LAB linear regression ISLR.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will work through the LAB for linear regression chapter in ISLR."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basic functions that perform least squares linear regression and other simple analyses come\n",
    "standard with the base distribution named MASS. So we use the library() function to run it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "lodalibraries=function(){\n",
    "    library('MASS')\n",
    "    library('ISLR')\n",
    "    print('Libraries Loaded')\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message:\n",
      "\"package 'ISLR' was built under R version 3.5.2\""
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Libraries Loaded\"\n"
     ]
    }
   ],
   "source": [
    "lodalibraries()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple linear regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "fix(Auto)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ horsepower, data = Auto)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-13.5710  -3.2592  -0.3435   2.7630  16.9240 \n",
       "\n",
       "Coefficients:\n",
       "             Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 39.935861   0.717499   55.66   <2e-16 ***\n",
       "horsepower  -0.157845   0.006446  -24.49   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 4.906 on 390 degrees of freedom\n",
       "Multiple R-squared:  0.6059,\tAdjusted R-squared:  0.6049 \n",
       "F-statistic: 599.7 on 1 and 390 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "attach(Auto)\n",
    "slrf=lm(mpg~horsepower,data=Auto)\n",
    "summary(slrf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Look at the cell below for results and how to get them:\n",
    "\n",
    "\n",
    "i- Since the p-value is small then there is a relation between the response and predictor.\n",
    "\n",
    "\n",
    "ii- We use the value of RSE/mean of the response to have an idea on the error and how much it's big for this partucular problem 20,92% and R squared which is the amount of variability in mpg explained by horsepower is: 60.59%.\n",
    "\n",
    "\n",
    "iii- As you can notice from the summary of the model, horsepower coefficient is negative then the relation between mpg and horsepower is negative, in the sense that the more we have horsepower the less we have mpg, which acctualy makes sense since high specs vehicules consume more gas.\n",
    "\n",
    "\n",
    "iv-Look at the cell below.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"The error rate is:\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "20.9237140669148"
      ],
      "text/latex": [
       "20.9237140669148"
      ],
      "text/markdown": [
       "20.9237140669148"
      ],
      "text/plain": [
       "[1] 20.92371"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"The percentage of contribution of horsepower in explaining mpg is:\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "60.5948257889435"
      ],
      "text/latex": [
       "60.5948257889435"
      ],
      "text/markdown": [
       "60.5948257889435"
      ],
      "text/plain": [
       "[1] 60.59483"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Predicting mpg for horsepower of 98:\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<strong>1:</strong> 24.4670771525124"
      ],
      "text/latex": [
       "\\textbf{1:} 24.4670771525124"
      ],
      "text/markdown": [
       "**1:** 24.4670771525124"
      ],
      "text/plain": [
       "       1 \n",
       "24.46708 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"The interval of confidence associated to this prediction is:\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>fit</th><th scope=col>lwr</th><th scope=col>upr</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>24.46708</td><td>23.97308</td><td>24.96108</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & fit & lwr & upr\\\\\n",
       "\\hline\n",
       "\t1 & 24.46708 & 23.97308 & 24.96108\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | fit | lwr | upr | \n",
       "|---|\n",
       "| 1 | 24.46708 | 23.97308 | 24.96108 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  fit      lwr      upr     \n",
       "1 24.46708 23.97308 24.96108"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"The interval of prediction associated to this prediction is:\"\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>fit</th><th scope=col>lwr</th><th scope=col>upr</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>1</th><td>24.46708</td><td>14.8094 </td><td>34.12476</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lll}\n",
       "  & fit & lwr & upr\\\\\n",
       "\\hline\n",
       "\t1 & 24.46708 & 14.8094  & 34.12476\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | fit | lwr | upr | \n",
       "|---|\n",
       "| 1 | 24.46708 | 14.8094  | 34.12476 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  fit      lwr     upr     \n",
       "1 24.46708 14.8094 34.12476"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('The error rate is:')\n",
    "100*summary(slrf)$sigma/mean(mpg)\n",
    "print('The percentage of contribution of horsepower in explaining mpg is:')\n",
    "100*summary(slrf)$r.squared\n",
    "print('Predicting mpg for horsepower of 98:')\n",
    "predict(slrf,data.frame(horsepower=98))\n",
    "print('The interval of confidence associated to this prediction is:')\n",
    "predict(slrf,data.frame(horsepower=98),interval = 'confidence')\n",
    "print('The interval of prediction associated to this prediction is:')\n",
    "predict(slrf,data.frame(horsepower=98),interval = 'prediction')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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utYFz374alSNja/H+n4KzWUsV1s4fMo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\ngJAAAf8D9IJJUz4lydUAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(horsepower,mpg,col='darkgoldenrod1',pch=20)\n",
    "abline(slrf,col='cornflowerblue',lwd=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Nlvj7Rb8llC+uZdLZgOCCkBsYkfO2of9TMTtbNhO+VI0crKU1I4fdxkTR1VNi0P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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow=c(2,2))\n",
    "plot(slrf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the first graphic Residuals Vs Fitted we notice signs of non linear relationship between predictor and response.\n",
    "\n",
    "From the Q-Q plot we the standarized residuals do not have a perfect normal distribution.\n",
    "\n",
    "We can also report having a number of data points with high leverage. But in the other hand we don't have much outliers. To make sure I'll draw two plots in the folowing cell to illustrate this more clearly. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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s4t6NcGRoFIuohVRc0gPPIIIukiZhXVPREieQSRdBG7isIdhnaeQSRdxLCCyQbv\nIJIuYllRM6l5I8wLIukidhX1CfDmraOKEM8eRNJFzCr6JxpGj/UYGgpAJF3EqmJgxm6sSBxk\nKUAkXcSqoupRu0kjahBJASLpIlYVry2/w4HRh0h4ZA4i6SJGFWV7bBzAI3sQSRcxqijvkC6j\nPt4O8oFIuohVRXlgd2Fk5hNE0kXMKioHSJXjJJTyAiLpIsYVLSKxc3IDIuki1hWNoR0T2X5A\nJF3EruJuS/UfvozZE4iki5hVlGbt6lfXPcKkmUAkXcSq4iFMTZN2j7Qm4WkXiKSLWFWcy1xK\nI7zsIrHH6wSRdBGziqpIz625uVln8AiT2kEkXcSuojzvXdqaY79R1gpE6gaRdBHDitfb+mbd\nmvGoE0TSRSwrSmO6ObdmPOoCkXQRw4rH0dH9B/26wEgQSRexq3gN55DIKYiki9hVlGa+Mckn\niKSLmFVUPMIklyCSLmJVUR7YIZJTEEkXMaoo24NHXkEkXcSoorIbwiOnIJIuYlXBbmgBIJIu\nYlRxP59B3w8TQCRdxKaifN43uAWRdBGbinPDJJxyCCLpIkYVdZH69k44NheIpItYVTQ96vKF\nEeBsIJIuYlVRH9h16sKx1Hwgki5iVVE6Q+jx48CCkB1E0kXMKmpnrPYdIuHRTCCSLmJXEX3G\nKh7NBSLpIsYVDNw8g0i6iHUFHjkGkXQR8wo88gsi6SKKClxyCiLpIoIKRndeQSRdxKwi6qwG\nmBVE0kWsKqpvkEUklyCSLmJUwVvNlwAi6SJGFbzVfAkgki5iVcFuaAEgki5iVpHJI3SdACLp\nIg4r+mDHNwVE0kUcVvTAjOAkEEkXcVjRAyJNApF0EYcVfeDRFBBJF3FY0QseTQCRdBGHFaAC\nkXQRhxWgApF0EYcVoAKRdBFVBccyDkEkXURUweyaRxBJF9FU8HqPSxBJF9FUIJJLEEkXMauo\neoNHHkEkXcSqom4OHjkEkXQRowrGcksAkXQRowpEWgKIpItYVeDRAkAkXcSsAo/8g0i6iMMK\nUIFIusiN01cIm8P9TnrvBZEWDCLpIgWnVbiyvd0JIr0riKSLFOzC/s+m/WpT3Im9SBw/+QCR\ndJGC1S14XK2PCpGY0XMCIukit9w9eNpsBCLxGpMXEEkXKViH0+PSBpHeF0TSRQr24et+6Rg2\nDO3eFkTSRW7snvYcApMNbwsi6SJ3frePS8evxr2EMskVMDuIpIs4rAAViKSLOKwAFYiki9Tu\nYPAeEGnBIJIuUrsDRHpnEEkXqd0BIr0ziKSL1O4Akd4ZRNJFaneASO8MIukitTtApHcGkXQR\nhxWgAnmz798AAAnmSURBVJF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQR\nhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKR\ndBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWg\nApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGH\nFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0\nEYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaAC\nkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcV\noAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXQRhxWgApF0EYcVoAKRdBGHFaACkXSR\nGSrO5+n3ASkgki6Sv+J8xqSZQCRdJHvF+YxJc4FIukj2CkSaD0TSRfJX4NFsIJIuMkMFHs0F\nIukiDitABSLpIg4rQAUi6SIOK0AFIukiDitABSLpIg4rQAUi6SIOK0AFIukiDitABSLpIg4r\nQAUi6SIV9quw3msrYEYQSRe58bsNq/3lO1zZaCpgfhBJFyn4LQzaha/T5bgNvfskRFowiKSL\nFHyF3eWyC6vr5VNYKyrAAYiki9xyRTBsSz9YV4ADEEkXueWK4M9tTHfbMVlXgAMQSRcp+Loe\nHd04FcM8+wpwACLpIgWn1XM8F/p3SNffBcCiGC9E+u5i99Bn1bI/CiXmflIAxpJTpGjmflIA\nxjJ+K+cUIegjaaNaPHOca9c/9W1SAfOBSLpI7Q6GRYLl8ifS3KswBwkepMhT1WTqPaSUztA5\nU+sHPdRFP8GI5Lz1gx7qop9gRHLe+kEPddFPMCI5b/2gh7roJ3iZU2r8nml1VopIzls/6KEu\n+glGJOetH/RQF/0EI5Lz1g96qIt+ghHJeesHPdRFP8GI5Lz1gx7qop9gRHLe+kEPddFPMCI5\nb/2gh7roJ3iZIgE4A5EADEAkAAMQCcAARAIwAJEADEAkAAMQCcAARAIwAJEADEAkAAMQCcAA\nRAIwAJEADEAkAAMQCcAA7yLtVmG1O7Vf8bqY/NHnCa2Xyz50LZahNOdD3a9bnuuMrcaPtaf0\n9BXC12/HYlE4F2lTPJPr1iteF3+Nn/G+1qKtY7EMpTkf6q64uDq1LZaj1fix9pWuiou/rYvF\n4Vukf2H1e/ldhX8tV5Qu/oZtrtbL9d/QvliO0owP9bf4vu19+LJ+qLGtto+1r3R3rdsVdakP\n1bdIu3D4+/9P+G65onRx/1pA3frXtblv043FcpRmfKjbW+O12PahxrbaPta+0lU43TuTH6pv\nkbbheKn8ZSpdUbq4D/tcrZewe3xvQGOxHKU5H+qNa7HtQ41ttX2sw6Vh1boqcfgWKYTyP9Ur\nShe34fAV2r5c3b718lu/3WgMH1ma86EWnMLG+qHGtto+1sHSXeFt6kN9E5EKNhlamz/mEOn1\nb+aHet0tHGYQqWi1fawDpT8h7FoXi737ySuoJFKkEH7+/ojtrEYCnkXK/FAvx9W2bbFMrZaP\ndaB0v10Vx0UfLdKNk9X0rGeRbmR7qKfVpnWxLK33H4we6/Bu8Ouq7HuKtKo/qtIVjdvMfs99\nraV/myuQofTS9pOudbNuXyxL651MT/BV2VX6Q/Ut0m0K5VifaTm+Zu2OtZkedWupp7kCGUov\nbT+pWo/rzbF9sSytd4we69ATfG9Kfai+RfouJvUPYddyReni7WUAs99zX+uV+2+2sViO0pwP\n9fA8zrd9qLGtto+1r/TRtE5/qL5FijyzYXd92KfbS2ni1iv3bTrnmQ3P0owP9fiaL8t4ZkOp\n1faxDp7ZcNpej5He88yGy/o1AXrbkkpXvC6ebqdKmb260td6eY011qYz0XGlGR/qV3id62b7\nUCNbjR9r3xO8atusRuFcpFNxKm5x8fbgS1fULq7tXgbva728RKpem7E0z0MNr03a+KGOabV7\nrL1P8Ksp8aE6FwlgGSASgAGIBGAAIgEYgEgABiASgAGIBGAAIgEYgEgABiASgAGIBGAAIgEY\ngEgABiASgAGIBGAAIgEYgEgABiASgAGIBGAAIgEYgEgABiASgAGIBGAAIgEYgEgABiASgAGI\nBGAAIgEYgEgABiASgAGIBGAAIgEYgEgABiDSrLR/Y3fnl6bGfcH3ofLtxeXM6SuE3dbo+2eh\nDCLNSqsZ685fSpRIx+Irulsz2xDC9ykcY1cPokGkWWk1o1uXKJE21S9ALWdC4dDO7EuV4Qki\nzYpApJ/qDqkm0vX/p/ATt3YQDyLNyt+WvQur7+vFw9+4q/g27eI7vU9hXSyw/tPieUshwk2G\n2//367C6fRf3YRPCpjj4WW+qV9wyp3XYPr8tfLPO+Rg/A0SalXDbvP9k+L5t5ru7SJdNMQo7\nhk3plrpINzWu4uxvy/zdz79QmPW64pb5W3T3FGkf/s32iN8VRJqVPw1Of9v1+nrp5zosC5e7\nJD/hup/6Dof6LS+RDtfwafO3yGUVfq/L/N3P7nqpfMUtszk9Un/8hl3r2kA6iDQrodg3vA5j\nXiJdirHdunnLS6RtcTR0Ctvrj4857U24K3MoBcN9F3QvOgWmG6xBpFkpH/AcD9+bkkhff2O7\n423XUbnlFQkPrvuhsP39fd1X7YqHqfV/wQye0VkpibR5HsLcrvz3N7bbFXuS6i2tIl2+V3//\nro4vRypXIJIcntFZeVnxFdb7w7Ek0mW1vv7XuKUsUvmuDrv145CocQUiyeEZnZWaFRWRdmFf\nTDjUbiku/LsdIx2a97Ypv4z0WL4mEMdI9iDSrJRF+nf5fRwJFefwHK8vJ11qt1znH/bXqbpw\nnZRb/V7nsrfXK3+es3bFvMLrihaR/jFrZw4izcpLpPurPFcN1n8HN9er17cdR+mW64LFK0Tb\n0mHV9UDo57nIv2IvVrqiRaRvXkcyB5FmpTTZ8BXC5t/hunv5t76J9HMfur1uecwrfL3ObAhf\nxe6rOJHhti8qndnwmFuvicSZDfYg0rtxGDy5+1g/toLpINLbsRk6AOLsbwGI9HbU3o/UgPcj\nKUCk9+Pw1XvzFwM7AYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAG\nIBKAAYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAGIBKAAYgEYAAiARiASAAGIBKAAYgEYAAi\nARiASAAG/A/FvRH3rKZKbwAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(hatvalues(slrf),rstudent(slrf),col='darkgoldenrod1',pch=20)\n",
    "abline(3,0,col='cornflowerblue',lwd=3)\n",
    "abline(-3,0,col='cornflowerblue',lwd=3)\n",
    "abline(v=4*2/nrow(Auto),col='cornflowerblue',lwd=3)\n",
    "\n",
    "#The data points outside the (-3,3) are likely to be outliers, we only have 2 of them!\n",
    "#Are considered high leverage observation the ones for which the hatvalue calculated by the leverage statistic is greatly \n",
    "#higher than the average which of the leverage statistic which is (p+1)/n for p predictors. In our case 2/n. I will consider\n",
    "#greatly high than average as more than 4 times higher."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiple linear regression:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0jFEym0uCUSyNjfJZKZJRZu36TWER3JjHZWoyX1GE4HnjpdC6d4zAFJp69UG36z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23OHqxTk9JR/B0d/WrvX5Oix9w1zfQl+W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\nqB8yZ8H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      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Scaterplots\n",
