regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fitting model to data. We start with fitting to a line. ie Linear Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import pearsonr\n",
    "from scipy.stats import linregress\n",
    "import seaborn as sns; sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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>5</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>7</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>16</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>20</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    x   y\n",
       "0   5   4\n",
       "1   7  12\n",
       "2  12  18\n",
       "3  16  21\n",
       "4  20  24"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(\n",
    "    [\n",
    "        [5,7,12,16,20],\n",
    "        [4,12,18,21,24]\n",
    "    ],\n",
    "    index=['x','y'])\n",
    "\n",
    "# use numpy to take the transform of data\n",
    "data_T = data.T\n",
    "data.T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x='x', y='y', data=data_T)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The equation of regression line is y=1.221x+1.151\n"
     ]
    }
   ],
   "source": [
    "df_x=data_T.iloc[:,0] \n",
    "df_y=data_T.iloc[:,1]\n",
    "slope, intercept, r_value, p_value, std_err = linregress(df_x,df_y)\n",
    "\n",
    "print(f'The equation of regression line is y={slope:.3f}x+{intercept:.3f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X_plot = np.linspace(0,20,100)\n",
    "Y_plot = slope*X_plot+intercept\n",
    "sns.scatterplot(x='x', y='y', data=data_T)\n",
    "plt.plot(X_plot, Y_plot, color='r')\n",
    "\n",
    "y1 = slope*df_x+intercept\n",
    "for i in range(len(df_x)):\n",
    "    xx = [df_x[i],df_x[i]]\n",
    "    yy = [df_y[i],y1[i]]\n",
    "    plt.plot(xx,yy, c='g')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How good is the fit?  How do we measure goodness of fit?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean square error: 4.658701298701301\n"
     ]
    }
   ],
   "source": [
    "def mse(actual, pred): \n",
    "    actual, pred = np.array(actual), np.array(pred)\n",
    "    return np.square(np.subtract(actual,pred)).mean()\n",
    "\n",
    "\n",
    "print(f'mean square error: {mse(df_y, slope*df_x +intercept)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## mean and standard deviation of the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x    12.0\n",
       "y    15.8\n",
       "dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_T.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "x    6.204837\n",
       "y    7.949843\n",
       "dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_T.std(ddof=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>x</th>\n",
       "      <td>38.5</td>\n",
       "      <td>47.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>47.0</td>\n",
       "      <td>63.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      x     y\n",
       "x  38.5  47.0\n",
       "y  47.0  63.2"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Covariance - std.std \n",
    "data_T.cov()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "## use st.linregress to calculate regression line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinregressResult(slope=1.2207792207792207, intercept=1.1506493506493527, rvalue=0.9528158084435786, pvalue=0.01221604904481553, stderr=0.2245414109335736)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import scipy.stats as st\n",
    "import statsmodels.api as sm\n",
    "x = data_T['x']\n",
    "y = data_T['y']\n",
    "\n",
    "distribution = getattr(st, 'linregress')\n",
    "params = distribution(x,y)\n",
    "params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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