07-线性回归原理-评价标准-假设检验及代码实现.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "简单线性回归及代码实现"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div  align=\"center\">    \n",
    "    <img src='./img/1.jpg', width= 600, height = 200>\n",
    "    <img src='./img/2.jpg', width= 600, height = 200>\n",
    "    <img src='./img/3.jpg', width= 600, height = 200>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x188a88aec50>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zov7byKiWDn4NeLRhWF9fi83mGsTrMTO/BTwVEeu/wf4KoPE3uPV0vobxl0RfBvw2sFStwQK8B/gpgMy8Bfg09bPFTwDfB24agkzXAr8fEc8Da8B1vS4C6lff3B4RI9R/YP8hM++NiL8EFjPzHup/EX08Ip6gfqR5XY8zNZvrHRFxNfVfZfgM9as4BmII5quZXIOYr1cAd1e9uAP4ZGZ+NiJ+Dwb2Wmw21yBejwBvB+6IiHOArwM39XO+fKeoJBVi6JZcJEntsdAlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSrE/wOKQnfT3fXg+QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 设置简单的数据\n",
    "X = np.array([2,3,4,5,6])\n",
    "Y = 2*X + np.random.normal(1, 2, 5)\n",
    "plt.scatter(X,Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### 根据推导得到的公式\n",
    "###### a=sum((xi−x¯)(yi−y¯)) / sum((xi−x¯)2) /n\n",
    "###### b=y¯−ax¯"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_mean = np.mean(X)\n",
    "y_mean = np.mean(Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 0.0\n",
    "d = 0.0\n",
    "for x,y in zip(X,Y):\n",
    "    n += (x-x_mean)*(y-y_mean)\n",
    "    d += (x-x_mean)**2\n",
    "    \n",
    "a = n/d\n",
    "b = y_mean-a*x_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x188a89a3eb8>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_predict = [a*x+b for x in X]\n",
    "plt.scatter(X,Y)\n",
    "plt.plot(X,y_predict,color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "评价标准"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.949906132005364\n"
     ]
    }
   ],
   "source": [
    "ss_residual = sum((y_predict - Y)**2)\n",
    "ss_total = sum((Y - y_mean)**2)\n",
    "\n",
    "Score = 1 - ss_residual / ss_total\n",
    "print(Score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "进行假设检验"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.004831946715685431\n"
     ]
    }
   ],
   "source": [
    "n = 5\n",
    "beta1_hat = a\n",
    "se_model = np.sqrt(ss_residual/(n-2))\n",
    "sss = np.sqrt(sum((X - x_mean)**2))\n",
    "\n",
    "t_val = beta1_hat/(se_model/sss)\n",
    "from scipy.stats import t\n",
    "p_val = 2*(1 - t.cdf(t_val, n-2))\n",
    "print(p_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 小于我们的0.05，所以拒绝零假设，所以有线性关系"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "END"
   ]
  }
 ],
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