    "pairs(Auto)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>mpg</th><th scope=col>cylinders</th><th scope=col>displacement</th><th scope=col>horsepower</th><th scope=col>weight</th><th scope=col>acceleration</th><th scope=col>year</th><th scope=col>origin</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>mpg</th><td> 1.0000000</td><td>-0.7776175</td><td>-0.8051269</td><td>-0.7784268</td><td>-0.8322442</td><td> 0.4233285</td><td> 0.5805410</td><td> 0.5652088</td></tr>\n",
       "\t<tr><th scope=row>cylinders</th><td>-0.7776175</td><td> 1.0000000</td><td> 0.9508233</td><td> 0.8429834</td><td> 0.8975273</td><td>-0.5046834</td><td>-0.3456474</td><td>-0.5689316</td></tr>\n",
       "\t<tr><th scope=row>displacement</th><td>-0.8051269</td><td> 0.9508233</td><td> 1.0000000</td><td> 0.8972570</td><td> 0.9329944</td><td>-0.5438005</td><td>-0.3698552</td><td>-0.6145351</td></tr>\n",
       "\t<tr><th scope=row>horsepower</th><td>-0.7784268</td><td> 0.8429834</td><td> 0.8972570</td><td> 1.0000000</td><td> 0.8645377</td><td>-0.6891955</td><td>-0.4163615</td><td>-0.4551715</td></tr>\n",
       "\t<tr><th scope=row>weight</th><td>-0.8322442</td><td> 0.8975273</td><td> 0.9329944</td><td> 0.8645377</td><td> 1.0000000</td><td>-0.4168392</td><td>-0.3091199</td><td>-0.5850054</td></tr>\n",
       "\t<tr><th scope=row>acceleration</th><td> 0.4233285</td><td>-0.5046834</td><td>-0.5438005</td><td>-0.6891955</td><td>-0.4168392</td><td> 1.0000000</td><td> 0.2903161</td><td> 0.2127458</td></tr>\n",
       "\t<tr><th scope=row>year</th><td> 0.5805410</td><td>-0.3456474</td><td>-0.3698552</td><td>-0.4163615</td><td>-0.3091199</td><td> 0.2903161</td><td> 1.0000000</td><td> 0.1815277</td></tr>\n",
       "\t<tr><th scope=row>origin</th><td> 0.5652088</td><td>-0.5689316</td><td>-0.6145351</td><td>-0.4551715</td><td>-0.5850054</td><td> 0.2127458</td><td> 0.1815277</td><td> 1.0000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|llllllll}\n",
       "  & mpg & cylinders & displacement & horsepower & weight & acceleration & year & origin\\\\\n",
       "\\hline\n",
       "\tmpg &  1.0000000 & -0.7776175 & -0.8051269 & -0.7784268 & -0.8322442 &  0.4233285 &  0.5805410 &  0.5652088\\\\\n",
       "\tcylinders & -0.7776175 &  1.0000000 &  0.9508233 &  0.8429834 &  0.8975273 & -0.5046834 & -0.3456474 & -0.5689316\\\\\n",
       "\tdisplacement & -0.8051269 &  0.9508233 &  1.0000000 &  0.8972570 &  0.9329944 & -0.5438005 & -0.3698552 & -0.6145351\\\\\n",
       "\thorsepower & -0.7784268 &  0.8429834 &  0.8972570 &  1.0000000 &  0.8645377 & -0.6891955 & -0.4163615 & -0.4551715\\\\\n",
       "\tweight & -0.8322442 &  0.8975273 &  0.9329944 &  0.8645377 &  1.0000000 & -0.4168392 & -0.3091199 & -0.5850054\\\\\n",
       "\tacceleration &  0.4233285 & -0.5046834 & -0.5438005 & -0.6891955 & -0.4168392 &  1.0000000 &  0.2903161 &  0.2127458\\\\\n",
       "\tyear &  0.5805410 & -0.3456474 & -0.3698552 & -0.4163615 & -0.3091199 &  0.2903161 &  1.0000000 &  0.1815277\\\\\n",
       "\torigin &  0.5652088 & -0.5689316 & -0.6145351 & -0.4551715 & -0.5850054 &  0.2127458 &  0.1815277 &  1.0000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | mpg | cylinders | displacement | horsepower | weight | acceleration | year | origin | \n",
       "|---|---|---|---|---|---|---|---|\n",
       "| mpg |  1.0000000 | -0.7776175 | -0.8051269 | -0.7784268 | -0.8322442 |  0.4233285 |  0.5805410 |  0.5652088 | \n",
       "| cylinders | -0.7776175 |  1.0000000 |  0.9508233 |  0.8429834 |  0.8975273 | -0.5046834 | -0.3456474 | -0.5689316 | \n",
       "| displacement | -0.8051269 |  0.9508233 |  1.0000000 |  0.8972570 |  0.9329944 | -0.5438005 | -0.3698552 | -0.6145351 | \n",
       "| horsepower | -0.7784268 |  0.8429834 |  0.8972570 |  1.0000000 |  0.8645377 | -0.6891955 | -0.4163615 | -0.4551715 | \n",
       "| weight | -0.8322442 |  0.8975273 |  0.9329944 |  0.8645377 |  1.0000000 | -0.4168392 | -0.3091199 | -0.5850054 | \n",
       "| acceleration |  0.4233285 | -0.5046834 | -0.5438005 | -0.6891955 | -0.4168392 |  1.0000000 |  0.2903161 |  0.2127458 | \n",
       "| year |  0.5805410 | -0.3456474 | -0.3698552 | -0.4163615 | -0.3091199 |  0.2903161 |  1.0000000 |  0.1815277 | \n",
       "| origin |  0.5652088 | -0.5689316 | -0.6145351 | -0.4551715 | -0.5850054 |  0.2127458 |  0.1815277 |  1.0000000 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "             mpg        cylinders  displacement horsepower weight    \n",
       "mpg           1.0000000 -0.7776175 -0.8051269   -0.7784268 -0.8322442\n",
       "cylinders    -0.7776175  1.0000000  0.9508233    0.8429834  0.8975273\n",
       "displacement -0.8051269  0.9508233  1.0000000    0.8972570  0.9329944\n",
       "horsepower   -0.7784268  0.8429834  0.8972570    1.0000000  0.8645377\n",
       "weight       -0.8322442  0.8975273  0.9329944    0.8645377  1.0000000\n",
       "acceleration  0.4233285 -0.5046834 -0.5438005   -0.6891955 -0.4168392\n",
       "year          0.5805410 -0.3456474 -0.3698552   -0.4163615 -0.3091199\n",
       "origin        0.5652088 -0.5689316 -0.6145351   -0.4551715 -0.5850054\n",
       "             acceleration year       origin    \n",
       "mpg           0.4233285    0.5805410  0.5652088\n",
       "cylinders    -0.5046834   -0.3456474 -0.5689316\n",
       "displacement -0.5438005   -0.3698552 -0.6145351\n",
       "horsepower   -0.6891955   -0.4163615 -0.4551715\n",
       "weight       -0.4168392   -0.3091199 -0.5850054\n",
       "acceleration  1.0000000    0.2903161  0.2127458\n",
       "year          0.2903161    1.0000000  0.1815277\n",
       "origin        0.2127458    0.1815277  1.0000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cor(subset(Auto,select=-name))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ ., data = auto)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-9.5903 -2.1565 -0.1169  1.8690 13.0604 \n",
       "\n",
       "Coefficients:\n",
       "               Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  -17.218435   4.644294  -3.707  0.00024 ***\n",
       "cylinders     -0.493376   0.323282  -1.526  0.12780    \n",
       "displacement   0.019896   0.007515   2.647  0.00844 ** \n",
       "horsepower    -0.016951   0.013787  -1.230  0.21963    \n",
       "weight        -0.006474   0.000652  -9.929  < 2e-16 ***\n",
       "acceleration   0.080576   0.098845   0.815  0.41548    \n",
       "year           0.750773   0.050973  14.729  < 2e-16 ***\n",
       "origin         1.426141   0.278136   5.127 4.67e-07 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 3.328 on 384 degrees of freedom\n",
       "Multiple R-squared:  0.8215,\tAdjusted R-squared:  0.8182 \n",
       "F-statistic: 252.4 on 7 and 384 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "auto=subset(Auto,select=-name)\n",
    "mlrf=lm(mpg~.,data=auto)\n",
    "summary(mlrf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "i- We have predictors that yielded small p-value inicating a significant relationship with the reponse, and others predictors for which we fail to reject the null hypothesis and thus are insignificant for predicting the response mpg.\n",
    "\n",
    "\n",
    "ii-displacement,weight,year and origin seem to statisticaly have a significant relationship to mpg.\n",
    "\n",
    "\n",
    "iii- The coefficient of year since positive and significant indicates that mpg increase by the year, which means through the years the industry is making vehicules that have more mpg ration. Which is a logical result.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
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6eKlo5CKohsRhUSWxa5f4Gb2tLkTe4WWzR0mhpKZ1h276Ob6KizkHg4dNjiIeom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\nAAUgJAAUgJAAUABCAkCB/wHitPG36iFckQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow=c(2,2))\n",
    "plot(mlrf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The plots indicate a non-linear relationship since the residuals seems to have a certain pattern.\n",
    "\n",
    "\n",
    "Also Q-Q plots indicate that the residuals follow a normal distribution except for some points which are suspect of being outliers. \n",
    "\n",
    "\n",
    "For high leverage points it seems to be that we don't have data points with unusual x values.\n",
    "\n",
    "I will draw my own plot now to confirm results!\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MJvSYSkxurq79XKYjSpVSRE+5vyza/7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\njO4XKOwAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(hatvalues(mlrf),rstudent(mlrf),col='darkgoldenrod1',pch=20)\n",
    "abline(3,0,col='cornflowerblue',lwd=3)\n",
    "abline(-3,0,col='cornflowerblue',lwd=3)\n",
    "abline(v=4*8/nrow(Auto),col='cornflowerblue',lwd=3)\n",
    "\n",
    "# As you can see we have 4-6 outliers and 2 high leverage data points, and luckly no combinaison of the two of them! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correlation matrix suggest strong relationships between predictors so we have a situation of collinearity that acctualy what explains that now horsepower is insignificant while it was significant for SLR model. The thing is that with collinearity we cannot distinguish the individual contributions of the predictors and fail to reject the null hypothesis for some predictors. Although since correlated these predictors have the same information about the response so we only remove these predictors representing redundant information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ displacement + weight + origin + year, data = Auto)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-9.8102 -2.1129 -0.0388  1.7725 13.2085 \n",
       "\n",
       "Coefficients:\n",
       "               Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  -1.861e+01  4.028e+00  -4.620 5.25e-06 ***\n",
       "displacement  5.588e-03  4.768e-03   1.172    0.242    \n",
       "weight       -6.575e-03  5.571e-04 -11.802  < 2e-16 ***\n",
       "origin        1.226e+00  2.670e-01   4.593 5.92e-06 ***\n",
       "year          7.714e-01  4.981e-02  15.486  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 3.346 on 387 degrees of freedom\n",
       "Multiple R-squared:  0.8181,\tAdjusted R-squared:  0.8162 \n",
       "F-statistic: 435.1 on 4 and 387 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mlrf1=lm(mpg~displacement+weight+origin+year,data=Auto)\n",
    "summary(mlrf1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ weight + origin + year, data = Auto)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-9.9440 -2.0948 -0.0389  1.7255 13.2722 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) -1.805e+01  4.001e+00  -4.510 8.60e-06 ***\n",
       "weight      -5.994e-03  2.541e-04 -23.588  < 2e-16 ***\n",
       "origin       1.150e+00  2.591e-01   4.439 1.18e-05 ***\n",
       "year         7.571e-01  4.832e-02  15.668  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 3.348 on 388 degrees of freedom\n",
       "Multiple R-squared:  0.8175,\tAdjusted R-squared:  0.816 \n",
       "F-statistic: 579.2 on 3 and 388 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ weight * origin + weight * year + origin * \n",
       "    year, data = Auto)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-9.3861 -1.7991 -0.2057  1.4539 12.0334 \n",
       "\n",
       "Coefficients:\n",
       "                Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   -1.046e+02  2.068e+01  -5.055 6.65e-07 ***\n",
       "weight         2.445e-02  5.221e-03   4.683 3.92e-06 ***\n",
       "origin         4.737e+00  5.116e+00   0.926  0.35506    \n",
       "year           1.864e+00  2.747e-01   6.784 4.43e-11 ***\n",
       "weight:origin -1.483e-03  4.755e-04  -3.119  0.00195 ** \n",
       "weight:year   -3.862e-04  7.103e-05  -5.437 9.65e-08 ***\n",
       "origin:year   -4.213e-03  6.566e-02  -0.064  0.94887    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 3.11 on 385 degrees of freedom\n",
       "Multiple R-squared:  0.8437,\tAdjusted R-squared:  0.8413 \n",
       "F-statistic: 346.3 on 6 and 385 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ I(log(weight)) + I(log(origin)) + I(log(year)), \n",
       "    data = Auto)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-9.9298 -2.0228 -0.0206  1.6119 13.1496 \n",
       "\n",
       "Coefficients:\n",
