoF+/MJaghCB1oNpHIg3Z7Nlh45tJk+DYY8NeBz/6UdxRSQOmloJIQ1RaCv/7v6FgXXFxqGg6YYISgtSbWgoiDc2ECaF18OmncN55MGAAtGq15etEUqCWgkhDsWwZXHwxHH98WIT2+uvwzDNKCJJWSgoi2c4dnn46zCh65hm45RaYORNOOinuyKQRUveRSCVl+x4sWVFK6x2i2fcgZXPnwhVXwPjxoaLpo4/C/vvHE4s0CUoKIhXUa+eydFq3Du6/H+68E7beGgYNCskhR417iZb+hYlUsGDZ6vKEAGGDmuuHz2DBstWZC+Lf/4aDDgoF7H72s1Da+sorlRAkI1L6V6bNbqSpqPXOZVuQSDjzS1bx7rxvmF+yikSihu1vly+H3/8+FK5bsQJGjYIXX4Tdd6/Ta4vURardR3PN7EXgSXefHWVAInEq27ms8h7Hm+1cloKUu6Lcw5t/r16wdGkoVXHnndC8mj2VRSKUanv0AOAT4DEzm2JmPcxshwjjEolFSjuXpSilrqjPP4fTT4ezz4Y2bcKeyQ8+qIQgsUmppeDuK4GhwFAzOwZ4Hngw2Xq4093nRhijSMbUuHNZLdXUFdV+5zwYODCsSgZ44IHQUthKcz8kXin9C0yOKfwMuBgoAB4AngWOBkYD+0YUn0jGbbZzWR1V1xXVbv4cOOtamD49DCQPGgR77VXPqEXSI9Xuo0+BM4D73L2buw9w9yXu/iIwNrrwRBquyl1Ru/haxix4ibanHAdffw3Dh8OrryohSFbZYksh2Up4yt3vqOp5d++V9qhEGoGKXVHrXn6FffrdwlZfLQzrDe6+G3baKe4QRTazxZZCcvezn2QgFpFGJ2fxItr//iI69jifrXbaESZPhsGDlRAka6U6qvVvM3sY+DtQPnXC3adHEpVIQ5dIwJAh0KdPWJ3cvz/ceGNYnSySxVJNCj9Ofq/YheTA8ekNR6QRmDkTevSAKVPgxBNDy2CffeKOSiQlqU5JVfeRyJb88APccUeoWbTTTqGy6XnngcVUTE+kDlKeFG1mPwO6AOVLO6sbfBZpcsaNCwPI8+eHPQ/uuw9atow7KpFaS7X20RDgN8DVgAFnATXOozOzPcxsgpnNMbNiM7smefzvZjYj+bXAzGYkjxeY2Q8VnhtSn19MJCOWLoXzz4eTT4ZmzeDNN8PWmEoI0kClPKbg7geY2Yfu3s/MHgBGbuGaDcAN7j7dzFoA08xsnLv/puyE5H2+r3DNPHfvWptfQCQW7vDkk3DTTbByZViZfOutkFf7Gkki2STVpPBD8vsaM9sdWAbsXdMF7r4IWJR8vNLM5gBtgdkAZmbA2WiwWhqajz8OeyRPnAhHHQWPPAKdO8cdlUhapLqi+TUz2wm4D5gOLABeSPVFzKwA6AZMrXD4aGCJu39a4djeZva+mU00s6OruVcPMysys6KSkpJUQxCpv7VroV8/OOAA+OCDsAvaxIlKCNKomHsN9d2rusBsGyDP3b/f4snh/ObARKC/u4+scHwwMNfdH6hw3+buvszMDgZeBrq4+4rq7l1YWOhFRUW1il+kTt5+O7QOPvoIzjknVDLdbbe4oxKpEzOb5u6FVT1XY/eRmf2yhueo+CZfzTm5wAjg2UoJYSvgl8DBZcfcfS2wNvl4mpnNIxTa07u+xOfbb+Hmm+Hxx6GgAMaMge7d445KJDJbGlM4vYbnnBoGm5NjBo8Dc9x9QKWnTwQ+cveFFc7PB751941m1h7oAMzfQnwi0XCH55+H666DZcvCgHLfvrB97fdVEGlIakwK7n5xPe59JHABMLNs2ilwq7uPBs4h7MlQ0THAHWa2AdgIXOHu39bj9UXqZv78sCfyv/4FhxwSvnftGndUIhkR2eI1d59EWNNQ1XMXVXFsBKGrSSQe69fDgAFhMLlZs7AJzpVXhsciTUSqm+wMAbYjVEt9DPg18F6EcYlk1tSpoV7Rhx/CmWeGhNCuXdxRiWRcqlNSf+zuvwW+c/d+wBHAHtGFJZIhK1bAVVfBEUeEsYOXXoKRI5UQpMlKNSmUJr+XLV7bwBYWr4lkvZdeCmsM/vrXkBhmz4Zf/CLuqERileqYwquVFq85MDSqoEQi9eWXcPXV8MorcOCBoWVw6KFxRyWSFVJNCh8BG919hJl1Bg4iLC4TaTg2boRBg+C228LjP/0Jrr0WcnPjjkwka6TaffS/yfpFRwEnAU8BgyOLSiTdZswI4wbXXBPqFRUXh7UHSggim0g1KWxMfv8ZMMTdXwG0r6Bkv9Wrw5t/YSF8/nlYkDZ6NOytITGRqqSaFL4ys0cIVU1HJ+sUpXqtSDzGjIEuXcJOaBdfDHPmhLpF2glNpFqpvrGfDfwL6O7uy4FdgJuiCkqkXhYvDm/+p54K224bitkNHQq77BJ3ZCJZL9U9mtdQoc5Rxb0SRLJGIgGPPQa9e8OaNdCvH4mbbmbBqg0smfcNrXfIo6Dl9uTkqKUgUp2Uy1yIZLXZs8OK5MmT4bjjYMgQEh32ZWzxYq4fPoPS9QnycnMYcHZXunfZTYlBpBoaF5CGrbQ0bIXZtWsYM3jyybBP8o9+xIJlq8sTAkDp+gTXD5/BgmWr441ZJIspKUjD9eabYRe0u+4KYwgffQQXXVQ+kLxkRWl5QihTuj7B0pWlVdxMREBJQRqib74Jb/4nnBDGEcaNg7/9DfLzNzmt9Q555OVu+k88LzeHVi3ySCSc+SWreHfeN8wvWUUiUbsdCEUaKyUFaTjcw5t/x47w7LNw660wcyaceGKVpxe03J4BZ3ctTwxlYwp77rwdY4sXc+rAdzh36FROHfgOY4sXKzGIUIc9mrOJ9mhuQj79FH7/exg/PqxMfvRR2G+/LV6WSDgLlq1m6cpSWrUIs48WLFvNqQPf2aRrKS83h9G9jqZ9fvMofwuRrFDTHs1qKUh2W7cO+veH/feH//wHBg+GSZNSSggAOTlG+/zmHN5+V9rnNycnxzTWIFIDTUmV8k/TS1aUZtdc/smT4fLLQ52