回帰分析

PressureLinearRegression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "X = np.array([1018.4, 1007.6, 1006.2, 1009.9, 1010.8, 1013.2, 1016.2, 1009.1, 1003.1, 1012.5, 1006.4, 1006.3, 1012.2, 1015.0, 1017.4, 1016.5, 1012.1, 1008.7, 1009.2, 1009.2])\n",
    "Y = np.array([1019.4, 1005.7, 1002.0, 1006.7, 1005.1, 1010.1, 1016.7, 1011.0, 999.5, 1006.9, 1001.9, 1007.5, 1014.4, 1014.3, 1014.6, 1009.0, 1006.7, 1009.4, 1011.8, 1009.4])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(995, 1020)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5675528ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, Y)\n",
    "plt.xlabel(\"(x)\")\n",
    "plt.ylabel(\"(y)\")\n",
    "plt.xlim(1000, 1020)\n",
    "plt.ylim(995, 1020)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "beta1: 16.08757061136646, beta2: 0.982213085448698\n"
     ]
    }
   ],
   "source": [
    "beta2 = np.sum((X - np.mean(X)) * (Y - np.mean(Y))) / np.sum((X - np.mean(X)) ** 2)\n",
    "beta1 = np.mean(Y) - beta2 * np.mean(X)\n",
    "print(\"beta1: {}, beta2: {}\".format(beta1, beta2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(995, 1020)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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R1KXASRLuzmsFu5iWl8/KzSX0bJ/Fz748nEkjupOe1iTe5Z1Q9WWy6lFqbbIy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5673219240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X, Y)\n",
    "xx = np.linspace(np.min(X), np.max(X), 100)\n",
    "yy = xx * beta2 + beta1\n",
    "plt.plot(xx, yy)\n",
    "plt.xlabel(\"(x)\")\n",
    "plt.ylabel(\"(y)\")\n",
    "plt.xlim(1000, 1020)\n",
    "plt.ylim(995, 1020)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "standard error: 3.1482209448805882, coefficient of determination: 0.6447631673233438\n"
     ]
    }
   ],
   "source": [
    "es = Y - (beta2 * X + beta1)\n",
    "se = np.sqrt(np.sum(es ** 2) / (X.shape[0] - 2))\n",
    "eta2 = 1 - np.sum(es ** 2) / np.sum((Y - np.mean(Y)) ** 2)\n",
    "print(\"standard error: {}, coefficient of determination: {}\".format(se, eta2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x7f5673129240>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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xs3xccW1txc+ZmOXjJGFtx8+ZmFXPSaIB3E7fzFpFIXUSkk6XdK+kbkm/kXRYxno/kPSI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\nHOi1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f56731538d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xx = np.arange(es.shape[0]) + 1\n",
    "plt.scatter(xx, es)\n",
    "plt.plot(xx, np.zeros_like(xx), color=\"k\")\n",
    "plt.plot(xx, np.zeros_like(xx) + se, color=\"k\", ls=\":\")\n",
    "plt.plot(xx, np.zeros_like(xx) - se, color=\"k\", ls=\":\")\n",
    "plt.plot(xx, np.zeros_like(xx) + 2 * se, color=\"k\", ls=\"--\")\n",
    "plt.plot(xx, np.zeros_like(xx) - 2 * se, color=\"k\", ls=\"--\")\n",
    "yticks = np.r_[np.arange(-7.5, 7.6, 2.5), np.array([-2 * se, -se, se, 2 * se])]\n",
    "yticklabels=np.r_[np.arange(-7.5, 7.6, 2.5), np.array([\"-2s\", \"-s\", \"s\", \"2s\"])]\n",
    "_ = plt.yticks(yticks, yticklabels)\n",
    "_ = plt.xticks(xx)\n",
    "plt.ylabel(\"residual\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "t2: 5.715804525698464\n"
     ]
    }
   ],
   "source": [
    "se_beta2 = se / np.sqrt(np.sum((X - np.mean(X)) ** 2))\n",
    "t2 = beta2 / se_beta2\n",
    "print(\"t2: {}\".format(t2))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
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