4-Linear-models-with-solutions.ipynb

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    "# Statistical foundations of Machine Learning\n",
    "\n",
    "## INFO-F-422 TP: Linear models\n",
    "\n",
    "Yann-Aël Le Borgne, Fabrizio Carcillo and Gianluca Bontempi\n",
    "\n",
    "April 18, 2017\n"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "\n",
    "## Repetition\n",
    "\n",
    "### Estimation using the mean square error\n",
    "\n",
    "Assume to have $N$ observation pairs $(x_i,y_i)$ generated by the following stochastic process\n",
    "\n",
    "\\begin{equation*}\n",
    " y_i=\\beta_0+\\beta_1 x_i +w_i,\n",
    "\\end{equation*}\n",
    "\n",
    "where the $w_i$ are iid realisations of a random variable $\\mathbf{w}$ with mean zero and constant variance $\\sigma^2_{\\mathbf{w}}$.\n",
    "\n",
    "The $x_i$ can be seen as *fixed*, the only random component in the sampleset $D_N$ is therefore contained in the $y_i$ (which are random due to the $w_i$).\n",
    "\n",
    "The coefficients $\\beta_0$ and $\\beta_1$ can be estimated using the least squares method. This method consists of taking those estimators $\\hat{\\beta_0}$ and $\\hat{\\beta_1}$ which minimize\n",
    "\n",
    "\\begin{equation}\n",
    " R_{emp}=\\sum_{i=1}^N (y_i-\\hat{y_i})^2\n",
    "\\end{equation}\n",
    "\n",
    "where \n",
    "\n",
    "\\begin{equation}\n",
    " \\hat{y_i}=\\hat{\\beta_0}+\\hat{\\beta_1} x_i.\n",
    "\\end{equation}\n",
    "\n",
    "This is equivalent to \n",
    "\n",
    "\\begin{equation}\n",
    " \\{\\hat{\\beta_0},\\hat{\\beta_1}\\}=\\arg\\min_{b_0,b_1}\\sum_{i=1}^N (y_i-b_0-b_1x_i)^2.\n",
    "\\end{equation}\n",
    "\n",
    "The solution is given by *(Eq. 1)*\n",
    "\n",
    "\\begin{equation}\n",
    " \\hat{\\beta_1}=\\frac{S_{xy}}{S_{xx}},\\quad \\hat{\\beta_0}=\\bar{y}-\\hat{\\beta_1}\\bar{x},  \n",
    "\\end{equation}\n",
    "\n",
    "where *(Eq. 2)*\n",
    "\n",
    "\\begin{equation}\n",
    " \\bar{x}=\\frac{\\sum_{i=1}^Nx_i}{N},\\quad\\bar{y}=\\frac{\\sum_{i=1}^Ny_i}{N},\\quad S_{xy}=\\sum_{i=1}^N (x_i-\\bar{x})y_i,\\quad S_{xx}=\\sum_{i=1}^N(x_i-\\bar{x})^2.\n",
    "\\end{equation}\n",
    "\n",
    "### Properties of the estimator\n",
    "\n",
    "* $E_{D_N}[\\hat{\\beta_1}]=\\beta_1$\n",
    "* $Var[\\hat{\\beta_1}]=\\frac{\\sigma^2}{S_{xx}}$\n",
    "* $E[\\hat{\\beta_0}]=\\beta_0$\n",
    "* $Var[\\hat{\\beta_0}]=\\sigma^2\\left( \\frac{1}{N}+\\frac{\\bar{x}^2}{S_{xx}}\\right)$\n",
    "* $\\hat{\\sigma}^2_{\\mathbf{w}}=\\frac{\\sum_{i=1}^N(y_i-\\hat{y_i})^2}{N-2}$ is a non-biased estimator of $\\sigma^2_{\\mathbf{w}}$.\n",
    "\n",
    "\n",
    "### Partitioning the variability\n",
    "\n",
    "The variability of the response $y_i$ can be expressed as follows\n",
    "\n",
    "\\begin{equation}\n",
    " \\sum_{i=1}^N(y_i-\\bar{y})^2=\\sum_{i=1}^N(\\hat{y_i}-\\bar{y})^2+\\sum_{i=1}^N(y_i-\\hat{y_i})^2,\n",
    "\\end{equation}\n",
    "\n",
    "that is\n",
    "\n",
    "\\begin{equation}\n",
    " SS_{tot}=SS_{mod}+SS_{res}.\n",
    "\\end{equation}\n",
    "\n",
    "### The F-test\n",
    "\n",
    "Goal: test if the variable $y$ is really influenced by the variable $x$. This can be formulated as a hypothesis test $\\beta_1=0$. If the test is rejected, it can be deduced that $x$ influences $y$ significantly.\n",
    "\n",
    "It can be shown that given a normally distributed $\\mathbf{w}$: *(Eq. 3)*\n",
    "\n",
    "\\begin{equation}\n",
    " \\frac{SS_{mod}}{SS_{res}/(N-2)} \\sim F_{1,N-2}\n",
    "\\end{equation}\n",
    "\n",
    "if the hypothesis $\\beta_1=0$ is true.\n",
    "\n",