is86Chx6CNm3qfduysYbKLYVWLfJquEqkaVBLoYlLJDz7+teXL4crrgiF61auhFdfheHD05IQoPqxhoKW26fl/iINmcYUmrj5Jauyp3/dHf7xj1DJdOnS8P2OO6B5+uOoaqwhK1pHIhlQ05iCuo+auJr61+ubFGrVLfX553DllaGC6UEHwWuvwcEH1+v1a1I21qCBZZFNRdZ9ZGZ7mNkEM5tjZsVmdk3y+P+Z2VdmNiP5dWqFa/qY2Vwz+9jMTokqNvmvmuby10fK3VIbNsADD4RtMSdOhAEDYOrUSBOCiFQvyjGFDcAN7t4JOBzomdy1DeBBd++a/BoNkHzuHKAL0B34q5k1izA+Ibr+9ZRKTBQVhW0wb7wRjj8+1C+67jrYSg1YkbhE9n9fxUqqyV3b5gBta7jkDOAFd18LfGZmc4FDgXejilFCN0r3LrvRsdfRae1fr7FbKs9DvaK//AVatw7jCL/6lfY5EMkCGZl9ZGYFQDdgavLQVWb2oZk9YWY7J4+1Bb6scNlCqkgiZtbDzIrMrKikpCTKsJuMquby11d13VIFk8eHjW8GDgzTTefMgV//WglBJEtEnhTMrDkwArjW3VcQ9nb+H6AroSXxQNmpVVy+2dQod3/U3QvdvTC/Uq0byR6Vu6X2/OFb3nr3YXb77Tmw445hDcJf/xoep0j1ikSiF2nnrZnlEhLCs+4+EsDdl1R4fijwWvLHhcAeFS5vB3wdZXwSnfJuqauOxB4Zwl6D7sI2rIc//jGMIeTm1up+ZQPX2htBJFpRzj4y4HFgjrsPqHC84gqkM4FZycejgHPMbBsz2xvoALwXVXxNTRyfsnOKZ9H+F6ewd9/e5Bx+GDZzJvTpU+uEACkOXItIvUXZUjgSuACYaWYzksduBc41s66ErqEFwOUA7l5sZsOB2YSZSz3dfWOE8TUZGf+UvWZNWHT2wAOw006hsun559dr3CDK9RQi8l9Rzj6aRNXjBKNruKY/0D+qmJqq6j5ld4xi1fLrr4dqpvPnw8UXw333QcuW9b6t6hWJZIZqHzUBGakKunQpnHcenHJKWGcwYQI88URaEgKoXpFIpmiVUBMQ6ads9/Dmf9NNsGoV/OEPYdwgL72f4KNaTyEim1JLoQmI7FP2Rx/BccfBZZeF/Q0++AD69Ut7QigTxXoKEdmUWgpNQNo/Za9dC3ffHb622w6GDoVLLoEcfcYQaeiUFJqItFUFnTgxrET++GM491x48EES+a2yc5MeEak1JQVJzbffws03w+OPw957w5gx0L17ytNdK5fR3nPn7fjiuzVKJCJZRkmhEUvLNpvu8PzzoXrpsmUhMfTtG7qNSG26a+XEsVfLbbn6+A7c/vIsrU4WyTLqBG6k0rLN5vz50L17mGpaUADTpsG995YnBEhtumvlxHHaAW3LE0LZ+VqdLJIdlBQaqXqVhVi/Prz577cfvPtuKHH973/DgQdudmoqm/RUThxmRL9uQkTqREmhkarzgrWpU6GwEG65JbQSZs+Gq66CZlXvd5TKdNdWLapOHJV/1upkkfgpKTRStd5mc8WK8OZ/xBFh7ODll2HkSGjXrsbXKZvuOrrX0bzQ4zBG9zp6s7GBZjlwzQkdyuN59YOv6Ht6F61OFslCGmhupMo+wVeeFbTZG687iREjSVx9Nc2WLGbFZVfQ4r57yNlxh5Rfa0vTXRd9X8rf3v2cS49qj1ly7Hrq5wy7+FAc1+pkkSyipNBIpbRg7csv8Z5XkfPqKD5u3Z7eFzzAJ607MuCL1XTv0iJtb9Ktd8jjuzXrGDRhbvmxvNwc8ltsowqnIllG3UeNWLVlITZuhIcegs6d8fFv8KcTLuW03z7Ih232jWQmkIrZiTQcaik0Ne+/Dz16QFER/PSnzOh9F38ds2iTU9K9T4GK2Yk0HGopNBWrV4dtMA85BL78El54Af75T3bqvG9GZgKpmJ1Iw6Ck0BSMHg1duoSd0C65BObMgd/8BszUtSMim1D3UWO2aBFcey0MHw6dOsE778BRR21yirp2RKQiJYXGKJEI5ax794bS0rBf8s03wzbbVHl62iqoikiDp6TQ2BQXh9LWkyfDT34CQ4bAvvvGHZWINBAaU2gsSkvh9tuhW7cwZvDkkzB+vBKCiNRKZEnBzPYwswlmNsfMis3smuTx+8zsIzP70MxeMrOdkscLzOwHM5uR/BoSVWyNzptvwv77Q//+cM45YZvMiy4KledERGohypbCBuAGd+8EHA70NLPOwDhgP3c/APgE6FPhmnnu3jX5dUWEsTUO33wDF14IJ5wQakeMGwd/+xvk58cdmYg0UJElBXdf5O7Tk49XAnOAtu7+urtvSJ42Bai54ppszh2GDYOOHeG55+DWW2HmTDjxxLgjE5EGLiNjCmZWAHQDplZ66hJgTIWf9zaz981sopkdXc29ephZkZkVlZSURBNwNvv00/Dmf9FF8KMfhRXK/fvDttvGHZmINAKRJwUzaw6MAK519xUVjt9G6GJ6NnloEbCnu3cDrgeeM7PNSnW6+6PuXujuhflNqZtk3Tq4664wdjBtGgweHNYd7Ldf3JGJSCMS6ZRUM8slJIRn3X1kheMXAqcBJ7i7A7j7WmBt8vE0M5sH7AsURRljgzB5cqhXNHs2nHVWKGbXpk3cUYlIIxTl7CMDHgfmuPuACse7A72Bn7v7mgrH882sWfJxe6ADMD+q+BqE5cvDmoOjjoJVq+DVV8PqZCUEEYlIlC2FI4ELgJlmNiN57FZgILANMC7kDaYkZxodA9xhZhuAjcAV7v5thPFlL/fw5n/NNVBSAtddF1YlN9eKYxGJVmRJwd0nAVVNlB9dzfkjCF1NTduCBdCzZyhid9BB8M9/wsEHxx2ViDQRWtGcLTZsCFVMu3SBiRNhwACYOlUJQUQySrWPskFRURhIfv99OO00GDQI9twz7qhEpAlSSyFOK1eG0taHHQaLF8M//gGjRikhiEhs1FKoIJFwFixbzZIVpbTeIeJ9BUaNCmMHX30FV1wBd98NO+4YzWuJiKRISSEpkXDGFi/m+uEzKF2fKN+BrHuX3dKbGL76Cnr1gpEjw8Kz4cPhiCPSd38RkXpQ91HSgmWryxMChM3rrx8+gwXLVqfnBTZuDGMFnTqFmUV//CNMn66EICJZRUkhacmK0vKEUKZ0fYKlK0vrf/MPPwwL0K66KowfzJwJffpAbm797y0ikkZKCkmtd8gr37y+TF5uDq1a5NX9pmvWwC23hGmlc+fC00/D66/DPvvUM1oRkWgoKSQVtNyeAWd3LU8MZWMKBS23r9sNX389FK+791644IKw8c3552vjGxHJahpoTsrJMbp32Y2OvY5m6cpSWrWo4+yjpUtDWYrnngtbYU6YAMcdF0nMIiLppqRQQU6O0T6/Oe3z61BjyB2eeAJuuikUr/vDH8K4QV49up9ERDJMSSEdPvooVDN9+204+mh45JEwy6iCjK6BEBGpIyWF+li7Niw6u/tu2G47GDoULrkEcjYdqsnYGggRkXrSQHNdTZwIBx4I/frBr34VWguXXbZZQoAMrIEQEUkTJYXa+vZbuPTSMHi8bh2MGRMGlVu3rvaSSNdAiIikkZJCqtzDm3/HjjBsGNx8M8yaBd27b/HSSNZAiIhEQEkhFfPmhTf/886DvfeGadPC+oPttkvp8rSvgRARiYgGmmuyfn3Y+KZfv1CSYuBAuPJKaNasVrdJ2xoIEZGIKSlUZ8qUsPHNzJlw5pkhIbRrV+fb1WsNhIhIhqj7qLLvvw/7HPz4x/Ddd/Dyy6HMdT0SgohIQ6GkUMY9vPl37gyDB8PVV8Ps2XDGGXFHJiKSMZElBTPbw8wmmNkcMys2s2uSx3cxs3Fm9mny+84VruljZnPN7GMzOyWq2Dbz5Zfhzf9Xv4JWrWDqVHjoIWjRIvKXTiSc+SWreHfeN8wvWUUi4ZG/pohIdaIcU9gA3ODu082sBTDNzMYBFwHj3f0eM7sFuAXobWadgXOALsDuwBtmtq+7b4wswo0b4S9/gdtvDy2F++4LeyZvlZmhFq10FpFsE1lLwd0Xufv05OOVwBygLXAGMCx52jDgF8nHZwAvuPtad/8MmAscGkVsiYSzcPwkVnU9GK67Dj/6GCguhhtvzFhCAK10FpHsk5ExBTMrALoBU4HW7r4IQuIAWiVPawt8WeGyhcljle/Vw8yKzKyopKSk1rEkEs57T46gzUnH8sNnn3Pdmb0Zc+9jJPbcq9b3qi+tdBaRbBP5x2Izaw6MAK519xVW/SYzVT2xWQe7uz8KPApQWFhY6w74BctWc9m8bbjkyHN56uDTWZHXnDH/+ICObXbI+HTRspXOFRODVjqLSJwibSmYWS4hITzr7iOTh5eYWZvk822ApcnjC4E9KlzeDvg63TEtWVHKqkQOA488lxV5IQnE9elcK51FJNtE1lKw0CR4HJjj7gMqPDUKuBC4J/n9lQrHnzOzAYSB5g7Ae+mOK5s+nWuls4hkmyhbCkcCFwDHm9mM5NephGRwkpl9CpyU/Bl3LwaGA7OBsUDPKGYe1eXTeZTTRstWOh/eflfa5zdXQhCRWJl7w50XX1hY6EVFRbW+rmwXtFQ+nWvaqIg0NmY2zd0Lq3quSa5ors2nc00bFZGmpEkmhdrQtFERaUqUFLZAG+SISFOipLAFmjYqIk2J9lPYAk0bFZGmREkhBdogR0SaCnUfiYhIOSUFEREpp6QgIiLllBRERKSckoKIiJRr0LWPzKwE+DzuOGppV+CbuIOIUVP//UF/A9DfAOL9G+zl7vlVPdGgk0JDZGZF1RWiagqa+u8P+huA/gaQvX8DdR+JiEg5JQURESmnpJB5j8YdQMya+u8P+huA/gaQpX8DjSmIiEg5tRRERKSckoKIiJRTUsgAM9vDzCaY2RwzKzaza+KOKS5m1szM3jez1+KOJQ5mtpOZvWhmHyX/PRwRd0yZZGbXJf8fmGVmz5tZo9+tysyeMLOlZjarwrFdzGycmX2a/L5znDFWpKSQGRuAG9y9E3A40NPMOsccU1yuAebEHUSMHgLGuntH4ECa0N/CzNoCvYBCd98PaAacE29UGfEU0L3SsVuA8e7eARif/DkrKClkgLsvcvfpyccrCW8EbeONKvPMrB3wM+CxuGOJg5ntABwDPA7g7uvcfXmsQWXeVsC2ZrYVsB3wdczxRM7d3wa+rXT4DGBY8vEw4BeZjKkmSgoZZmYFQDdgasyhxOHPwM1AIuY44tIeKAGeTHahPWZmTWZfV3f/Crgf+AJYBHzv7q/HG1VsWrv7IggfGoFWMcdTTkkhg8ysOTACuNbdV8QdTyaZ2WnAUnefFncsMdoKOAgY7O7dgNVkUbdB1JL95mcAewO7A9ub2fnxRiWVKSlkiJnlEhLCs+4+Mu54YnAk8HMzWwC8ABxvZs/EG1LGLQQWuntZK/FFQpJoKk4EPnP3EndfD4wEfhxzTHFZYmZtAJLfl8YcTzklhQwwMyP0I89x9wFxxxMHd+/j7u3cvYAwuPimuzepT4nuvhj40sx+lDx0AjA7xpAy7QvgcDPbLvn/xAk0oYH2SkYBFyYfXwi8EmMsm9gq7gCaiCOBC4CZZjYjeexWdx8dX0gSk6uBZ81sa2A+cHHM8WSMu081sxeB6YQZee+TpaUe0snMngeOA3Y1s4VAX+AeYLiZXUpIlmfFF+GmVOZCRETKqftIRETKKSmIiEg5JQURESmnpCAiIuWUFEREpJySgoiIlFNSEBGRckoKInVkZndW3BvDzPqbWa9qzr3JzP5jZh+aWb/MRSlSO0oKInX3OMlSBWaWQyjf8Wzlk8zsZKADcCjQFTjYzI7JXJgiqVOZC5E6cvcFZrbMzLoBrYH33X1ZFaeenPx6P/lzc0KSeDszkYqkTklBpH4eAy4CdgOeqOYcA+5290cyFZRIXan2kUg9JAvbzQRygQ7uvrGKc04G7gROcPdVyW0p17t71pRLFimjloJIPbj7OjObACyvKiEkz3ndzDoB74aK0awCzieLauiLlFFLQaQekgPM04Gz3P3TuOMRqS/NPhKpIzPrDMwFxishSGOhloJImpjZ/sDTlQ6vdffD4ohHpC6UFEREpJy6j0REpJySgoiIlFNSEBGRckoKIiJS7v8DcCk8tICfZHwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line\n",