       "               Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)    -80.2021    17.1444  -4.678 4.01e-06 ***\n",
       "I(log(weight)) -19.0831     0.7406 -25.765  < 2e-16 ***\n",
       "I(log(origin))   1.4299     0.4417   3.237  0.00131 ** \n",
       "I(log(year))    58.9116     3.4076  17.288  < 2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 3.135 on 388 degrees of freedom\n",
       "Multiple R-squared:  0.8399,\tAdjusted R-squared:  0.8387 \n",
       "F-statistic: 678.4 on 3 and 388 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ poly(weight, 2) + poly(origin, 2) + poly(year, \n",
       "    2), data = Auto)\n",
       "\n",
       "Residuals:\n",
       "   Min     1Q Median     3Q    Max \n",
       "-9.077 -1.628  0.045  1.457 12.996 \n",
       "\n",
       "Coefficients:\n",
       "                  Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)        23.4459     0.1463 160.229  < 2e-16 ***\n",
       "poly(weight, 2)1 -100.6436     3.8471 -26.161  < 2e-16 ***\n",
       "poly(weight, 2)2   29.3866     3.0594   9.605  < 2e-16 ***\n",
       "poly(origin, 2)1    9.9958     3.7489   2.666  0.00799 ** \n",
       "poly(origin, 2)2   -8.3782     3.0007  -2.792  0.00550 ** \n",
       "poly(year, 2)1     61.7015     3.1205  19.773  < 2e-16 ***\n",
       "poly(year, 2)2     16.1691     2.9340   5.511 6.55e-08 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 2.897 on 385 degrees of freedom\n",
       "Multiple R-squared:  0.8643,\tAdjusted R-squared:  0.8622 \n",
       "F-statistic: 408.8 on 6 and 385 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Now displacement is insignificant!\n",
    "mlrf2=lm(mpg~weight+origin+year,data=Auto)\n",
    "summary(mlrf2)\n",
    "#Now let's include include interractions terms, to cover any synergies within predictors.\n",
    "mlrf3=lm(mpg~weight*origin+weight*year+origin*year,data=Auto)\n",
    "summary(mlrf3)\n",
    "#Now let's include modifications on the predictors to cover the non-linearity of the relationship\n",
    "mlrf4=lm(mpg~I(log(weight))+I(log(origin))+I(log(year)),data=Auto)\n",
    "summary(mlrf4)\n",
    "mlrf5=lm(mpg~poly(weight,2)+poly(origin,2)+poly(year,2),data=Auto)\n",
    "summary(mlrf5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we move towards a non-linear predictors we get better R-squared and less error rate, although we must keep in mind this is only the training error and judging the quality of the model from it is certainly biased."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'call'</li>\n",
       "\t<li>'terms'</li>\n",
       "\t<li>'residuals'</li>\n",
       "\t<li>'coefficients'</li>\n",
       "\t<li>'aliased'</li>\n",
       "\t<li>'sigma'</li>\n",
       "\t<li>'df'</li>\n",
       "\t<li>'r.squared'</li>\n",
       "\t<li>'adj.r.squared'</li>\n",
       "\t<li>'fstatistic'</li>\n",
       "\t<li>'cov.unscaled'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'call'\n",
       "\\item 'terms'\n",
       "\\item 'residuals'\n",
       "\\item 'coefficients'\n",
       "\\item 'aliased'\n",
       "\\item 'sigma'\n",
       "\\item 'df'\n",
       "\\item 'r.squared'\n",
       "\\item 'adj.r.squared'\n",
       "\\item 'fstatistic'\n",
       "\\item 'cov.unscaled'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'call'\n",
       "2. 'terms'\n",
       "3. 'residuals'\n",
       "4. 'coefficients'\n",
       "5. 'aliased'\n",
       "6. 'sigma'\n",
       "7. 'df'\n",
       "8. 'r.squared'\n",
       "9. 'adj.r.squared'\n",
       "10. 'fstatistic'\n",
       "11. 'cov.unscaled'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"call\"          \"terms\"         \"residuals\"     \"coefficients\" \n",
       " [5] \"aliased\"       \"sigma\"         \"df\"            \"r.squared\"    \n",
       " [9] \"adj.r.squared\" \"fstatistic\"    \"cov.unscaled\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "names(summary(mlrf))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col>Model</th><th scope=col>Predictors</th><th scope=col>R.squared</th><th scope=col>RSE</th><th scope=col>Error</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>1                                                                </td><td>lm, mpg ~ displacement + weight + origin + year, Auto            </td><td>0.8180977                                                        </td><td>3.345995                                                         </td><td>14.27112                                                         </td></tr>\n",
       "\t<tr><td>2                                                                </td><td>lm, mpg ~ weight + origin + year, Auto                           </td><td>0.8174522                                                        </td><td>3.347605                                                         </td><td>14.27798                                                         </td></tr>\n",
       "\t<tr><td>3                                                                </td><td>lm, mpg ~ weight * origin + weight * year + origin * year, Auto  </td><td>0.8436896                                                        </td><td>3.109748                                                         </td><td>13.26350                                                         </td></tr>\n",
       "\t<tr><td>4                                                                </td><td>lm, mpg ~ I(log(weight)) + I(log(origin)) + I(log(year)), Auto   </td><td>0.8398884                                                        </td><td>3.135142                                                         </td><td>13.37181                                                         </td></tr>\n",
       "\t<tr><td>5                                                                </td><td>lm, mpg ~ poly(weight, 2) + poly(origin, 2) + poly(year, 2), Auto</td><td>0.8643326                                                        </td><td>2.897138                                                         </td><td>12.35668                                                         </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       " Model & Predictors & R.squared & RSE & Error\\\\\n",
       "\\hline\n",
       "\t 1                                                                                  & lm, mpg \\textasciitilde{} displacement + weight + origin + year, Auto             & 0.8180977                                                                          & 3.345995                                                                           & 14.27112                                                                          \\\\\n",
       "\t 2                                                                                  & lm, mpg \\textasciitilde{} weight + origin + year, Auto                            & 0.8174522                                                                          & 3.347605                                                                           & 14.27798                                                                          \\\\\n",
       "\t 3                                                                                  & lm, mpg \\textasciitilde{} weight * origin + weight * year + origin * year, Auto   & 0.8436896                                                                          & 3.109748                                                                           & 13.26350                                                                          \\\\\n",
       "\t 4                                                                                  & lm, mpg \\textasciitilde{} I(log(weight)) + I(log(origin)) + I(log(year)), Auto    & 0.8398884                                                                          & 3.135142                                                                           & 13.37181                                                                          \\\\\n",
       "\t 5                                                                                  & lm, mpg \\textasciitilde{} poly(weight, 2) + poly(origin, 2) + poly(year, 2), Auto & 0.8643326                                                                          & 2.897138                                                                           & 12.35668                                                                          \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "Model | Predictors | R.squared | RSE | Error | \n",
       "|---|---|---|---|---|\n",
       "| 1                                                                 | lm, mpg ~ displacement + weight + origin + year, Auto             | 0.8180977                                                         | 3.345995                                                          | 14.27112                                                          | \n",
       "| 2                                                                 | lm, mpg ~ weight + origin + year, Auto                            | 0.8174522                                                         | 3.347605                                                          | 14.27798                                                          | \n",
       "| 3                                                                 | lm, mpg ~ weight * origin + weight * year + origin * year, Auto   | 0.8436896                                                         | 3.109748                                                          | 13.26350                                                          | \n",
       "| 4                                                                 | lm, mpg ~ I(log(weight)) + I(log(origin)) + I(log(year)), Auto    | 0.8398884                                                         | 3.135142                                                          | 13.37181                                                          | \n",
       "| 5                                                                 | lm, mpg ~ poly(weight, 2) + poly(origin, 2) + poly(year, 2), Auto | 0.8643326                                                         | 2.897138                                                          | 12.35668                                                          | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "  Model Predictors                                                       \n",
       "1 1     lm, mpg ~ displacement + weight + origin + year, Auto            \n",
       "2 2     lm, mpg ~ weight + origin + year, Auto                           \n",
       "3 3     lm, mpg ~ weight * origin + weight * year + origin * year, Auto  \n",
       "4 4     lm, mpg ~ I(log(weight)) + I(log(origin)) + I(log(year)), Auto   \n",
       "5 5     lm, mpg ~ poly(weight, 2) + poly(origin, 2) + poly(year, 2), Auto\n",
       "  R.squared RSE      Error   \n",
       "1 0.8180977 3.345995 14.27112\n",
       "2 0.8174522 3.347605 14.27798\n",
       "3 0.8436896 3.109748 13.26350\n",
       "4 0.8398884 3.135142 13.37181\n",
       "5 0.8643326 2.897138 12.35668"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "models=list(mlrf1,mlrf2,mlrf3,mlrf4,mlrf5)\n",
    "pred=list()\n",
    "r=list()\n",
    "rse=list()\n",
    "error=list()\n",
    "for (model in models) {\n",
    "    pred=append(pred,toString(summary(model)$call))\n",
    "    r=append(r,summary(model)$r.squared)\n",
    "    rse=append(rse,summary(model)$sigma) \n",
    "    #error=append(error,)\n",
    "}\n",
    "pred=unlist(pred)\n",
    "r=unlist(r)\n",
    "rse=unlist(rse)\n",
    "results=data.frame(\"Model\"=1:5,\"Predictors\"=pred,\"R-squared\"=r,\"RSE\"=rse,'Error'=100*rse/mean(mpg))\n",
    "results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(1)\n",
    "x=rnorm(100)\n",
    "y=2*x+rnorm(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x + 0)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-1.9154 -0.6472 -0.1771  0.5056  2.3109 \n",
       "\n",
       "Coefficients:\n",
       "  Estimate Std. Error t value Pr(>|t|)    \n",
       "x   1.9939     0.1065   18.73   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.9586 on 99 degrees of freedom\n",
       "Multiple R-squared:  0.7798,\tAdjusted R-squared:  0.7776 \n",
       "F-statistic: 350.7 on 1 and 99 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "slrwi1=lm(y~x+0)\n",
    "summary(slrwi1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have an estimate for beta equal to 1,9939 really close to the actual value 2. The p-value corresponding to null hypothesis is almost so the relationship as we know exists and we reject the null hypothesis. R squared is 0,7798 is a little lower than you would expect but it's high enough the RSE is small and equal to 0,9586."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = x ~ y + 0)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-0.8699 -0.2368  0.1030  0.2858  0.8938 \n",
