Practice Run - Linear Regression Age vs Blood Pressure.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Small dataset for linear regression from:<br>\n",
    "http://people.sc.fsu.edu/~jburkardt/datasets/regression/x03.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x03 = pd.read_excel(\"x03.xlsx\")\n",
    "#      I,  the index;\n",
    "#      A0, 1,\n",
    "#      A1, the age;\n",
    "#      B,  the systolic blood pressure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>I</th>\n",
       "      <th>A0</th>\n",
       "      <th>A1</th>\n",
       "      <th>B</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>39</td>\n",
       "      <td>144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>47</td>\n",
       "      <td>220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>45</td>\n",
       "      <td>138</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   I  A0  A1    B\n",
       "0  1   1  39  144\n",
       "1  2   1  47  220\n",
       "2  3   1  45  138"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x03.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x116a59da0>"
      ]
     },
     "execution_count": 4,
     "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.scatter(x03[\"A1\"], x03[\"B\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.65756728],\n",
       "       [0.65756728, 1.        ]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(x03[\"A1\"], x03[\"B\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9708703514427236 98.71471813821842 0.4323947319275954\n"
     ]
    }
   ],
   "source": [
    "# Using the linregress() function returns 5 values, which we name here for convenience:\n",
    "slope, intercept, r_value, p_value, std_err = stats.linregress(x03[\"A1\"], x03[\"B\"])\n",
    "\n",
    "# Slope = m from our equation, Intercept = b, r_value = our correlation co-efficient\n",
    "print(slope, intercept, r_value**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def get_B():\n",
    "    return slope * x03[\"A1\"] + intercept\n",
    "\n",
    "plt.scatter(x03[\"A1\"], x03[\"B\"])\n",
    "plt.plot(x03[\"A1\"], get_B(), c='r')\n",
    "plt.show()"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}