    "### The t-test\n",
    "\n",
    "It can be shown that given a normally distributed $\\mathbf{w}$:\n",
    "\n",
    "\\begin{equation}\n",
    " \\hat{\\beta_1}\\sim \\mathcal{N}(\\beta_1,\\sigma^2 / S_{xx})\n",
    "\\end{equation}\n",
    "\n",
    "and\n",
    "\n",
    "\\begin{equation}\n",
    " \\frac{\\hat{\\beta_1}-\\beta_1}{\\hat{\\sigma}}\\sqrt{S_{xx}} \\sim \\mathcal{T}_{N-2}.\n",
    "\\end{equation}\n",
    "\n",
    "This can be used for testing the following hypothesis: $\\hat{\\beta_1}=\\beta_1$.\n",
    "\n",
    "### Confidence intervals\n",
    "\n",
    "With a probability $1-\\alpha$, the true parameter $\\beta_1$ lies in the interval *(Eq. 4)*\n",
    "\n",
    "\\begin{equation}\n",
    " \\hat{\\beta_1}\\pm t_{\\alpha/2,N-2}\\cdot \\sqrt{\\frac{\\hat{\\sigma}^2}{S_{xx}}}.\n",
    "\\end{equation}\n",
    "\n",
    "### Variance of the response\n",
    "\n",
    "Let\n",
    "\n",
    "\\begin{equation}\n",
    " \\hat{\\mathbf{y}}(x)=\\hat{\\beta_0}+\\hat{\\beta_1} x.\n",
    "\\end{equation}\n",
    "\n",
    "We can show that for all $x$:\n",
    "\n",
    "\\begin{equation}\n",
    " E_{D_N}[ \\hat{\\mathbf{y}}(x)]=E_{[y]}[ {\\mathbf{y}}(x)]\n",
    "\\end{equation}\n",
    "\n",
    "and\n",
    "\n",
    "\\begin{equation}\n",
    " Var[ \\hat{\\mathbf{y}}(x)]=\\sigma^2\\left[\\frac{1}{N}+\\frac{(x-\\bar{x})^2}{S_{xx}}\\right].\n",
    "\\end{equation}\n",
    "\n"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear regression exercises\n",
    "\n",
    "### Exercise 1\n",
    "\n",
    "Compare with the theoretical part of this course (slide 21 of the chapter [Regression Modelling](http://uv.ulb.ac.be/pluginfile.php/863619/mod_resource/content/1/linregr.pdf)). \n",
    "\n",
    "The goal of this exercise is to investigate the link between two variables originating from medical data by studying the *ventricular shortening velocity* in function of *blood glucose*. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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   "outputs": [],
   "source": [
    "library(ISwR)\n",
    "data(thuesen)\n",
    "\n",
    "I <-! is.na(thuesen[,\"short.velocity\"])\n",
    "Y<-thuesen[I,\"short.velocity\"]\n",
    "X<-thuesen[I,\"blood.glucose\"]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*(a)*\n",
    "\n",
    "*  Apply the mean square method \"by hand\" using equations (Eq. 1) and (Eq. 2) to compute the coefficients $\\beta_0$ and $\\beta_1$ of a linear model for our data. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>24</li>\n",
       "\t<li>2</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 24\n",
       "\\item 2\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 24\n",
       "2. 2\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 24  2"
      ]
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    }
   ],
   "source": [
    "dim(thuesen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "N<-length(Y)\n",
    "x.bar<-mean(X)\n",
    "y.bar<-mean(Y)\n",
    "S.xy<-sum((X-x.bar)*Y)\n",
    "S.xx<-sum((X-x.bar)^2)\n",
    "beta.hat.1<-S.xy/S.xx\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "beta.hat.0<-y.bar-beta.hat.1*x.bar\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"beta.hat.0 =  1.09781487777238\"\n",
      "[1] \"beta.hat.1 =  0.0219625222599968\"\n"
     ]
    }
   ],
   "source": [
    "print(paste(\"beta.hat.0 = \", beta.hat.0))\n",
    "print(paste(\"beta.hat.1 = \", beta.hat.1))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*  Test the hypothesis $\\beta_1=0$ using an F-test using equation *(Eq. 3)* and the F distribution function `pf` followed by a t-test using equation *(Eq. 4)* and the t distribution function `pt` \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "Y.hat<-beta.hat.0+beta.hat.1*X\n",