       "\n",
       "Coefficients:\n",
       "  Estimate Std. Error t value Pr(>|t|)    \n",
       "y  0.39111    0.02089   18.73   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.4246 on 99 degrees of freedom\n",
       "Multiple R-squared:  0.7798,\tAdjusted R-squared:  0.7776 \n",
       "F-statistic: 350.7 on 1 and 99 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "slrwi2=lm(x~y+0)\n",
    "summary(slrwi2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can say the exact same thing about the reverse regression, but instead in this situation beta actual value would be 0,5 and we will try to estimate that by least squares the estimate is 0,391 which is off by 0,1, worst estimate than for y~x coefficient. \n",
    "\n",
    "\n",
    "c- We trying to modelize the same problem first $y=2*x+\\varepsilon$  and after $x=0,5*(y-\\varepsilon)$ instead. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "d- For simple linear regression without intercept we have: \n",
    "         $SE(\\hat{\\beta})=\\sqrt{\\frac{\\sum_{i=1}^{n}(y_i-\\hat{\\beta} x_i)^2}{(n-1)\\sum_{i=1}^{n}x_i^2}}$ and $\\hat{\\beta}=\\frac{\\sum_{i=1}^{n}y_ix_i}{\\sum_{i=1}^{n}x_i^2}$\n",
    "  \n",
    "  \n",
    "  $t=\\frac{\\hat\\beta}{SE(\\hat{\\beta})}$ \n",
    "  \n",
    "  $t=\\frac{\\sum_{i=1}^{n}y_ix_i}{\\sum_{i=1}^{n}x_i^2} \\sqrt{\\frac{(n-1)\\sum_{i=1}^{n}x_i^2}{\\sum_{i=1}^{n}(y_i-\\hat{\\beta} x_i)^2}}$ \n",
    "  \n",
    "  $t=\\frac{\\sqrt{n-1}\\sum_{i=1}^{n}y_ix_i}{\\sqrt{\\sum_{i=1}^{n}x_i^2(\\sum_{i=1}^{n}y_i^2-2\\hat{\\beta}\\sum_{i=1}^{n}y_ix_i+\\hat{\\beta}^2\\sum_{i=1}^{n}x_i^2)}}$\n",
    "\n",
    "Let A be: \n",
    "\n",
    "$A=\\sum_{i=1}^{n}x_i^2(\\sum_{i=1}^{n}y_i^2-2\\hat{\\beta}\\sum_{i=1}^{n}y_ix_i+\\hat{\\beta}^2\\sum_{i=1}^{n}x_i^2)$\n",
    "\n",
    "then:\n",
    "\n",
    "$A=(\\sum_{i=1}^{n}x_i^2)(\\sum_{i=1}^{n}y_i^2)-2\\frac{\\sum_{i=1}^{n}y_ix_i}{\\sum_{i=1}^{n}x_i^2}\\sum_{i=1}^{n}y_ix_i\\sum_{i=1}^{n}x_i^2+(\\frac{\\sum_{i=1}^{n}y_ix_i}{\\sum_{i=1}^{n}x_i^2})^2(\\sum_{i=1}^{n}x_i^2)^2$\n",
    "\n",
    "it is finally simple to get to:\n",
    "\n",
    "$A=(\\sum_{i=1}^{n}x_i^2)(\\sum_{i=1}^{n}y_i^2)-(\\sum_{i=1}^{n}y_ix_i)^2$\n",
    "  \n",
    "And we conclude that: \n",
    "\n",
    "$t=\\frac{\\sqrt{n-1}\\sum_{i=1}^{n}y_ix_i}{\\sqrt{A}}=\\frac{\\sqrt{n-1}\\sum_{i=1}^{n}y_ix_i}{\\sqrt{(\\sum_{i=1}^{n}x_i^2)(\\sum_{i=1}^{n}y_i^2)-(\\sum_{i=1}^{n}y_ix_i)^2}}$\n",
    "  \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "100"
      ],
      "text/latex": [
       "100"
      ],
      "text/markdown": [
       "100"
      ],
      "text/plain": [
       "[1] 100"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "100"
      ],
      "text/latex": [
       "100"
      ],
      "text/markdown": [
       "100"
      ],
      "text/plain": [
       "[1] 100"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] 18.72593\n"
     ]
    }
   ],
   "source": [
    "#let's compare t-values for both models, well by inspecting formula more closely you will notice we'll have same t-value for both models:\n",
    "length(x)\n",
    "length(y)\n",
    "t=sqrt(length(x)-1)*sum(y*x)/sqrt(sum(x^2)*sum(y^2)-(sum(y*x))^2)\n",
    "print(t)\n",
    "#We get the same result as both models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(e) We just proved that algebraically and in R.\n",
    "\n",
    "(f) Let's prove the last result for SLR with intercept."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-1.8768 -0.6138 -0.1395  0.5394  2.3462 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) -0.03769    0.09699  -0.389    0.698    \n",
       "x            1.99894    0.10773  18.556   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.9628 on 98 degrees of freedom\n",
       "Multiple R-squared:  0.7784,\tAdjusted R-squared:  0.7762 \n",
       "F-statistic: 344.3 on 1 and 98 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = x ~ y)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.90848 -0.28101  0.06274  0.24570  0.85736 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  0.03880    0.04266    0.91    0.365    \n",
       "y            0.38942    0.02099   18.56   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.4249 on 98 degrees of freedom\n",
       "Multiple R-squared:  0.7784,\tAdjusted R-squared:  0.7762 \n",
       "F-statistic: 344.3 on 1 and 98 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "set.seed(1)\n",
    "x=rnorm(100)\n",
    "y=2*x+rnorm(100)\n",
    "slr1=lm(y~x)\n",
    "slr2=lm(x~y)\n",
    "summary(slr1)\n",
    "summary(slr2)\n",
    "#As you see below both t-values of the intercept null hypothesis are equal for the 2 models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "12- Easy exercise, I'll just leave the hint and move on. The intercept is the same for both models of y on x and x on y is when: $\\sum_{i=1}^{n}x_i^2=\\sum_{i=1}^{n}y_i^2$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 13-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(5)\n",
    "x=rnorm(100)\n",
    "eps=rnorm(100,mean=0,sd=0.25)\n",
    "y=-1+0.5*x+eps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta0=-1\n",
    "beta1=0.5\n",
    "leny=length(y) #100 obviously!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 214,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ani+YiOKnBnw/LpqAAhQYCQIKBXSAu9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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x,y,col='darkgoldenrod1',pch=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 215,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.62059 -0.15387  0.02532  0.18585  0.68291 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) -0.99693    0.02611  -38.18   <2e-16 ***\n",
       "x            0.53328    0.02775   19.22   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.261 on 98 degrees of freedom\n",
       "Multiple R-squared:  0.7903,\tAdjusted R-squared:  0.7882 \n",
       "F-statistic: 369.4 on 1 and 98 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "slrff1=lm(y~x)\n",
    "summary(slrff1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model have a little error term 0.261 and somehow high $R^2$ value of 0,79 this due to the values of $\\hat{\\beta_0}$ and $\\hat{\\beta_1}$ that are close to the actual values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 216,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Hpt18UeiV6EhDF0NAEhYUTVEdO6EYSU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\nTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x,y,col='darkgoldenrod1',pch=20)\n",
    "abline(slrff1,lwd=3,col='cornflowerblue')\n",
    "abline(-1,0.5,lwd=3,col='brown2')\n",
    "legend(-2.25,0.2,legend=c('Real','Estimate'),col=c('brown2','cornflowerblue'),lwd=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 217,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ poly(x, 2))\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.61154 -0.16155  0.01887  0.20026  0.68997 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) -0.98005    0.02617 -37.448   <2e-16 ***\n",
       "poly(x, 2)1  5.01572    0.26171  19.165   <2e-16 ***\n",
       "poly(x, 2)2 -0.17489    0.26171  -0.668    0.506    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.2617 on 97 degrees of freedom\n",
       "Multiple R-squared:  0.7913,\tAdjusted R-squared:  0.787 \n",
       "F-statistic: 183.9 on 2 and 97 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "slrfq=lm(y~poly(x,2))\n",
    "summary(slrfq)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We notice very slight decrease in $R^2$ and $RSE$ this is to be expected, as we get the model more flexible we fit more the learning data, although this change is not that significant, since the p-value related the the null hypothesis concerning the coefficient for $x^2$ is very large. So no, no improvement have been introduced by the quadratic term. Logical enough since the true relationship is linear."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [],
   "source": [
    "#We change the value of eps to 0.1\n",
    "set.seed(5)\n",
    "x=rnorm(100)\n",
    "eps=rnorm(100,mean=0,sd=0.1)\n",
    "y=-1+0.5*x+eps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.24824 -0.06155  0.01013  0.07434  0.27316 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) -0.99877    0.01044  -95.62   <2e-16 ***\n",
       "x            0.51331    0.01110   46.25   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.1044 on 98 degrees of freedom\n",
       "Multiple R-squared:  0.9562,\tAdjusted R-squared:  0.9557 \n",
       "F-statistic:  2139 on 1 and 98 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "slrff2=lm(y~x)\n",
    "summary(slrff2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PM4nYF9vRdCKo/fpx95XH1ESC+EVBy/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\nNKHWhgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x,y,col='darkgoldenrod1',pch=20)\n",
    "abline(slrff2,lwd=3,col='cornflowerblue')\n",
    "abline(-1,0.5,lwd=3,col='brown2')\n",
    "legend(-2.25,0.25,legend=c('Real','Estimate'),col=c('brown2','cornflowerblue'),lwd=3)\n",
    "#As you can see the two lines the estimated and real are almost identical  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you would expect reducing the variance of the irreductible error will make the linear regression perform better and get close as possible to the actual function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 229,
   "metadata": {},
   "outputs": [],
   "source": [
    "#We change the value of eps to 0.5\n",
    "set.seed(5)\n",
    "x=rnorm(100)\n",
    "eps=rnorm(100,mean=0,sd=0.5)\n",
    "y=-1+0.5*x+eps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 230,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-1.24118 -0.30774  0.05064  0.37170  1.36583 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) -0.99385    0.05222  -19.03   <2e-16 ***\n",
       "x            0.56656    0.05549   10.21   <2e-16 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.5219 on 98 degrees of freedom\n",
       "Multiple R-squared:  0.5154,\tAdjusted R-squared:  0.5105 \n",
       "F-statistic: 104.2 on 1 and 98 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "slrff3=lm(y~x)\n",
    "summary(slrff3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 233,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XUijqOKto4ICYvEzajkZIOaTWCNdkcb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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x,y,col='darkgoldenrod1',pch=20)\n",
    "abline(slrff3,lwd=3,col='cornflowerblue')\n",
    "abline(-1,0.5,lwd=3,col='brown2')\n",
    "legend(-2.25,0.5,legend=c('Real','Estimate'),col=c('brown2','cornflowerblue'),lwd=3)\n",
    "#As you can see the two lines the estimated and real are almost identical  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you would expect increasing the variance of the irreductible error will make the linear regression perform worse than before and be largely off the actual function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 234,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'call'</li>\n",
       "\t<li>'terms'</li>\n",
       "\t<li>'residuals'</li>\n",
       "\t<li>'coefficients'</li>\n",
       "\t<li>'aliased'</li>\n",
       "\t<li>'sigma'</li>\n",
       "\t<li>'df'</li>\n",
       "\t<li>'r.squared'</li>\n",
       "\t<li>'adj.r.squared'</li>\n",
       "\t<li>'fstatistic'</li>\n",
       "\t<li>'cov.unscaled'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'call'\n",
       "\\item 'terms'\n",
       "\\item 'residuals'\n",
       "\\item 'coefficients'\n",
       "\\item 'aliased'\n",
       "\\item 'sigma'\n",
       "\\item 'df'\n",
       "\\item 'r.squared'\n",
       "\\item 'adj.r.squared'\n",
       "\\item 'fstatistic'\n",
       "\\item 'cov.unscaled'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'call'\n",
       "2. 'terms'\n",
       "3. 'residuals'\n",
       "4. 'coefficients'\n",
       "5. 'aliased'\n",
       "6. 'sigma'\n",
       "7. 'df'\n",
       "8. 'r.squared'\n",
       "9. 'adj.r.squared'\n",
       "10. 'fstatistic'\n",
       "11. 'cov.unscaled'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"call\"          \"terms\"         \"residuals\"     \"coefficients\" \n",
       " [5] \"aliased\"       \"sigma\"         \"df\"            \"r.squared\"    \n",
