arithmetic_coefficient_estimation.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.patches as mpatches\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "plt.style.use(\"seaborn-whitegrid\")"
   ]
  },
  {
   "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": [
    "# The dataset insurance involves predicting the total payment(Y) for all the claims \n",
    "# given the total number of claims (X).\n",
    "# Linear regression y = b0 + b1 * x to predict the total payment\n",
    "\n",
    "df = pd.read_csv(\"./data/insurance.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'Total payment')"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(df.X, df.Y, 'o', color='black')\n",
    "plt.xlabel('No of claims')\n",
    "plt.ylabel('Total payment')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "36    61\n",
       "11    48\n",
       "24    29\n",
       "43    37\n",
       "34    22\n",
       "Name: X, dtype: int64"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# split the data into training and test set\n",
    "\n",
    "train_x,test_x,train_y,test_y = train_test_split(df.X,df.Y,test_size=0.2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x stats: mean=23.580 variance=29876.180\n",
      "y stats: mean=102.296 variance=432694.819\n"
     ]
    }
   ],
   "source": [
    "# Calculate the mean value of a list of numbers\n",
    "\n",
    "def mean(values):\n",
    "    return np.sum(values) / len(values)\n",
    "\n",
    "# Calculate the variance of a list of numbers\n",
    "\n",
    "def variance(values, mean):\n",
    "    var = 0\n",
    "    for x in values:\n",
    "        var += (x - mean)**2\n",
    "    return var\n",
    "\n",
    "mean_x, mean_y = mean(train_x), mean(train_y)\n",
    "var_x, var_y = variance(train_x, mean_x), variance(train_y, mean_y)\n",
    "\n",
    "print('x stats: mean=%.3f variance=%.3f' % (mean_x, var_x))\n",
    "print('y stats: mean=%.3f variance=%.3f' % (mean_y, var_y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance: 50096.918\n"
     ]
    }
   ],
   "source": [
    "# Calculate covariance\n",
    "# The covariance of two groups of numbers describes how those numbers change together\n",
    "\n",
    "def covariance(x, x_mean, y, y_mean):\n",
    "    covar=0.0\n",
    "    for i,j in zip(x,y):\n",
    "        covar += (i - x_mean) * (j - y_mean)\n",
    "    return covar\n",
    "\n",
    "covar = covariance(train_x, mean_x, train_y, mean_y)\n",
    "print('Covariance: %.3f' % (covar))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients: B0=17.900, B1=3.461\n"
     ]
    }
   ],
   "source": [
    "# Calculate regression co-efficients\n",
    "# B1 = sum((x(i) - mean(x)) * (y(i) - mean(y))) / sum( (x(i) - mean(x))^2 )\n",
    "# B1 = covariance(x,y)/variance(x)\n",
    "# B0 = mean(y) - B1 * mean(x)\n",
    "\n",
    "def estimate_coefficients(x,y):\n",
    "    x_mean, y_mean = mean(x), mean(y)\n",
    "    b1 = covariance(x, x_mean, y, y_mean)/ variance(x, x_mean)\n",
    "    b0 = y_mean - b1 * x_mean\n",
    "    return[b0,b1]\n",
    "\n",
    "b0, b1 = estimate_coefficients(train_x, train_y)\n",
    "print('Coefficients: B0=%.3f, B1=%.3f' % (b0, b1))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,1,'Regression line on training set')"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_train, y_train, 'o', color='black')\n",
    "plt.plot(x_train, b0+x_train*b1, 'r')\n",
    "plt.title(\"Regression line on training set\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Simple linear regression algorithm\n",
    "\n",
    "def linear_regression(x_train, y_train, x_test):\n",
    "    predictions=list()\n",
    "    b0, b1=estimate_coefficients(x_train, y_train)\n",
    "    for row in x_test:\n",
    "        yhat= b0 + b1 * row\n",
    "        predictions.append(yhat)\n",
    "    return predictions\n",
    "\n",
    "predicted = linear_regression(train_x,train_y,test_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1a2030d208>"
      ]
     },
     "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": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_test, y_test, 'o', color='black')\n",
    "plt.plot(predicted, y_test, 'x', color='red')\n",
    "plt.title(\"Prediction vs Actual\")\n",
    "red_patch = mpatches.Patch(color='red', label='Predicted values')\n",
    "black_patch = mpatches.Patch(color='black', label='Actual values')\n",
    "plt.legend(loc=0,handles=[red_patch, black_patch])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 34.431\n"
     ]
    }
   ],
   "source": [
    "# Calculate root mean squared error\n",
    "\n",
    "def rmse_matric(actual, predicted):\n",
    "    sum_error = 0.0\n",
    "    for i,j in zip(actual,predicted):\n",
    "        prediction_error = j - i\n",
    "        sum_error += (prediction_error ** 2)\n",
    "        mean_error = sum_error / float(len(actual))\n",
    "    return np.sqrt(mean_error)\n",
    "\n",
    "rmse = rmse_matric(test_y, predicted)\n",
    "\n",
    "print('RMSE: %.3f' % (rmse))"
   ]
  }
 ],
 "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": "3.7.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}