    "plt.plot(X,model4.params[0]+model4.params[1]*(X),\"r\")\n",
    "sn.scatterplot(X,sq_Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "d3526c13",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>sq_Y</td>       <th>  R-squared:         </th> <td>   0.950</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.948</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   530.2</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>9.78e-20</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:31:26</td>     <th>  Log-Likelihood:    </th> <td> -114.33</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    30</td>      <th>  AIC:               </th> <td>   232.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    28</td>      <th>  BIC:               </th> <td>   235.5</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>  180.7002</td> <td>    4.446</td> <td>   40.646</td> <td> 0.000</td> <td>  171.594</td> <td>  189.807</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>y_e</th>       <td>   17.0565</td> <td>    0.741</td> <td>   23.025</td> <td> 0.000</td> <td>   15.539</td> <td>   18.574</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.621</td> <th>  Durbin-Watson:     </th> <td>   1.610</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.270</td> <th>  Jarque-Bera (JB):  </th> <td>   1.906</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.439</td> <th>  Prob(JB):          </th> <td>   0.386</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.131</td> <th>  Cond. No.          </th> <td>    13.2</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                   sq_Y   R-squared:                       0.950\n",
       "Model:                            OLS   Adj. R-squared:                  0.948\n",
       "Method:                 Least Squares   F-statistic:                     530.2\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           9.78e-20\n",
       "Time:                        16:31:26   Log-Likelihood:                -114.33\n",
       "No. Observations:                  30   AIC:                             232.7\n",
       "Df Residuals:                      28   BIC:                             235.5\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept    180.7002      4.446     40.646      0.000     171.594     189.807\n",
       "y_e           17.0565      0.741     23.025      0.000      15.539      18.574\n",
       "==============================================================================\n",
       "Omnibus:                        2.621   Durbin-Watson:                   1.610\n",
       "Prob(Omnibus):                  0.270   Jarque-Bera (JB):                1.906\n",
       "Skew:                           0.439   Prob(JB):                        0.386\n",