       " [9] \"adj.r.squared\" \"fstatistic\"    \"cov.unscaled\" "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(slrff3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>(Intercept)</th><td>-1.0487431</td><td>-0.9451071</td></tr>\n",
       "\t<tr><th scope=row>x</th><td> 0.4782154</td><td> 0.5883401</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t(Intercept) & -1.0487431 & -0.9451071\\\\\n",
       "\tx &  0.4782154 &  0.5883401\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % | \n",
       "|---|---|\n",
       "| (Intercept) | -1.0487431 | -0.9451071 | \n",
       "| x |  0.4782154 |  0.5883401 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "            2.5 %      97.5 %    \n",
       "(Intercept) -1.0487431 -0.9451071\n",
       "x            0.4782154  0.5883401"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>(Intercept)</th><td>-1.0194973</td><td>-0.9780428</td></tr>\n",
       "\t<tr><th scope=row>x</th><td> 0.4912861</td><td> 0.5353361</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t(Intercept) & -1.0194973 & -0.9780428\\\\\n",
       "\tx &  0.4912861 &  0.5353361\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % | \n",
       "|---|---|\n",
       "| (Intercept) | -1.0194973 | -0.9780428 | \n",
       "| x |  0.4912861 |  0.5353361 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "            2.5 %      97.5 %    \n",
       "(Intercept) -1.0194973 -0.9780428\n",
       "x            0.4912861  0.5353361"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>2.5 %</th><th scope=col>97.5 %</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>(Intercept)</th><td>-1.0974863</td><td>-0.8902142</td></tr>\n",
       "\t<tr><th scope=row>x</th><td> 0.4564307</td><td> 0.6766803</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|ll}\n",
       "  & 2.5 \\% & 97.5 \\%\\\\\n",
       "\\hline\n",
       "\t(Intercept) & -1.0974863 & -0.8902142\\\\\n",
       "\tx &  0.4564307 &  0.6766803\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | 2.5 % | 97.5 % | \n",
       "|---|---|\n",
       "| (Intercept) | -1.0974863 | -0.8902142 | \n",
       "| x |  0.4564307 |  0.6766803 | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "            2.5 %      97.5 %    \n",
       "(Intercept) -1.0974863 -0.8902142\n",
       "x            0.4564307  0.6766803"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "confint(slrff1)\n",
    "confint(slrff2)\n",
    "confint(slrff3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We notice that for the noiser the data is the wider the confidence interval is for both coefficients, logical enough since adding incertainty to data adds incertainty to the estimation based on this same data :\n",
    "\n",
    "$\\sigma=0,25 => \\beta_0max-\\beta_0min=0,103636$ & $\\beta_1max-\\beta_1min=0.1101247$\n",
    "\n",
    "$\\sigma=0,1 => \\beta_0max-\\beta_0min=0.0414545$ & $\\beta_1max-\\beta_1min=0.04405$\n",
    "\n",
    "$\\sigma=0,5 => \\beta_0max-\\beta_0min=0.2072721$ & $\\beta_1max-\\beta_1min=0.2202496$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 14-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "set.seed(10)\n",
    "x1=runif(100) #100 random number from the uniform distribution!\n",
    "x2=0.5*x1+rnorm(100)/10\n",
    "y=2+2*x1+0.3*x2+rnorm(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\\beta_0=2$,   $\\beta_1=2$ and $\\beta_2=0,3$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TU7+S4YVLP35Y/mB1iFkK7yy0YvGlXr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\nggAhQYCQIEBIECAkCBASBAgJAv4DNCdDRdNG9WgAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(x1,x2,col='darkgoldenrod1',pch=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We notice the existence of somehow linear a relationship between x1 and x2, since as x1 increases x2 increases too! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x1 + x2)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-2.02507 -0.64102 -0.04811  0.64382  2.09265 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   1.7651     0.1876   9.409 2.54e-15 ***\n",
       "x1            3.1604     0.6444   4.904 3.77e-06 ***\n",
       "x2           -1.3863     0.9787  -1.417     0.16    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.9377 on 97 degrees of freedom\n",
       "Multiple R-squared:  0.321,\tAdjusted R-squared:  0.307 \n",
       "F-statistic: 22.93 on 2 and 97 DF,  p-value: 7.002e-09\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lmlrf=lm(y~x1+x2)\n",
    "summary(lmlrf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We couldn't reject the null hypothesis for $\\hat{\\beta_2}$ because we have collinearity between predictors. How is that? Well as we have seen in the collinearity section, if we have collinearity the cost function will tend to have a wider section (compared to when there is no collinearity) of values close to the minimum value of the cost function which means any slight change of data points could cause the least square estimates to change. This unwanted sense of uncertainty tends to reduce the accuracy of the coefficient estimates and thus we get a larger Standard error and hence it causes a decline in the t-statistic and we fail to reject the null hypothesis for some significant predictors such as x2 in this case."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x1)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-2.14104 -0.68538 -0.07084  0.71946  2.09537 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   1.7858     0.1880   9.499 1.48e-15 ***\n",
       "x1            2.4065     0.3653   6.588 2.23e-09 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.9425 on 98 degrees of freedom\n",
       "Multiple R-squared:  0.307,\tAdjusted R-squared:  0.2999 \n",
       "F-statistic: 43.41 on 1 and 98 DF,  p-value: 2.235e-09\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x2)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.5776 -0.7731  0.1079  0.7634  2.4292 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   2.2717     0.1741  13.051  < 2e-16 ***\n",
       "x2            2.5773     0.6134   4.202 5.85e-05 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 1.042 on 98 degrees of freedom\n",
       "Multiple R-squared:  0.1527,\tAdjusted R-squared:  0.144 \n",
       "F-statistic: 17.65 on 1 and 98 DF,  p-value: 5.847e-05\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lslrf1=lm(y~x1)\n",
    "lslrf2=lm(y~x2)\n",
    "summary(lslrf1)\n",
    "summary(lslrf2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We reject the null hypothesis for both models because the p-value for the null hypothesis is baisacly zero. Which means that individually both predictors are significant.\n",
    "\n",
    "14-c There is no contradiction since predictors are collinear and collinearity causes that we cannot detect the individual contributions of predictors to the response."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x1 + x2)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.3001 -0.8156 -0.0130  0.7543  3.0327 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   1.9029     0.1995   9.540 1.21e-15 ***\n",
       "x1            1.6371     0.5730   2.857  0.00523 ** \n",
       "x2            1.1258     0.8324   1.353  0.17932    \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 1.013 on 98 degrees of freedom\n",
       "Multiple R-squared:  0.2574,\tAdjusted R-squared:  0.2423 \n",
       "F-statistic: 16.99 on 2 and 98 DF,  p-value: 4.636e-07\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x1)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.2238 -0.7532 -0.0511  0.6951  3.8657 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   1.9137     0.2001   9.562 9.88e-16 ***\n",
       "x1            2.2061     0.3907   5.646 1.57e-07 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 1.017 on 99 degrees of freedom\n",
       "Multiple R-squared:  0.2436,\tAdjusted R-squared:  0.2359 \n",
       "F-statistic: 31.88 on 1 and 99 DF,  p-value: 1.572e-07\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = y ~ x2)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-2.58188 -0.81333  0.07991  0.74748  2.37107 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)   2.2197     0.1717  12.928  < 2e-16 ***\n",
       "x2            2.8716     0.5853   4.906 3.65e-06 ***\n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 1.049 on 99 degrees of freedom\n",
       "Multiple R-squared:  0.1956,\tAdjusted R-squared:  0.1875 \n",
       "F-statistic: 24.07 on 1 and 99 DF,  p-value: 3.65e-06\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x1=c(x1,0.1)\n",
    "x2=c(x2,0.8)\n",
    "y=c(y,6)\n",
    "lslrf1=lm(y~x1)\n",
    "lslrf2=lm(y~x2)\n",
    "lmlrf=lm(y~x1+x2)\n",
    "summary(lmlrf)\n",
    "summary(lslrf1)\n",
    "summary(lslrf2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th></th><th scope=col>hatvalues</th><th scope=col>rstudent</th><th scope=col>x1</th><th scope=col>x2</th><th scope=col>y</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>101</th><td>0.3968186</td><td>4.164214 </td><td>0.1      </td><td>0.8      </td><td>6        </td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{r|lllll}\n",
       "  & hatvalues & rstudent & x1 & x2 & y\\\\\n",
       "\\hline\n",
       "\t101 & 0.3968186 & 4.164214  & 0.1       & 0.8       & 6        \\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "| <!--/--> | hatvalues | rstudent | x1 | x2 | y | \n",
       "|---|\n",
       "| 101 | 0.3968186 | 4.164214  | 0.1       | 0.8       | 6         | \n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "    hatvalues rstudent x1  x2  y\n",
       "101 0.3968186 4.164214 0.1 0.8 6"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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M5oOJ2biI6QBAQ+syEMQhIQLaSIB0mE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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(hatvalues(lmlrf),rstudent(lmlrf),col='darkgoldenrod1',pch=20)\n",
    "l=data.frame('hatvalues'=hatvalues(lmlrf),'rstudent'=rstudent(lmlrf),'x1'=x1,'x2'=x2,'y'=y)\n",
    "outlihlev=subset(l,hatvalues>0.12 & (rstudent>3 || rstudent<3))\n",
    "outlihlev\n",
    "abline(v=12/100,col='cornflowerblue',lwd=3)\n",
    "abline(a=3,b=0,col='cornflowerblue',lwd=3)\n",
    "abline(a=-3,b=0,col='cornflowerblue',lwd=3)\n",
    "text(outlihlev$hatvalues,outlihlev$rstudent,labels = paste('x1=',outlihlev$x1,sep = \"\"),pos = 1, cex=0.7)\n",
    "text(outlihlev$hatvalues,outlihlev$rstudent,labels = paste('x2=',outlihlev$x2,sep = \"\"),pos=2,cex=0.7)\n",
    "text(outlihlev$hatvalues,outlihlev$rstudent,labels = paste('y=',outlihlev$y,sep = \"\"),pos=3,cex=0.7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see above the point added is clearly both an outlier and a high leverage point. This is a nasty combinaison as it affects the fit for the data and also the measures of quality of the fit. So it's better to delete before working with the data!\n",
    "\n",
    "Reminder: We consider as outlier data points foe which the studentized value is larger in absolute value than 3. And is considered a high leverage data points each point for which the leverage statistic (hatvalue in R) is 'greatly' larger than the average of this statistic which is: $\\frac{p+1}{n}$ with: $p$=number of predictors for the model and $n$ number of observations. I defined 'greatly' larger as 4 times higher than the average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 15-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "The following objects are masked from Boston (pos = 3):\n",
      "\n",
      "    age, black, chas, crim, dis, indus, lstat, medv, nox, ptratio, rad,\n",
      "    rm, tax, zn\n",
      "\n",
      "The following objects are masked from Boston (pos = 4):\n",
      "\n",
      "    age, black, chas, crim, dis, indus, lstat, medv, nox, ptratio, rad,\n",
      "    rm, tax, zn\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "      crim                zn             indus            chas        \n",
       " Min.   : 0.00632   Min.   :  0.00   Min.   : 0.46   Min.   :0.00000  \n",
       " 1st Qu.: 0.08204   1st Qu.:  0.00   1st Qu.: 5.19   1st Qu.:0.00000  \n",
       " Median : 0.25651   Median :  0.00   Median : 9.69   Median :0.00000  \n",
       " Mean   : 3.61352   Mean   : 11.36   Mean   :11.14   Mean   :0.06917  \n",
       " 3rd Qu.: 3.67708   3rd Qu.: 12.50   3rd Qu.:18.10   3rd Qu.:0.00000  \n",
       " Max.   :88.97620   Max.   :100.00   Max.   :27.74   Max.   :1.00000  \n",
       "      nox               rm             age              dis        \n",