    "SS.mod <- sum((Y.hat-mean(Y))^2)\n",
    "SS.res <- sum((Y-Y.hat)^2)\n",
    "F.value<-SS.mod/(SS.res/(N-2))\n",
    "F.pr<-(1-pf(F.value,df1=1,df2=N-2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"F-test result: F.value=  4.41401843314627\"\n",
      "[1] \"Pr[F >= F.value]=  0.0478959109075709\"\n"
     ]
    }
   ],
   "source": [
    "print(paste(\"F-test result: F.value= \",\n",
    " F.value))\n",
    " print(paste(\"Pr[F >= F.value]= \", F.pr))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "var.hat.w<-sum((Y-Y.hat)^2)/(N-2)\n",
    "beta<-0\n",
    "t.value<-(beta.hat.1-beta)*sqrt(S.xx)/(sqrt(var.hat.w))\n",
    "t.pr<-(1-pt(t.value,df=N-2))*2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"t-test result: t.value=  2.10095655194158\"\n",
      "[1] \"Pr[|T| >= t.value]=  0.0478959109075709\"\n"
     ]
    }
   ],
   "source": [
    "print(paste(\"t-test result: t.value= \",t.value))\n",
    "print(paste(\"Pr[|T| >= t.value]= \", t.pr))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*  Compute the confidence interval for $\\beta_1$ using equation (Eq. 4) and the function `qt`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alpha<-0.05\n",
    "conf.interval.min<-beta.hat.1-qt(alpha/2,df=N-2,lower.tail=FALSE)*sqrt(var.hat.w/S.xx)\n",
    "conf.interval.max<-beta.hat.1+qt(alpha/2,df=N-2,lower.tail=FALSE)*sqrt(var.hat.w/S.xx)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Confidence interval for beta1=\"\n",
      "[1] \"( 0.000223107746726493 , 0.043701936773267 )\"\n"
     ]
    }
   ],
   "source": [
    "print(paste(\"Confidence interval for beta1=\"))\n",
    "print(paste(\"(\", conf.interval.min, \",\", conf.interval.max, \")\"))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "*  Use the function `lm`(Y$^{\\sim}$X) to obtain the same results automatically and compare these with the ones obtained earlier.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = Y ~ X)\n",
       "\n",
       "Residuals:\n",
       "     Min       1Q   Median       3Q      Max \n",
       "-0.40141 -0.14760 -0.02202  0.03001  0.43490 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  1.09781    0.11748   9.345 6.26e-09 ***\n",
       "X            0.02196    0.01045   2.101   0.0479 *  \n",
       "---\n",
       "Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
       "\n",
       "Residual standard error: 0.2167 on 21 degrees of freedom\n",
       "Multiple R-squared:  0.1737,\tAdjusted R-squared:  0.1343 \n",
       "F-statistic: 4.414 on 1 and 21 DF,  p-value: 0.0479\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "summary(lm(Y~X))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*  Visualize the data and the regression line\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"sigma.hat =  0.216695562262916\"\n"
     ]
    },
    {
     "data": {
      "image/png": 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Xpj8tTkuOR3ycOSXZJ7J49Obko0AgQIECBAgAABAgQIjI3AC9KTKnSOTp6UvCg5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\nECBAgACBJgv8f9Q/EpC52VGoAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Histogram of Y\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow=c(1,2))\n",
    "#thuesen\n",
    "\n",
    "hist(Y)\n",
    "plot(X,Y)\n",
    "sigma.hat = sqrt( sum( (Y-Y.hat)^2 ) / (N-2) )\n",
    "\n",
    "print(paste(\"sigma.hat = \", sigma.hat))\n",
    "x<-seq(min(X),max(X),by=.1)\n",