       "Kurtosis:                       2.131   Cond. No.                         13.2\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 194,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model4.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "971d8e12",
   "metadata": {},
   "source": [
    "#### Accuracy is Around 94.8%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "877eaa2a",
   "metadata": {},
   "source": [
    "## 5. Square Root Transformation on X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "id": "93ced80a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model5=smf.ols(\"salary~sq_X\",data=d_2).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "id": "45f5c824",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='y_e', ylabel='salary'>"
      ]
     },
     "execution_count": 197,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line\n",
    "plt.plot(sq_X,model5.params[0]+model5.params[1]*(sq_X),\"r\")\n",
    "sn.scatterplot(sq_X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 198,
   "id": "f44972ac",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>         <td>salary</td>      <th>  R-squared:         </th> <td>   0.931</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.929</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   377.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>8.57e-18</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:37:41</td>     <th>  Log-Likelihood:    </th> <td> -308.52</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    30</td>      <th>  AIC:               </th> <td>   621.0</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    28</td>      <th>  BIC:               </th> <td>   623.8</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>-1.606e+04</td> <td> 4921.599</td> <td>   -3.262</td> <td> 0.003</td> <td>-2.61e+04</td> <td>-5974.331</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>sq_X</th>      <td>  4.15e+04</td> <td> 2135.122</td> <td>   19.437</td> <td> 0.000</td> <td> 3.71e+04</td> <td> 4.59e+04</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.588</td> <th>  Durbin-Watson:     </th> <td>   1.031</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.745</td> <th>  Jarque-Bera (JB):  </th> <td>   0.638</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.011</td> <th>  Prob(JB):          </th> <td>   0.727</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.286</td> <th>  Cond. No.          </th> <td>    9.97</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                 salary   R-squared:                       0.931\n",
       "Model:                            OLS   Adj. R-squared:                  0.929\n",
       "Method:                 Least Squares   F-statistic:                     377.8\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           8.57e-18\n",
       "Time:                        16:37:41   Log-Likelihood:                -308.52\n",
       "No. Observations:                  30   AIC:                             621.0\n",