       " Min.   :0.3850   Min.   :3.561   Min.   :  2.90   Min.   : 1.130  \n",
       " 1st Qu.:0.4490   1st Qu.:5.886   1st Qu.: 45.02   1st Qu.: 2.100  \n",
       " Median :0.5380   Median :6.208   Median : 77.50   Median : 3.207  \n",
       " Mean   :0.5547   Mean   :6.285   Mean   : 68.57   Mean   : 3.795  \n",
       " 3rd Qu.:0.6240   3rd Qu.:6.623   3rd Qu.: 94.08   3rd Qu.: 5.188  \n",
       " Max.   :0.8710   Max.   :8.780   Max.   :100.00   Max.   :12.127  \n",
       "      rad              tax           ptratio          black       \n",
       " Min.   : 1.000   Min.   :187.0   Min.   :12.60   Min.   :  0.32  \n",
       " 1st Qu.: 4.000   1st Qu.:279.0   1st Qu.:17.40   1st Qu.:375.38  \n",
       " Median : 5.000   Median :330.0   Median :19.05   Median :391.44  \n",
       " Mean   : 9.549   Mean   :408.2   Mean   :18.46   Mean   :356.67  \n",
       " 3rd Qu.:24.000   3rd Qu.:666.0   3rd Qu.:20.20   3rd Qu.:396.23  \n",
       " Max.   :24.000   Max.   :711.0   Max.   :22.00   Max.   :396.90  \n",
       "     lstat            medv      \n",
       " Min.   : 1.73   Min.   : 5.00  \n",
       " 1st Qu.: 6.95   1st Qu.:17.02  \n",
       " Median :11.36   Median :21.20  \n",
       " Mean   :12.65   Mean   :22.53  \n",
       " 3rd Qu.:16.95   3rd Qu.:25.00  \n",
       " Max.   :37.97   Max.   :50.00  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "library(MASS)\n",
    "attach(Boston)\n",
    "summary(Boston)\n",
    "fix(Boston)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "?Boston"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that the chas variable is qualitative, and is equal to 1 if a given neighborhood bounds the river, 0 if not. Let's let R know about this by changing that variable to quantitative."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "Boston$chas=factor(Boston$chas,labels = c('N','Y'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'crim'</li>\n",
       "\t<li>'zn'</li>\n",
       "\t<li>'indus'</li>\n",
       "\t<li>'chas'</li>\n",
       "\t<li>'nox'</li>\n",
       "\t<li>'rm'</li>\n",
       "\t<li>'age'</li>\n",
       "\t<li>'dis'</li>\n",
       "\t<li>'rad'</li>\n",
       "\t<li>'tax'</li>\n",
       "\t<li>'ptratio'</li>\n",
       "\t<li>'black'</li>\n",
       "\t<li>'lstat'</li>\n",
       "\t<li>'medv'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'crim'\n",
       "\\item 'zn'\n",
       "\\item 'indus'\n",
       "\\item 'chas'\n",
       "\\item 'nox'\n",
       "\\item 'rm'\n",
       "\\item 'age'\n",
       "\\item 'dis'\n",
       "\\item 'rad'\n",
       "\\item 'tax'\n",
       "\\item 'ptratio'\n",
       "\\item 'black'\n",
       "\\item 'lstat'\n",
       "\\item 'medv'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'crim'\n",
       "2. 'zn'\n",
       "3. 'indus'\n",
       "4. 'chas'\n",
       "5. 'nox'\n",
       "6. 'rm'\n",
       "7. 'age'\n",
       "8. 'dis'\n",
       "9. 'rad'\n",
       "10. 'tax'\n",
       "11. 'ptratio'\n",
       "12. 'black'\n",
       "13. 'lstat'\n",
       "14. 'medv'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"crim\"    \"zn\"      \"indus\"   \"chas\"    \"nox\"     \"rm\"      \"age\"    \n",
       " [8] \"dis\"     \"rad\"     \"tax\"     \"ptratio\" \"black\"   \"lstat\"   \"medv\"   "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "names(Boston)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ zn)\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-4.429 -4.222 -2.620  1.250 84.523 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)  4.45369    0.41722  10.675  < 2e-16 ***\n",
      "zn          -0.07393    0.01609  -4.594 5.51e-06 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 8.435 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.04019,\tAdjusted R-squared:  0.03828 \n",
      "F-statistic:  21.1 on 1 and 504 DF,  p-value: 5.506e-06\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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0Q6iegbd/JONux/t8bdKimANJFCv9du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\nStJbpCLjWEQaiV2QRaSs/HtQYh3pEETyJG762zTC3wcAPf86Si3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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ indus)\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-11.972  -2.698  -0.736   0.712  81.813 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept) -2.06374    0.66723  -3.093  0.00209 ** \n",
      "indus        0.50978    0.05102   9.991  < 2e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.866 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.1653,\tAdjusted R-squared:  0.1637 \n",
      "F-statistic: 99.82 on 1 and 504 DF,  p-value: < 2.2e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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qQYShCp+KSzY+JuVtzvnCDkdTHmApEq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\nCIBIAAIgEoAA/weXbl/2P6i0gQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ chas)\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-3.738 -3.661 -3.435  0.018 85.232 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)   3.7444     0.3961   9.453   <2e-16 ***\n",
      "chas         -1.8928     1.5061  -1.257    0.209    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 8.597 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.003124,\tAdjusted R-squared:  0.001146 \n",
      "F-statistic: 1.579 on 1 and 504 DF,  p-value: 0.2094\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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q/dTFnfIlmTZa+Puvp+60Ryqmk6oudx6rfzAYsds9rrq3YIbr02ijQmZGXEc1rk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\nAARAJAABEAlAAEQCEACRAARAJAAB/g99Zg1b2roCaQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ nox)\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-12.371  -2.738  -0.974   0.559  81.728 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)  -13.720      1.699  -8.073 5.08e-15 ***\n",
      "nox           31.249      2.999  10.419  < 2e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.81 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.1772,\tAdjusted R-squared:  0.1756 \n",
      "F-statistic: 108.6 on 1 and 504 DF,  p-value: < 2.2e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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giqIyaardqlrrqR606n0+4NlWeZ9u10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",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ rm)\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-6.604 -3.952 -2.654  0.989 87.197 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)   20.482      3.365   6.088 2.27e-09 ***\n",
      "rm            -2.684      0.532  -5.045 6.35e-07 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 8.401 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.04807,\tAdjusted R-squared:  0.04618 \n",
      "F-statistic: 25.45 on 1 and 504 DF,  p-value: 6.347e-07\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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LzXbpZVO5czcXKQj/aPNkcSC89xDdJG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\ntPzB/qWIxN1/UkVSXT6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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ age)\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-6.789 -4.257 -1.230  1.527 82.849 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept) -3.77791    0.94398  -4.002 7.22e-05 ***\n",
      "age          0.10779    0.01274   8.463 2.85e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 8.057 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.1244,\tAdjusted R-squared:  0.1227 \n",
      "F-statistic: 71.62 on 1 and 504 DF,  p-value: 2.855e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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Kkh1UQisxFE8mKbJDZ99tfkj/2VjOxP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\nqUWib1TYD4QngfrNF7X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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ dis)\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-6.708 -4.134 -1.527  1.516 81.674 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)   9.4993     0.7304  13.006   <2e-16 ***\n",
      "dis          -1.5509     0.1683  -9.213   <2e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.965 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.1441,\tAdjusted R-squared:  0.1425 \n",
      "F-statistic: 84.89 on 1 and 504 DF,  p-value: < 2.2e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZJDFWIdiv6lthBE4kLWT1Q9QaRRMav042UdoB7rmvfHbO9DJ/h8FS+fof0eT75+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\nD0SagCZXhU+fw9TuiK5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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ rad)\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-10.164  -1.381  -0.141   0.660  76.433 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept) -2.28716    0.44348  -5.157 3.61e-07 ***\n",
      "rad          0.61791    0.03433  17.998  < 2e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 6.718 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.3913,\tAdjusted R-squared:   0.39 \n",
      "F-statistic: 323.9 on 1 and 504 DF,  p-value: < 2.2e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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8Ft9+Nm7eLWQ1YzAocgkkqkROLqk1Ig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\ndO16h2KzdjaFRDoe9p4pUvfYHdILcYqMkQ5Nq1uk7cmG6eXWobP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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ tax)\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-12.513  -2.738  -0.194   1.065  77.696 \n",
      "\n",
      "Coefficients:\n",
      "             Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept) -8.528369   0.815809  -10.45   <2e-16 ***\n",
      "tax          0.029742   0.001847   16.10   <2e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 6.997 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.3396,\tAdjusted R-squared:  0.3383 \n",
      "F-statistic: 259.2 on 1 and 504 DF,  p-value: < 2.2e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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LIZU3YxqpKG6moM4e+nR3ZNm/EE7eruWWFfs6Hd+HLvlXtKt+a8rrzgtN5U4JDc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\nJ+E6kol895tlXxJrdkubllxbjWSqM+JIihFJa2gXdk02gydjI7r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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ ptratio)\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-7.654 -3.985 -1.912  1.825 83.353 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept) -17.6469     3.1473  -5.607 3.40e-08 ***\n",
      "ptratio       1.1520     0.1694   6.801 2.94e-11 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 8.24 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.08407,\tAdjusted R-squared:  0.08225 \n",
      "F-statistic: 46.26 on 1 and 504 DF,  p-value: 2.943e-11\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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Wdy0e2i4r+vCJFyUy78HblratHNouI+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\nBPg/fB5+/B7I31oAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ black)\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-13.756  -2.299  -2.095  -1.296  86.822 \n",
      "\n",
      "Coefficients:\n",
      "             Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept) 16.553529   1.425903  11.609   <2e-16 ***\n",
      "black       -0.036280   0.003873  -9.367   <2e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.946 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.1483,\tAdjusted R-squared:  0.1466 \n",