    "lines(x,beta.hat.0+beta.hat.1*x)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercise 2\n",
    "\n",
    "The goal of this exercise is to experimentally study the bias and the variance of $\\hat{\\beta_0}$, $\\hat{\\beta_1}$, $\\hat{\\sigma}$ and $\\hat{\\mathbf{y}}(x_i)$. See also the theoretical part of this course (slide 22 of the chapter [Regression Modelling](http://uv.ulb.ac.be/pluginfile.php/863619/mod_resource/content/1/linregr.pdf). \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rm(list=ls())\n",
    "X<-seq(-10,10,by=1) # the x_i are fixed\n",
    "beta0<--1 # y_i = -1 + x_i + Normal(0,5)\n",
    "beta1<-1\n",
    "sd.w<-5\n",
    "N<-length(X)\n",
    "R<-100#00 # number of iterations for the simulation\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "beta.hat.1<-numeric(R)\n",
    "beta.hat.0<-numeric(R)\n",
    "var.hat.w<-numeric(R)\n",
    "Y.hat<-array(NA,c(R,N))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*(a)*\n",
    "\n",
    "* Compute $\\hat{\\beta}_0$, $\\hat{\\beta}_1$ and $\\hat{\\sigma}$ and plot their distributions.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "\n",
    "x.bar<-mean(X)\n",
    "S.xx<-sum((X-x.bar)^2)\n",
    "for (r in 1:R){\n",
    "  Y<-beta0+beta1*X+rnorm(N,sd=sd.w)\n",
    "  y.bar<-mean(Y)\n",
    "  S.xy<-sum((X-x.bar)*Y)\n",
    "\n",
    "  beta.hat.1[r]<-S.xy/S.xx\n",
    "  beta.hat.0[r]<-y.bar-beta.hat.1[r]*x.bar\n",
    "\n",
    "  Y.hat[r,]<-beta.hat.0[r]+beta.hat.1[r]*X\n",
    "  var.hat.w[r]<-sum((Y-Y.hat[r,])^2)/(N-2)\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Theoretical var beta1= 0.0324675324675325 ; Observed = 0.0398213850963544\"\n",
      "[1] \"Theoretical var beta0= 1.19047619047619 ; Observed = 0.912236211955172\"\n"
     ]
    },
    {
     "data": {
      "image/png": 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DdOrpt8Lqn+5vtJlepDHrRzao896o2bk5P9kkcmxybvT+rY1Z8NK3WjMumvrUzS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\nIECAwPAC/x9xbT0z0GJK2AAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Distribution of var.hat.w: \n",
       " var w= 25\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# result for beta_1\n",
    "par(mfrow=c(1,3))\n",
    "var.beta.hat.1<-(sd.w^2)/S.xx\n",
    "print(paste(\"Theoretical var beta1=\", var.beta.hat.1,\"; Observed =\", var(beta.hat.1) ))\n",
    "hist(beta.hat.1, main=paste(\"Distribution of beta.hat.1: \\n beta1=\", beta1))\n",
    "\n",
    "# result for beta_0\n",
    "var.beta.hat.0<-(sd.w^2)*(1/N+(x.bar^2)/S.xx)\n",
    "print(paste(\"Theoretical var beta0=\", var.beta.hat.0, \"; Observed =\", var(beta.hat.0) ))\n",
    "hist(beta.hat.0,main=paste(\"Distribution of beta.hat.0: \\n beta0=\",beta0))\n",
    "\n",
    "# result for sigma_w\n",
    "hist(var.hat.w,main=paste(\"Distribution of var.hat.w: \\n var w=\", sd.w^2))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Illustrate the theorem $Var[y(x)]=\\sigma^2\\left(\\frac{1}{N}+\\frac{(x-\\bar{x})^2}{S_{xx}}\\right)$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Theoretical var predic= 4.43722943722944\"\n",
      "[1] \"Observed = 4.82130896235035\"\n",
      "[1] \"-----------------------------\"\n",
      "[1] \"Theoretical var predic= 3.82034632034632\"\n",
      "[1] \"Observed = 4.07200922144365\"\n",
      "[1] \"-----------------------------\"\n",
      "[1] \"Theoretical var predic= 3.26839826839827\"\n",
      "[1] \"Observed = 3.40235225072965\"\n",
      "[1] \"-----------------------------\"\n",
      "[1] \"Theoretical var predic= 2.78138528138528\"\n",
      "[1] \"Observed = 2.81233805020836\"\n",
      "[1] \"-----------------------------\"\n",
