3_linear_regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Linear Regression is one of the easiest algorithms in machine learning. \n",
    "2. Linear Regression aims to establish a linear relationship between the input variables(X) and single output variable(Y). When the input(X) is a single variable this model is called Simple Linear Regression and when there are mutiple input variables(X), it is called Multiple Linear Regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this problem we have an input variable - X and one output variable - Y. And we want to build linear relationship between these variables. Here the input variable is called Independent Variable and the output variable is called Dependent Variable. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The β_{1} is called a scale factor or coefficient and β_{0} is called bias coefficient. The bias coeffient gives an extra degree of freedom to this model. \n",
    "\n",
    "This equation is similar to the line equation y = mx + by=mx+b with m = β_{1} (Slope) and b = β_{0} (Intercept). So in this Simple Linear Regression model we want to draw a line between X and Y which estimates the relationship between X and Y."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$y = β_{0} + β_{1}x $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "But how do we find these coefficients? That’s the learning procedure. We can find these using different approaches. One is called Ordinary Least Square Method and other one is called Gradient Descent Approach. We will use Ordinary Least Square Method in Simple Linear Regression and Gradient Descent Approach in Multiple Linear Regression in post."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ordinary Least Square Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As the name suggests the idea behind this method is to reduce sum of squares of distance of each point from the regression line. While reducing the error, we will achieve the perfect values for $β_{0}$ and $β_{1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ordinary Least Square method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
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       "        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>gender</th>\n",
       "      <th>age_range</th>\n",
       "      <th>head_size</th>\n",
       "      <th>brain_weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4512</td>\n",
       "      <td>1530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3738</td>\n",
       "      <td>1297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4261</td>\n",
       "      <td>1335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3777</td>\n",
       "      <td>1282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4177</td>\n",
       "      <td>1590</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   gender  age_range  head_size  brain_weight\n",
       "0       1          1       4512          1530\n",
       "1       1          1       3738          1297\n",
       "2       1          1       4261          1335\n",
       "3       1          1       3777          1282\n",
       "4       1          1       4177          1590"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Reading Data and renaming column names\n",
    "df = pd.read_csv('headbrain.csv')\n",
    "df.columns = ['gender', 'age_range', 'head_size', 'brain_weight']\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = df['head_size'].values\n",
    "y = df['brain_weight'].values\n",
    "\n",
    "x_mean = np.mean(x)\n",
    "y_mean = np.mean(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.26342933948939945 325.57342104944223\n"
     ]
    }
   ],
   "source": [
    "# Initializing input and output variabled from the dataset\n",
    "val1 = 0\n",
    "val2 = 0\n",
    "for i in range(len(df)):\n",
    "    a = x[i] - x_mean\n",
    "    b = y[i] - y_mean\n",
    "    c = a ** 2\n",
    "    val1 = val1 + (a * b)\n",
    "    val2 = val2 + c\n",
    "    \n",
    "B1 = val1 / val2\n",
    "B0 = y_mean - (B1 * x_mean)\n",
    "\n",
    "print(B1, B0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### BrainWeight = 325.573421049 + 0.263429339489 ∗ HeadSize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f447278f978>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "max_x = np.max(x) + 100\n",
    "min_x = np.min(x) - 100\n",
    "\n",
    "x_plot = np.linspace(min_x, max_x, 1000)\n",
    "y_plot = B0 + (B1 * x_plot)\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (20.0, 10.0)\n",
    "\n",
    "plt.plot(x_plot, y_plot, c='green', label='Regression Line')\n",
    "plt.scatter(x, y, c='red', label='Data')\n",
    "\n",
    "plt.xlabel('Head Size (cm3)')\n",
    "plt.ylabel('Brain Weight (gms)')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.1206213783709\n"
     ]
    }
   ],
   "source": [
    "# Calculating Root Mean Squares Error\n",
    "rmse = 0\n",
    "for i in range(len(df)):\n",
    "    y_pred = B0 + B1 * x[i]\n",
    "    rmse += (y[i] - y_pred) ** 2\n",
    "rmse = np.sqrt(rmse/len(df))\n",