      "F-statistic: 87.74 on 1 and 504 DF,  p-value: < 2.2e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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972fTpH8uvGvhmbIwmownHbjSeSci9X6Je84PrigyLbdhfMkSrwRQpcR3Kfbq4j\n0UqxYdXkXndyQykbkYwqRMMBgAGIBAADEAkABiASAAxAJAAYgEgAMACRAGAAIgHAAEQCgAGI\nBAADEAkABiASAAxAJAAYgEgAMACRAGAAIgHAAEQCgAGIBAADEAkABiASAAxAJAAYgEgAMACR\nAGAAIgHAAEQCgAGIBAADEAkABiASAAxAJAAYgEgAMACRAGAAIgHAAEQCgAGIBAADEAkABiAS\nAAxAJAAYgEgAMACRAGAAIgHAAEQCgAGIBAADEAkABiASAAxAJAAYgEgAMACRAGAAIgHAAEQC\ngAGIBAADEAkABiASAAxAJAAYgEgAMACRAGAAIgHAAEQCgAGIBAADEAkABiASAAxAJAAYgEgA\nMACRAGAAIgHAAEQCgAGIBAADEAkABiASAAxAJAAYgEgAMACRAGAAIgHAAEQCgAGIBAADEAkA\nBiASAAxAJAAYgEgAMACRAGAAIgHAAEQCgAGIBAADEAkABkYR6d/Hq1Jvn9H3VfhAIi+H+CoM\nfzPUwtvvRIjQZjRMVpoloc9lkKz+e1nq8eVfJMBhkV5VWfi7oTRRkyDSAPxQb3+n6e+b+ogE\nOCzSSJV2Bmv5fKi3/MAFbzCEPpdBsqrU3BX9K60hiMSFLp+scoJIUnGL9ONl7qAe85r3x2jv\nwwb4fFUvn7H9Hm++fsYimEctJJolpFJ/39XLzyaHNBieSLakv94eM6cv886jaD8mW5Tzo1dN\nZo8n/9Tr/P/r41TpvDFtau+ZIA1uM/E4z76qd5oQyUigWTRgEJE+1I+/5smbni39XEbtiwiP\nh/dlPkz2I1XxZt8MREBFsiEfoZ6bMMkf2tmS/lyK8JOW3bsrkldNdo+ZN/Ws2b+PyLw3nNoz\nCdrgJBNzkh80oSUjPyLNokX5tI2ejUe5vH4s89xf6u3fY9I0t/5fz6fPY3g+fD3f+Pemgue0\nX+rlz/TnZdkjEsHySEKqZ8jP9SR4b8xiw5/JKemX5wu/nkVEy84RyStlu8fMr/k89fMRl/cG\nrT2boA1OMjHXk5PQl81IoFm0KJ+msTPy9ePZizwL4/25cPRPveh3TA29zxOpf88+3nlv5n0u\nyK/lTBaJQEdjQi5rVCMN1Zuhl7+fHtGSVqaBLmX3LLAvb2hn3l69cpv0bM5r4A2n9myCOriT\nid/eXroSw82iASO1kd8/X54FRtv136+fb6SGVuz7Xj3qcJEInLdDjeHGzIXw+vK1PjEl/fEY\nVv35o0NEys4pZbvHwo/HYO3vc3zgv+HUnknQBCevmYBedcaaRQPGaiN/9BBi5c2UkFtizssL\nYZHevJAQKVDzieMAACAASURBVMZcCL/VPENx2ubP5zTy5W+q7LxSNnss/H4M1j7mLsV7IyyS\nCR4Qya9OiORhCsH14Id6/fz6S0Sy4fNE8iKASHGWQnhfBkhuiXx9vOoTXLDsNqWs91h5eX3+\nC7yxqT0nOHlt3dwm5A9A2jFGG3lfl3Lmic2bmeLMRWQL7n07n9zOkd4TEbhzpHeIRFgK4c+y\n2LApad1glzd+m/Zrt5z27Ww9+pdPsjC69cNLUAcnrxFt1oScOVLbZYY1Cx3SOM6jPj4fM8bf\nb0+hPp+rMB/LKPn39MeOieclo8fbwcUGshYXieAvjUav2rmR3Ji1EJYuiZT067JStvZIZLHs\n9VFX/94WkZxqsnusPJr+vB6wecOrvbVqdXDymhHJJEQyEmgWLcqnaexsfOhFo+cTcxlIv6pX\nIJYhMhlkT2R4HLqORCJ4VaaLoteRpgkizayF8G/pkmxJ/3KrYL5mM1++ma8Kva+rCzSM3UPz\nulTL5o1N7S1VuwYnr62ZIwnp6VK4WbQon6ax8/Hnx+Ps8vZrefJc3pmL5cfzdmQyCPt86PCD\nFhidZ36+2DsbthH8fjUi2ZAQyaAL4WM5s9uSnm9HsFcJfpobCh5bP5Ytr5rMHppf6+DLf8Op\nPVu1Orh9TWfOJrTcvfI70iwagDYCLkzr+xlISr0SAqAj800O/96jnxbgT7BXQgB0ZL3t7mU/\nJBMQCVySz/nuzH7pQSQAGIBIADAAkQBgACIBwAC/SApkwl70NXX0X1XWvzvudSr5RcpfSewx\nXpQzRbKb/1VF8F2XbuVu5wGRBkCGSJXUKQGRmqR9c4YWqZLRTIJIAyBDpLqh3V2QJZLSN1Gr\nRkmOyeAi1XYuQ3VKMkTSAi1/Sm9CpAUZIlVTLcT3QCqJEEmRJ4r4BJEWBhfpQNcyjkkSRHLG\ncaRHgkgrMkSqnyONo0M9wkTCHCnE6CLdwSRhIqFHCiFDpJMYREIJIkXmSBJqUQa3FmmQJQcR\nIkVW7STUoghkiHTedaQRTJIhknkFc6QQdxdpBGSJBILIEOkgI3QrB4BIA3AJkY6ZJF5DiDQA\nMkQ6OrQ75oL0JQeINADXEOloryJbJYg0ADJEAikairT7GVxUUiYQySC2V2onktpsHI3xtsgQ\niWP5+7gHUgd4zURSwc0jMd4XsSKVfOfHAoMGMk2CSAMgQ6Twm4V5k2kBAxBpAISKVHX7CYtJ\nAnXEHGkAZIi0GdrV3cd1UZOwajcAlxKJySRpKuE60gDIECn8JipxASINgFSRKlbtWJHUK0Gk\nAZAhEuPHKLgMEDTAKxCpujrdHWu+d/zmQKR4TFJU6iHS8bRvTruCOmtBSErz56NQpMpfsjia\n9s1pVlDnXaLgNElEr1TVI61K9Uv75rQqqLKL5rwfNWdt/AJUqhFJkb/9vXAd6TBXFOlqtBNp\nVigZbPf2E++7UG6LDJGEc3Kn1EwkZXfJrySjjCJp4LLfBedIT5ib/rnju6Yi7dxEsnndRuqL\ndG9qSiBvHluyasc/tONu+WeqVLfYoPZ7iQqRbGg1OSJhaFe1C0dX3naOJGCRgIt215FsB3ZU\npNv3St1F6nfRnN+kk+RseEGWTney0jYiqcntkSBS1S7MPVIbGjT7U1QqFqnlBVlT+4ou+UEk\nGSINtfzd3aWGPVJF2lZO9EiEqsWGnHns/klxVJG6d0uyRPLew3WkhfbL3/2TJjRq8n1Vql21\nw712HWlXULsxd6mjKyzeVV5HYhlu3VokemVg75zUsKB2LzTZzZZDu2YmdXP0gEjyV4QEowet\n8+O0Y1TxemmTBaGmc6R27b2TSpUijbG0KhhlL5fZsowV6okF1S3pps29g0wQ6RQUHdq55Rko\nlTuI1JjmKtUtNkCkg/giKXaRBhvazYy85lC3/K1Y1qTvK5JyrVGKvUdqsCDU4TpSY5O+G/ZL\nUq8jXRvTVzjDZc450qALQs1HYM0SgEgnEZgjsa3akTgHE6nL8K6JTFWLDbgge5zG15EaiNTp\nFqEeE6UGKh3okTBH6kXVYsOoIg3KkaEdeqROVBXUyAtCXZbveJceINIA3O86UqeFcEaVINIA\nyBCp69Cu3yUlJpkg0gDULDaMeEGW0vHiLItKR1bt+qV9c+oLaug66nmjw+EJE64jDcCBghp6\n1ND3c0rHUoNIAyBDpDOWv7vffVdtU7FI+DWK/kgV6ZLfAVCpUlWPFL27Mi+eXt+ZdhlkiBR8\nr30dnvE59O/v4jlT1WJD8b5H0745B1btGiZ96HRawhBf6QCRBkDmdaRuIp1HgcIQaQAg0mkf\n+ptVykm7/xypJu2bU1pQnRaE+syRNGcO8DLSrlv+5lkqgEiZVN79XblnftKd14tOVymVPq4j\nDUDl55Eqd40lLeJjFOeuOyRUhkgDAJEsJy/hLT1TIA8QaQBkiCQFCYvhW5XK72xocmcxSCF1\njnQaElzy7nPVBZWxLIEe6SyqCop9QUjG0G5ByDVakg21eSUGRDoNmdeRzqWVSrQnzzsTLfcT\nLSG/y3oklZ1IOsajEdwFGSIJpMGXASnyOBUYVTO0UxNNpB7ZlSQIiBSDvV8q+nEDZ0edo7wk\nzD4QqSPFdzY0WRCSNbTT8JpU9uMG7p65+YFIpyGjR5Ip0sT8XUCuSOkfN3D3XDOznwZEOgsZ\nIgmGSyXlLza07ZGyfjE7gzEqSQAQqROFP27g7Lr+j+VvwdRekOVdWRU7tFvh+ebUwBypaNUu\nIwWIdBaVtwgxD7+lizQVfHooTvl1JLpfVkhFtxWDBtUx3O3rHmSINAyn3PZQJZIi07IuaW/3\nG7GCq4FIhZygUo1I/JVU1MVkLaJcChkiDTC0o3SWSYRIZZFBpKx92FdWBxOps0oNRdq9tq6c\n/7NzcgeR3GLD8nc13WRqN0dSm41YiFIzrj9H8o4QIh2AYSUvh+pVu71ZTUY7qBXp8qt2foFU\nHS37yupwQztK856p2XWkApFu0MWUwSES/8rq0CI1V6l2jlQS8a5Il+9iCmEQ6d7L3zEqvtM7\nl2YiFcyRrkr96eH4HAkidaadSPmrdhflSDs+vGqH60gpGvRMtat2fdMeEcZVesyR5FPVI+Hr\nuDI4WSR8rXQGjD1Ts1U71rRH5GyReLh2Ha1w+NRDJHfH2/xiH9+ifuUciTlpDO1SoEdqB9up\nAiL14UjPBJEGQIZI96FGJ4g0AJWrdmclfQWKVWookhnZ7N/ZAJLU9Eh3+V67lpQM9dqJpMw+\nEOkgMlbt7ifSSpZPxSLl/j4p6Y0g0kFkiHR7kjYduLMhvauy/0Okg0AkISQ+23TkXrucHum5\nAZEOIkOk2w7tfIIjPWXeS4WaQ5aJREyCSAeBSBIJ/WIf6bGi48BSkfY/RwGRMpEhEtiw/jQz\n/aExbVDi98/L5kgZoJIygUjy2YgUXekr/M6G7LTBLhVX8HAdqTOhHmlvjsSbNtil/s4GfB6p\nF5s50gSRxHHgXruMldU7f4qZjzqRTv4S/bvRVKTkzSeoo1yqhnYqeZ21MG2wS0uR8u+HxNAu\nhXMd6XvyV8dpSGc5O3XrT2Ha08T3yZ1r0mqOFBUpuFgBkVLU3tnAKtINPi57iKqyyfw23Pwe\nCaSQINLyuwmosmjDb1U0dqpbN0fC6c9SIxL3HEkxLV4MTvzc1LBo9n79JTW0UzDJUiUS8wVZ\n9EhPEl1D7dCOd2XVF0mxDEsGwKmZ42PgdteRINITZpHar6yun9q8fL05x6lso/XWZwrj44Tk\nCasNzCLxr6xu37qTSEpfbyMdk3PktYsNZftGYjQxny6SBI9Z50gNRArMkUjLuizeeozaPE6b\n7Z0Ilb/FvGp3YluWMdjnXLXrIdI91ohairTzpSbZMZL45kZ0VqXsLAGfjsw50iSjIw/iNPdD\nuVRTS5F4z3Z2iHBStVxRpDt+1MV+AZyzPnA0TqfbYJ8jMfTqNEKePu5QRuS2mRNzlhzaCcM2\nbnd9gCNeXySWVTvlv1CJ3V+xnDyO5USuRxApC9uEnGnN8Y45KFI4UFZ0vki8S6t+W+47/BY7\n2J+RIZJ0YiJNXY6iRiT+tOfln82vPQ5UiW2pXLWr3PVo0mdh5PHXB+4j0tYa6bOWvtSItDMS\nqUha+tDOLoJ56wMyRVLTwS9o337WJWANRKJU9Ui8lyimAUSagk3qRkO7wN3fEIlSObTjaEKD\nVgFtP33mvyJEUtvoMUci1M6ROC9RgDTlQzv+70xTKnDakL2O1pf6xQZ8r10vqnokpoGXN7SD\nODFkrNpBpBQSriPp24NgUgRcR5KPBJHOvmdVPBBJPhBpAEoL5vAlimDSGNqlkDFHWqr+aHw6\nOok3Fx29lf8sIFImdcvfzF9+wvrFdn0XzjNTO5YpGSKBFFKvIx2MtFf9Z6Z2MFPFQzv+SxRg\nhyNzJK60IVLW7jX7sA2/Jwzt0ogQifPD/xDJ2aXtYgOumhtkiBSKtfqm2EBc7ZA6R2ogUuDN\ns7/8SRAHVu340g5VSH3TG3TVLhFCqEg3+WLPvBqu6pG4J7KByJR+42Aaw5A6cQidI93jO9sL\nxhyZEbZbtaOP9NsbbnSV1h514ORRVQbs3yK0FekOPVLuCUmGSObMpvVf73ToO985E1NfoUM+\nsQjSQ7sbTJKaisT+MQodm861mpMjn/Ecsr5KMk2OfNrUyoE50lF4RBqy+hZaihQ5bxZjRTIP\nJCU6yBuyZyrL9BpasEj1c6Qhq0/TcI6k65utRzIVQkUiIzumiXNfSjPt9smBqCpSP05CJJU7\nRxqy+iwNV+2mbE+z0qbLC5MzvnG+DWawmqjMNNcciam0EtGo3Hskh6y+UkSIRM5s9rys/ICD\n1URq4JNqfsod2S5Rlafe/l677ASGrL5S6hYbskTarUrlhPT39UMOVxHxTO8fjvv5rBMPPT60\nW/uj3GHPcNVXSJVIZNSVEXM0HDFzN7Lxln3iPdL+GXrVyB37nkJUJKXPf1kmjVd9pdSJVBZx\nbMfNWPFSxHXZFcn/EouqOVLjoZ1aJkmXvyCbiwSRrnmrybki5Y2+s+JJJHDFequkWKTcD42V\niEQWGy5E/RxJ6RM+CV+euKrc1Y9HE5kjXa7e6qhdbNjfNX+OJH1Vp/oDHdH99mL0WmidSKwr\nq1PwOhJEMtSIlDniyF61E94j9Z/BhX7jpjgKdpG27+n6bW7TALo2FCk7bdFjbeeacKckyaO/\nWRJJL5Gan2lGWIySIJLkT1qqqUND2abpnliqEufpKRJDOz2SaD4ylz70n2k3RypI244Qcmq/\np3SK/Mvf6WAGN0PdE9tQxhwJIj2pEqmwC3FDblf99Jfoq1WldKa69g9LYmXjzgMZ/Ka4MZ5E\nYoYLkSh1IvGmbSrErPkmkupbqktuig69KIPf3wF3NncMlB5t7iWKnKj208Ac6YkMkabJdEZ7\nozuuYWXm4ZTX4X4Gg70OzZo/mKxcbKjcMxDNjHeLEFEVq3a1cyTesx09ey5nuMRYiqeB0Gny\nTsjSwzSTPUKo30nt7522Ko6WfUFoK9KaTfFNvA9HVu240nbPbXtjBY5+vmbqkx+58SBTnUDe\ntje/l2aiftdgPNs3cGeDgwyRJlMxZh0jOcv1NgLvpV9T5B8zBX1PmECXK1MkpnHJRWgmUsaE\n1+uRpnVgp5v4Xh0FdAsZSF6zCrKLRNw5OvjcHoTEOZK+jQkiLbTrkfZDBUQiU4Rgt6T8XATO\n3KFGqPSDMenoYlNwvU2ndexEvdm5Ki6e3iIukjHpcBqXoG6xgSdqOrSjIpEL+4kep1gk5929\n8WOI3FGbnSQxcWJbTSUNkQhVPVLm6Dj3fUVPbimRXBW2AQLz9JhIgZAu31t2DodGzDv9kikS\n5kiUqh6JOe2llesqWZe/d0UKz5G2a3EmWMas4eA6wTabG62rSrFqH95LFFNkjgSRVkSIpM1Z\nW6C91yw4V6A94zaTgam6IlaqQE/DYk8wm35mUsPJRJOsKHmuysoRCTJNtXMk5rOdjo2KEqwf\ntyEqtXEqKNJEuxr2CUwA1yF/bhlOPOlYXRY4iMfjLMrCpKo5Urray9PWMyRXpHAm3GZJ9NHd\nmDc9Wbsa0vtNHUyitwxmiZQcd0oUybu4wTGCHZoDIh2uLNu43U/gbCwN9n9kAKX1Wf9fQzoK\nVYl0tD2kRXJiH0Ck+L12fnp5p9lr2VYpEkuXZMVRZCYzbYp4lcPTyVSg/c4dZfYlE556kY4f\nox8Dfe4NU51cBqKpSZqBGpGSx+KEupBJgkSKNW/T3yhnSS4i0nbVwGuxairw6LBJ0VW7UG8V\nS6umR+JftYsksJ0jZRUcR+m2oqbYakTimiSRXsJZbdgG0/3R5Juk7Pvf3myI5ly5zzIHdk4m\nudnEzrtqx0UiT9FVu9FFUjUqVYlUl1Q87fTij1Nh9CrRmgW6dM057u4s0m7YU4gP7Win973d\nKWdkJ1MkfeIu3is3JPtBZ4mkFSIqmXfMbaLmjlf2/B0/W8Ry5Y84EylVzZHYh3bx60ibC3A5\n6eaWbvc1Cf97bnP3yg7pzU5Y50iRb+Ra+6CQR5thXIPJK1OvGzPJzpd2rsXUzJG4zgPxdwyP\niviuKKy8HXaOooFmA4ukdfHSW+XRPa0ZRywXVr0syBwqZE4XMj7LWJ6wqtw1L2my2PCoi+8W\n5zGbfrJk+E1StvzydyqKfnIKkFGkTYS2D9IiLWMIsyI3tkj0WBX5l4qlOOGMVrZbk/E5kvXo\nEWhzXuMiHW+jVHWjK9qnIPbyfTLTNtMg85QMwNe/9f4eLxODiuQ08RNF2q/SHJHscoNIkWrO\n+Il9Im/ViMQFFWmZJ+knxiLqkOlz7d6N50gMBHPl1r8ekbPOkbImSSq4mZc0Hdg1FClnzLt/\nssjMlz9rjQUJvVchkm7u2XtGY7QbeoChXMh0SA/v3H7MzaA8j8K58upfRYJ54UsT3i+RqEi2\nBv579EPhv+d7z7/vyPtcf8E8KPJ/Io+b8Llprn/BeFTwvXKRdLM+fvohSmwUWiWyy1nkyxyq\n0pJk2WZYupO7Vlkv65EiQ7t1evTds4Rt89tNNX/Ib0NG93l2vpHP3RSLRB6PFlxcJD0hsoO8\ndeQXWiPPTUqYSSr6NBi8WT7SKeyKtHo02W+JZcxfMlN5CRWLlPzA2nLZMuxYLk1F8i1yh3q6\nJ9rej5dZbyUl3wUn37u5q8i48v6P50Ml+8OdOdJSU/ML3zp4+2Iuqs5tlvZEiXd2phnG8pSV\noY1CTUQiXZGe2elHXeXrEepn2SkJEsnhRJGy49m+YepqDURa4ME0MzOVsN+5dyykit7ficMd\n1QXbloqeuyWIFOqMlFmzcyZH5M+cGuIH56V0G5HcQfEhUkO7ta7WUB1F0k1gdxC2F4fXeLZb\nW5NSd3xlZr61SN68SHtkv86B9kDrJn3cS0qqR/u5O9AjHSUlkqfrtxkqZA+5k+xNViKm2EzE\n3lqfrI+Rwo8O7yIUi6T7Boa6oiJ5Fintz/YuvK1IOdnhqNl2se7Ec+IpIDm0oyPwZ8Of/MFD\nEWUdSjzDSTeU8yzReJR+N/M4ykXSA6ra2t0OO+wowRWJhKa9rpeJyHdJ9qBXP1eehi67dklv\n62peGSYVm5n4QXEm9zgV+ecH83JlT8Ux7eJ9WzB4dnazg+bGaGIOsXY69kCpSXawx9dBFtMt\n3eIkTANgGzVMyaHdpO87oXcU531P1/GvQHNGLNqO+GDN3TFRiWUnBLki0UGde2pQdtVO8TWZ\ncsI10yyh0vAFp9OspGOfR/K+lfD5Rz4ktpfAYZFox5LsiiNaJHIZ2yMUfaFIXks/RkQkO5zT\nqcb6WFMGrVpwmvBYoVlCpeG5Rdq8Zc91+mK5ra/5ppSMAjnuER24TLtehBSIN57gHnYo5L+a\nR7ceyVTO2veaGZLvDB3YnYJbznUjvZxzQJVIPAPP9P6kT9JDOaXfWCc+eyIdbFZrknSWlPCi\nOLHAHubMrrYvZ8ZZmIn9GE3Mfnc02Q7POem5bdft1M/AKeeqlmtb4E6g0kj5RfJ/1sWGcSay\n5nH+t7OIUPPJWjd7pG30wT9nkJczI2AfPwVEmujITktDBpK0deyuHnYe8FHxS/chFRE7CZbm\npJ9INrAe/lup1JRyaf5Q4JFTtCot8OPYQ6wVadJNmjNLy/+b+ZFZ17YVshVpZwzebMqSTrAo\nWXIuUDSSQKjCnPB4VB+BaW9PYqvb36TMjqfSidUhdUSkdYtJp9DQTnecujEo3RUGeqR0L8nU\nkkogc4TcPZbd7C7B3csP4uC1viNJ2yy4+4ZkOizSbmeenb2SNNfJhtP6akQ6nBMvRtoLrW3K\nri7oQV7ghE22o+Ohvier8mTtMbCKxEbR0G4XT6ZvcsashS4+TWVnsCP6OhN3HWF+0uQZ49nO\nXWeYdF+jT9dK0Z7HOQv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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ lstat)\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-13.925  -2.822  -0.664   1.079  82.862 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept) -3.33054    0.69376  -4.801 2.09e-06 ***\n",
      "lstat        0.54880    0.04776  11.491  < 2e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.664 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.2076,\tAdjusted R-squared:  0.206 \n",
      "F-statistic:   132 on 1 and 504 DF,  p-value: < 2.2e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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d8qlE6p3Ed7WSrvd19k1KIGiCSDBiIp7+/t5DL6UkYtanDOXzbOs99xQyIO8i1g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\nICXtF+FopNbbUbUfJlI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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ medv)\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-9.071 -4.022 -2.343  1.298 80.957 \n",
      "\n",
      "Coefficients:\n",
      "            Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept) 11.79654    0.93419   12.63   <2e-16 ***\n",
      "medv        -0.36316    0.03839   -9.46   <2e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.934 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.1508,\tAdjusted R-squared:  0.1491 \n",
      "F-statistic: 89.49 on 1 and 504 DF,  p-value: < 2.2e-16\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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LxyaS0k2aMMOc6MZRpOE1J1G9+oj1bG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\nQ9kZeWqrEXCxA2KSvW7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      "text/plain": [
       "Plot with title \"\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lf1=lm(crim~zn) #Significant\n",
    "lf2=lm(crim~indus)#Significant\n",
    "lf3=lm(crim~chas)#insignificant\n",
    "lf4=lm(crim~nox)#Significant\n",
    "lf5=lm(crim~rm)#Significant\n",
    "lf6=lm(crim~age)#Significant\n",
    "lf7=lm(crim~dis)#Significant\n",
    "lf8=lm(crim~rad)#Significant\n",
    "lf9=lm(crim~tax)#Significant\n",
    "lf10=lm(crim~ptratio)#Significant\n",
    "lf11=lm(crim~black)#Significant\n",
    "lf12=lm(crim~lstat)#Significant\n",
    "lf13=lm(crim~medv)#Significant\n",
    "models=list(lf1,lf2,lf3,lf4,lf5,lf6,lf7,lf8,lf9,lf10,lf11,lf12,lf13)\n",
    "pred=list(zn,indus,chas,nox,rm,age,dis,rad,tax,ptratio,black,lstat,medv)\n",
    "\n",
    "for (model in models){\n",
    "    summary(model)\n",
    "    par(mfrow=c(2,2))\n",
    "    plot(model)\n",
    "    print(summary(model))\n",
    "}\n",
    "#All models except chas have very small p-values and we can reject the null hypothesis which mwans there is some kind of relation \n",
    "#between the predictor and the response."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = crim ~ ., data = Boston)\n",
       "\n",
       "Residuals:\n",
       "   Min     1Q Median     3Q    Max \n",
       "-9.924 -2.120 -0.353  1.019 75.051 \n",
       "\n",
       "Coefficients:\n",
       "              Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  17.033228   7.234903   2.354 0.018949 *  \n",
       "zn            0.044855   0.018734   2.394 0.017025 *  \n",
       "indus        -0.063855   0.083407  -0.766 0.444294    \n",
       "chasY        -0.749134   1.180147  -0.635 0.525867    \n",
       "nox         -10.313535   5.275536  -1.955 0.051152 .  \n",
       "rm            0.430131   0.612830   0.702 0.483089    \n",
