Linear_Regression_using_scikit_learn.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_csv('C:/Technical/Teaching/DataScience/ML/implementation/datasets/Regression/swedish_insurance_univariate.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(63, 2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>X</th>\n",
       "      <th>Y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>108</td>\n",
       "      <td>392.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>19</td>\n",
       "      <td>46.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>13</td>\n",
       "      <td>15.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>124</td>\n",
       "      <td>422.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>40</td>\n",
       "      <td>119.4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     X      Y\n",
       "0  108  392.5\n",
       "1   19   46.2\n",
       "2   13   15.7\n",
       "3  124  422.2\n",
       "4   40  119.4"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x280fa29c308>"
      ]
     },
     "execution_count": 7,
     "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": [
    "plt.scatter(data['X'], data['Y'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr_model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = data['X'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(63,)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X.reshape(len(X), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(63, 1)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = data['Y'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y = Y.reshape(len(Y), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(63, 1)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_model.fit(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8333466719794502"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_model.score(X, Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.41382356]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_model.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([19.99448576])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_model.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions = lr_model.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "63"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x280fb739588>"
      ]
     },
     "execution_count": 22,
     "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": [
    "plt.scatter(X, Y, label = 'Actual')\n",
    "plt.plot(X, predictions, color = 'red', label = 'Predicted')\n",
    "plt.legend(loc = 'upper left')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}