    "print(rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.6393117199570003\n"
     ]
    }
   ],
   "source": [
    "# Calculating R2 Score\n",
    "ss_t = 0\n",
    "ss_r = 0\n",
    "for i in range(len(df)):\n",
    "    y_pred = B0 + B1 * x[i]\n",
    "    ss_t += (y[i] - y_mean) ** 2\n",
    "    ss_r += (y[i] - y_pred) ** 2\n",
    "r2 = 1 - (ss_r/ss_t)\n",
    "print(r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scikit Learn Approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root Mean Square Error -  72.1206213783709\n",
      "R2 Score -  0.639311719957\n"
     ]
    }
   ],
   "source": [
    "x = x.reshape((len(df), 1))\n",
    "\n",
    "model = LinearRegression()\n",
    "\n",
    "model.fit(x, y)\n",
    "\n",
    "y_pred = model.predict(x)\n",
    "\n",
    "mse = mean_squared_error(y, y_pred)\n",
    "rmse = np.sqrt(mse)\n",
    "\n",
    "r2 = model.score(x, y)\n",
    "\n",
    "print('Root Mean Square Error - ', rmse)\n",
    "print('R2 Score - ', r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Root Mean Square Error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Root Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors). Residuals are a measure of how far from the regression line data points are; RMSE is a measure of how spread out these residuals are. In other words, it tells you how concentrated the data is around the line of best fit. Root mean square error is commonly used in climatology, forecasting, and regression analysis to verify experimental results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When standardized observations and forecasts are used as RMSE inputs, there is a direct relationship with the correlation coefficient. For example, if the correlation coefficient is 1, the RMSE will be 0, because all of the points lie on the regression line (and therefore there are no errors)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### R2 Score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The definition of R-squared is fairly straight-forward; it is the percentage of the response variable variation that is explained by a linear model. Or:\n",
    "\n",
    "R-squared = Explained variation / Total variation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ways to evaluate an OLS Model\n",
    "1. R squared score or value\n",
    "2. Root Mean Square Value\n",
    "3. Overall F-Test\n",
    "\n",
    "All these values depend upon :\n",
    "1. Sum of Square Total (SST) - which means how far the data are from the mean\n",
    "2. Sum of Squared Errors (SSE) - which means how far the data are from the model's predicted values\n",
    "\n",
    "* SST - SSE = improvement in prediction from regression model, compared to mean model. \n",
    "* (SST -SSE)/SST = R2 Score. It is the proportional improvement in prediction from the regression model, compared to the mean model. It indicates the goodness of fit of the model.\n",
    "\n",
    "#### R Squared\n",
    "R-squared has the useful property that its scale is intuitive: it ranges from zero to one, with zero indicating that the proposed model does not improve prediction over the mean model, and one indicating perfect prediction. Improvement in the regression model results in proportional increases in R-squared.\n",
    "\n",
    "####  F-Test\n",
    "The F-test evaluates the null hypothesis that all regression coefficients are equal to zero versus the alternative that at least one is not. An equivalent null hypothesis is that R-squared equals zero. A significant F-test indicates that the observed R-squared is reliable and is not a spurious result of oddities in the data set. Thus the F-test determines whether the proposed relationship between the response variable and the set of predictors is statistically reliable and can be useful when the research objective is either prediction or explanation.\n",
    "\n",
    "#### RMSE\n",
    "The RMSE is the square root of the variance of the residuals. It indicates the absolute fit of the model to the data–how close the observed data points are to the model’s predicted values. Whereas R-squared is a relative measure of fit, RMSE is an absolute measure of fit. As the square root of a variance, RMSE can be interpreted as the standard deviation of the unexplained variance, and has the useful property of being in the same units as the response variable. Lower values of RMSE indicate better fit. RMSE is a good measure of how accurately the model predicts the response, and it is the most important criterion for fit if the main purpose of the model is prediction."
   ]
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  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
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     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.arange(10)\n",
    "b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = b.reshape((len(b), 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "a = np.arange(10)\n",
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 10)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(b * a).shape"
   ]
  }
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