       "Df Residuals:                      28   BIC:                             623.8\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept  -1.606e+04   4921.599     -3.262      0.003   -2.61e+04   -5974.331\n",
       "sq_X         4.15e+04   2135.122     19.437      0.000    3.71e+04    4.59e+04\n",
       "==============================================================================\n",
       "Omnibus:                        0.588   Durbin-Watson:                   1.031\n",
       "Prob(Omnibus):                  0.745   Jarque-Bera (JB):                0.638\n",
       "Skew:                           0.011   Prob(JB):                        0.727\n",
       "Kurtosis:                       2.286   Cond. No.                         9.97\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 198,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model5.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c59d4e8",
   "metadata": {},
   "source": [
    "#### Accuracy is Around 92.9%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74ad695e",
   "metadata": {},
   "source": [
    "## 6. With Boxcox Transformation of Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "id": "316fa337",
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "#BOXCOX TRANSFORMATION of X and Y\n",
    "bc_X=stats.boxcox(X)\n",
    "bc_X=list(bc_X)\n",
    "bc_X.pop()\n",
    "bc_X=bc_X[0]\n",
    "d_2[\"bc_X\"]=bc_X\n",
    "\n",
    "bc_Y=stats.boxcox(Y)\n",
    "bc_Y=list(bc_Y)\n",
    "bc_Y.pop()\n",
    "bc_Y=bc_Y[0]\n",
    "d_2[\"bc_Y\"]=bc_Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "id": "ac582405",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x16ce1edeb80>"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting original and boxcox Transformed Data\n",
    "plt.suptitle(\"Years Experienced\")\n",
    "sn.distplot(X)\n",
    "sn.distplot(bc_X)\n",
    "labels=(\"Original\",\"box cox Transformed\")\n",
    "plt.legend(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "id": "a712be92",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Building Linear Regression Model\n",
    "model6=smf.ols(\"bc_Y~y_e\",data=d_2).fit()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "id": "c9d7c0f8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='y_e'>"
      ]
     },
     "execution_count": 217,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot of best fit line\n",
    "plt.plot(X,model6.params[0]+model6.params[1]*(X),\"r\")\n",
    "sn.scatterplot(X,bc_Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "id": "05f6d4e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>bc_Y</td>       <th>  R-squared:         </th> <td>   0.935</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.933</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   404.