       "age           0.001452   0.017925   0.081 0.935488    \n",
       "dis          -0.987176   0.281817  -3.503 0.000502 ***\n",
       "rad           0.588209   0.088049   6.680 6.46e-11 ***\n",
       "tax          -0.003780   0.005156  -0.733 0.463793    \n",
       "ptratio      -0.271081   0.186450  -1.454 0.146611    \n",
       "black        -0.007538   0.003673  -2.052 0.040702 *  \n",
       "lstat         0.126211   0.075725   1.667 0.096208 .  \n",
       "medv         -0.198887   0.060516  -3.287 0.001087 ** \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 6.439 on 492 degrees of freedom\n",
       "Multiple R-squared:  0.454,\tAdjusted R-squared:  0.4396 \n",
       "F-statistic: 31.47 on 13 and 492 DF,  p-value: < 2.2e-16\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mlf=lm(crim~.,data=Boston)\n",
    "summary(mlf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can reject the null hypothesis for: zn, dis, rad, black and medv."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAA0gAAANICAMAAADKOT/pAAAAM1BMVEUAAABNTU1oaGh8fHyM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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sc=c(lf1$coefficients[2],lf2$coefficients[2],lf3$coefficients[2],lf4$coefficients[2],lf5$coefficients[2],lf6$coefficients[2],lf7$coefficients[2],lf8$coefficients[2],lf9$coefficients[2],lf10$coefficients[2],lf11$coefficients[2],lf12$coefficients[2],lf13$coefficients[2])\n",
    "mc=c(mlf$coefficients[2:14])\n",
    "plot(sc,mc,col='darkgoldenrod1',pch=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We notice that all variables apart from nox have approximately the same coefficient value for both single and multiple linear regression fits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(zn, 3))\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-4.821 -4.614 -1.294  0.473 84.130 \n",
      "\n",
      "Coefficients:\n",
      "             Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)    3.6135     0.3722   9.709  < 2e-16 ***\n",
      "poly(zn, 3)1 -38.7498     8.3722  -4.628  4.7e-06 ***\n",
      "poly(zn, 3)2  23.9398     8.3722   2.859  0.00442 ** \n",
      "poly(zn, 3)3 -10.0719     8.3722  -1.203  0.22954    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 8.372 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.05824,\tAdjusted R-squared:  0.05261 \n",
      "F-statistic: 10.35 on 3 and 502 DF,  p-value: 1.281e-06\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(indus, 3))\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-8.278 -2.514  0.054  0.764 79.713 \n",
      "\n",
      "Coefficients:\n",
      "                Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)        3.614      0.330  10.950  < 2e-16 ***\n",
      "poly(indus, 3)1   78.591      7.423  10.587  < 2e-16 ***\n",
      "poly(indus, 3)2  -24.395      7.423  -3.286  0.00109 ** \n",
      "poly(indus, 3)3  -54.130      7.423  -7.292  1.2e-12 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.423 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.2597,\tAdjusted R-squared:  0.2552 \n",
      "F-statistic: 58.69 on 3 and 502 DF,  p-value: < 2.2e-16\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(chas, 1))\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-3.738 -3.661 -3.435  0.018 85.232 \n",
      "\n",
      "Coefficients:\n",
      "              Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)     3.6135     0.3822   9.455   <2e-16 ***\n",
      "poly(chas, 1) -10.8036     8.5966  -1.257    0.209    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 8.597 on 504 degrees of freedom\n",
      "Multiple R-squared:  0.003124,\tAdjusted R-squared:  0.001146 \n",
      "F-statistic: 1.579 on 1 and 504 DF,  p-value: 0.2094\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(nox, 3))\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-9.110 -2.068 -0.255  0.739 78.302 \n",
      "\n",
      "Coefficients:\n",
      "              Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)     3.6135     0.3216  11.237  < 2e-16 ***\n",
      "poly(nox, 3)1  81.3720     7.2336  11.249  < 2e-16 ***\n",
      "poly(nox, 3)2 -28.8286     7.2336  -3.985 7.74e-05 ***\n",
      "poly(nox, 3)3 -60.3619     7.2336  -8.345 6.96e-16 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.234 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.297,\tAdjusted R-squared:  0.2928 \n",
      "F-statistic: 70.69 on 3 and 502 DF,  p-value: < 2.2e-16\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(rm, 3))\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-18.485  -3.468  -2.221  -0.015  87.219 \n",
      "\n",
      "Coefficients:\n",
      "             Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)    3.6135     0.3703   9.758  < 2e-16 ***\n",
      "poly(rm, 3)1 -42.3794     8.3297  -5.088 5.13e-07 ***\n",
      "poly(rm, 3)2  26.5768     8.3297   3.191  0.00151 ** \n",
      "poly(rm, 3)3  -5.5103     8.3297  -0.662  0.50858    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 8.33 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.06779,\tAdjusted R-squared:  0.06222 \n",
      "F-statistic: 12.17 on 3 and 502 DF,  p-value: 1.067e-07\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(age, 3))\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-9.762 -2.673 -0.516  0.019 82.842 \n",
      "\n",
      "Coefficients:\n",
      "              Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)     3.6135     0.3485  10.368  < 2e-16 ***\n",
      "poly(age, 3)1  68.1820     7.8397   8.697  < 2e-16 ***\n",
      "poly(age, 3)2  37.4845     7.8397   4.781 2.29e-06 ***\n",
      "poly(age, 3)3  21.3532     7.8397   2.724  0.00668 ** \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.84 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.1742,\tAdjusted R-squared:  0.1693 \n",
      "F-statistic: 35.31 on 3 and 502 DF,  p-value: < 2.2e-16\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(dis, 3))\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-10.757  -2.588   0.031   1.267  76.378 \n",
      "\n",
      "Coefficients:\n",
      "              Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)     3.6135     0.3259  11.087  < 2e-16 ***\n",
      "poly(dis, 3)1 -73.3886     7.3315 -10.010  < 2e-16 ***\n",
      "poly(dis, 3)2  56.3730     7.3315   7.689 7.87e-14 ***\n",
      "poly(dis, 3)3 -42.6219     7.3315  -5.814 1.09e-08 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.331 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.2778,\tAdjusted R-squared:  0.2735 \n",
      "F-statistic: 64.37 on 3 and 502 DF,  p-value: < 2.2e-16\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(rad, 3))\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-10.381  -0.412  -0.269   0.179  76.217 \n",
      "\n",
      "Coefficients:\n",
      "              Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)     3.6135     0.2971  12.164  < 2e-16 ***\n",
      "poly(rad, 3)1 120.9074     6.6824  18.093  < 2e-16 ***\n",
      "poly(rad, 3)2  17.4923     6.6824   2.618  0.00912 ** \n",
      "poly(rad, 3)3   4.6985     6.6824   0.703  0.48231    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 6.682 on 502 degrees of freedom\n",
      "Multiple R-squared:    0.4,\tAdjusted R-squared:  0.3965 \n",
      "F-statistic: 111.6 on 3 and 502 DF,  p-value: < 2.2e-16\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(tax, 3))\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-13.273  -1.389   0.046   0.536  76.950 \n",
      "\n",
      "Coefficients:\n",
      "              Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)     3.6135     0.3047  11.860  < 2e-16 ***\n",
      "poly(tax, 3)1 112.6458     6.8537  16.436  < 2e-16 ***\n",
      "poly(tax, 3)2  32.0873     6.8537   4.682 3.67e-06 ***\n",
      "poly(tax, 3)3  -7.9968     6.8537  -1.167    0.244    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 6.854 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.3689,\tAdjusted R-squared:  0.3651 \n",
      "F-statistic:  97.8 on 3 and 502 DF,  p-value: < 2.2e-16\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(ptratio, 3))\n",
      "\n",
      "Residuals:\n",
      "   Min     1Q Median     3Q    Max \n",
      "-6.833 -4.146 -1.655  1.408 82.697 \n",
      "\n",
      "Coefficients:\n",
      "                  Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)          3.614      0.361  10.008  < 2e-16 ***\n",
      "poly(ptratio, 3)1   56.045      8.122   6.901 1.57e-11 ***\n",
      "poly(ptratio, 3)2   24.775      8.122   3.050  0.00241 ** \n",
      "poly(ptratio, 3)3  -22.280      8.122  -2.743  0.00630 ** \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 8.122 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.1138,\tAdjusted R-squared:  0.1085 \n",
      "F-statistic: 21.48 on 3 and 502 DF,  p-value: 4.171e-13\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(black, 3))\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-13.096  -2.343  -2.128  -1.439  86.790 \n",
      "\n",
      "Coefficients:\n",
      "                Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)       3.6135     0.3536  10.218   <2e-16 ***\n",
      "poly(black, 3)1 -74.4312     7.9546  -9.357   <2e-16 ***\n",
      "poly(black, 3)2   5.9264     7.9546   0.745    0.457    \n",
      "poly(black, 3)3  -4.8346     7.9546  -0.608    0.544    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.955 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.1498,\tAdjusted R-squared:  0.1448 \n",
      "F-statistic: 29.49 on 3 and 502 DF,  p-value: < 2.2e-16\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(lstat, 3))\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-15.234  -2.151  -0.486   0.066  83.353 \n",
      "\n",
      "Coefficients:\n",
      "                Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)       3.6135     0.3392  10.654   <2e-16 ***\n",
      "poly(lstat, 3)1  88.0697     7.6294  11.543   <2e-16 ***\n",
      "poly(lstat, 3)2  15.8882     7.6294   2.082   0.0378 *  \n",
      "poly(lstat, 3)3 -11.5740     7.6294  -1.517   0.1299    \n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 7.629 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.2179,\tAdjusted R-squared:  0.2133 \n",
      "F-statistic: 46.63 on 3 and 502 DF,  p-value: < 2.2e-16\n",
      "\n",
      "\n",
      "Call:\n",
      "lm(formula = crim ~ poly(medv, 3))\n",
      "\n",
      "Residuals:\n",
      "    Min      1Q  Median      3Q     Max \n",
      "-24.427  -1.976  -0.437   0.439  73.655 \n",
      "\n",
      "Coefficients:\n",
      "               Estimate Std. Error t value Pr(>|t|)    \n",
      "(Intercept)       3.614      0.292  12.374  < 2e-16 ***\n",
      "poly(medv, 3)1  -75.058      6.569 -11.426  < 2e-16 ***\n",
      "poly(medv, 3)2   88.086      6.569  13.409  < 2e-16 ***\n",
      "poly(medv, 3)3  -48.033      6.569  -7.312 1.05e-12 ***\n",
      "---\n",
      "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
      "\n",
      "Residual standard error: 6.569 on 502 degrees of freedom\n",
      "Multiple R-squared:  0.4202,\tAdjusted R-squared:  0.4167 \n",
      "F-statistic: 121.3 on 3 and 502 DF,  p-value: < 2.2e-16\n",
      "\n"
     ]
    }
   ],
   "source": [
    "cf1=lm(crim~poly(zn,3)) #Significant till the quadratic fit but non significant after the third power term.\n",
    "cf2=lm(crim~poly(indus,3))#Significant till the last power term.\n",
    "cf4=lm(crim~poly(nox,3))#Significant till the last power term.\n",
    "cf5=lm(crim~poly(rm,3))#Significant till the quadratic fit but non significant after the third power term.\n",
    "cf6=lm(crim~poly(age,3))#Significant till the last power term.\n",
    "cf7=lm(crim~poly(dis,3))#Significant till the last power term.\n",
    "cf8=lm(crim~poly(rad,3))#Significant till the quadratic fit but non significant after the third power term.\n",
    "cf9=lm(crim~poly(tax,3))#Significant till the quadratic fit but non significant after the third power term.\n",
    "cf10=lm(crim~poly(ptratio,3))#Significant till the last power term.\n",
    "cf11=lm(crim~poly(black,3))#Non-Significant starting at the quadratic fit.\n",
    "cf12=lm(crim~poly(lstat,3))#Significant starting at the quadratic fit.\n",
    "cf13=lm(crim~poly(medv,3))#Significant till the last power term.\n",
    "models=list(cf1,cf2,cf3,cf4,cf5,cf6,cf7,cf8,cf9,cf10,cf11,cf12,cf13)\n",
    "pred=list(zn,indus,chas,nox,rm,age,dis,rad,tax,ptratio,black,lstat,medv)\n",
    "for (model in models){\n",
    "    print(summary(model))\n",
    "}"
   ]
  }
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