class 18 is done

6_systolic_blood_pressure.ipynb

+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt\n",
+    "import pandas as pd"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_r2(X, Y):\n",
+    "    A = X.T.dot(X)\n",
+    "    b = X.T.dot(Y)\n",
+    "    w = np.linalg.solve(A, b)\n",
+    "    Yhat = X.dot(w)\n",
+    "    d1 = Y - Yhat\n",
+    "    d2 = Y - Y.mean()\n",
+    "    ssr = d1.dot(d1)\n",
+    "    sst = d2.dot(d2)\n",
+    "    r2 = 1 - ssr / sst\n",
+    "    return r2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "*** No CODEPAGE record, no encoding_override: will use 'ascii'\n"
+     ]
+    },
+    {
+     "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>X1</th>\n",
+       "      <th>X2</th>\n",
+       "      <th>X3</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>132</td>\n",
+       "      <td>52</td>\n",
+       "      <td>173</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>143</td>\n",
+       "      <td>59</td>\n",
+       "      <td>184</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>153</td>\n",
+       "      <td>67</td>\n",
+       "      <td>194</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>162</td>\n",
+       "      <td>73</td>\n",
+       "      <td>211</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>154</td>\n",
+       "      <td>64</td>\n",
+       "      <td>196</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "    X1  X2   X3\n",
+       "0  132  52  173\n",
+       "1  143  59  184\n",
+       "2  153  67  194\n",
+       "3  162  73  211\n",
+       "4  154  64  196"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "df = pd.read_excel('../files/systolic.xls')\n",
+    "df.head()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "df['ones'] = 1"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "X = np.array(df[['ones','X2','X3']].values)\n",
+    "Y = df['X1'].values"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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\n",
+      "text/plain": [
+       "<Figure size 432x288 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plt.scatter(X[:,1], Y, edgecolors='k')\n",
+    "plt.xlabel('Age in years')\n",
+    "plt.ylabel('Blood pressure')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "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": [
+    "plt.scatter(X[:,2], Y, edgecolors='k')\n",
+    "plt.xlabel('Weight in pounds')\n",
+    "plt.ylabel('Blood pressure')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "r-squared for both X2 and X3 is equal 0.976847104150209\n"
+     ]
+    }
+   ],
+   "source": [
+    "print('r-squared for both X2 and X3 is equal', get_r2(X, Y))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "r-squared for X2 is equal 0.9578407208147354\n"
+     ]
+    }
+   ],
+   "source": [
+    "X2only = df[['ones', 'X2']]\n",
+    "print('r-squared for X2 is equal', get_r2(X2only, Y))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "r-squared for X3 is equal 0.9419952085293064\n"
+     ]
+    }
+   ],
+   "source": [
+    "X3only = df[['ones', 'X3']]\n",
+    "print('r-squared for X3 is equal', get_r2(X3only, Y))"
+   ]
+  }
+ ],
+ "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": "3.5.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}