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Sat, 07 Jan 2023</td> <th>  Prob (F-statistic):</th> <td>3.48e-18</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>16:46:17</td>     <th>  Log-Likelihood:    </th> <td>  4.5449</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    30</td>      <th>  AIC:               </th> <td>  -5.090</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    28</td>      <th>  BIC:               </th> <td>  -2.287</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>   15.7521</td> <td>    0.085</td> <td>  186.351</td> <td> 0.000</td> <td>   15.579</td> <td>   15.925</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>y_e</th>       <td>    0.2834</td> <td>    0.014</td> <td>   20.118</td> <td> 0.000</td> <td>    0.255</td> <td>    0.312</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.091</td> <th>  Durbin-Watson:     </th> <td>   1.466</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.580</td> <th>  Jarque-Bera (JB):  </th> <td>   0.976</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.237</td> <th>  Prob(JB):          </th> <td>   0.614</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.255</td> <th>  Cond. No.          </th> <td>    13.2</td>\n",
       "</tr>\n",
       "</table><br/><br/>Notes:<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:                   bc_Y   R-squared:                       0.935\n",
       "Model:                            OLS   Adj. R-squared:                  0.933\n",
       "Method:                 Least Squares   F-statistic:                     404.7\n",
       "Date:                Sat, 07 Jan 2023   Prob (F-statistic):           3.48e-18\n",
       "Time:                        16:46:17   Log-Likelihood:                 4.5449\n",
       "No. Observations:                  30   AIC:                            -5.090\n",
       "Df Residuals:                      28   BIC:                            -2.287\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     15.7521      0.085    186.351      0.000      15.579      15.925\n",
       "y_e            0.2834      0.014     20.118      0.000       0.255       0.312\n",
       "==============================================================================\n",
       "Omnibus:                        1.091   Durbin-Watson:                   1.466\n",
       "Prob(Omnibus):                  0.580   Jarque-Bera (JB):                0.976\n",
       "Skew:                           0.237   Prob(JB):                        0.614\n",
       "Kurtosis:                       2.255   Cond. No.                         13.2\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 218,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model6.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db84b3be",
   "metadata": {},
   "source": [
    "#### Accuracy is 93%"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d26b46f9",
   "metadata": {},
   "source": [
    "## The Accuracy Of the model Where No transformation applied to Data is more 95%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d643f517",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}