      "[1] \"Theoretical var predic= 2.35930735930736\"\n",
      "[1] \"Observed = 2.30196661987978\"\n",
      "[1] \"-----------------------------\"\n"
     ]
    }
   ],
   "source": [
    "for (i in 1:5){\n",
    "  var.y.hat<-var(Y.hat[,i])\n",
    "  th.var.y.hat<-sd.w^2*(1/N+((X[i]-x.bar)^2)/S.xx)\n",
    "  print(paste(\"Theoretical var predic=\",th.var.y.hat))\n",
    "  print(paste( \"Observed =\",var.y.hat ))\n",
    "  print(\"-----------------------------\")\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multiple regression exercise\n",
    "\n",
    "This example is taken from the theoretical part of this course (slide 31 of the chapter [Regression Modelling](http://uv.ulb.ac.be/pluginfile.php/863619/mod_resource/content/1/linregr.pdf)).\n",
    "\n",
    "Mutiple linear dependence occurs when the variable $x$ is a vector instead of a scalar. The goal of this exercise is to verify the theoretical results for the estimators $\\hat{\\mathbf{\\sigma}}^2$ and $\\hat{\\mathbf{\\beta} }$ obtained for the least squares method (no bias and analytical results concerning $Var[\\hat{\\mathbf{\\beta}}]$).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "rm(list=ls())\n",
    "library(MASS)\n",
    "\n",
    "# initial values for n, (sigma_w) and beta\n",
    "n<-3 # number of input variables\n",
    "p<-n+1\n",
    "beta<-seq(2,p+1) # beta =(2,3,...,n+2)\n",
    "sd.w<-5  \n",
    "\n",
    "# generating data D_N\n",
    "N<-100 # number of samples\n",
    "X<-array(runif(N*n,min=-20,max=20),c(N,n))\n",
    "X<-cbind(array(1,c(N,1)),X)\n",
    "\n",
    "\n",
    "R<-100#00 # number of iterations\n",
    "beta.hat<-array(0,c(p,R))\n",
    "var.hat.w<-numeric(R)\n",
    "Y.hat<-array(NA,c(R,N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*(a)*\n",
    "\n",
    "* Compute $\\hat{Y}$, $\\hat{\\beta}$ and $\\hat{\\sigma}$ following the equations in the course slides 34 and 41.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# computation beta, Y and sigma_w\n",
    "for (r in 1:R){\n",
    "  Y<-X%*%beta+rnorm(N,sd=sd.w)\n",
    " \n",
    "  beta.hat[,r]<-ginv(t(X)%*%X)%*%t(X)%*%Y\n",
    "\n",
    "  Y.hat[r,]<-X%*%beta.hat[,r]\n",
    "  e<-Y-Y.hat[r,]\n",
    "  var.hat.w[r]<-(t(e)%*%e)/(N-p)\n",
    "}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Plot the histograms for $\\hat{\\sigma}$ and for each $\\hat{\\beta}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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aKlx94Yn3b3VMSjkre3HpTiWCrvNKtlgVSJj/fDxVLsj8fR06SZpWhZ8/F6SrxT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\nAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Distribution of beta.hat. 3 : beta 3 = 5\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "par(mfrow=c(3,2))\n",
    "hist(var.hat.w,main=paste(\"Distribution of var.hat.w: var w=\", sd.w^2))\n",
    "for (i in 1:p){\n",
    "  hist(beta.hat[i,], main=paste(\"Distribution of beta.hat.\",i-1,\": beta\",i-1,\"=\", beta[i]))\n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBA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      "text/plain": [
       "Plot with title \"Histogram of prediction_bias\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Histograms of the prediction bias \n",
    "prediction_bias<-apply(Y.hat,2,mean)-X%*%beta\n",
    "hist(prediction_bias)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IY7tDpYt9a9szVfk/X0ujcn9djvf040AgQIECBAgAABAgQGJtD3AqmeVPf1pB7Q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\nYOkI/B+MVzAABNlBvwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Histogram of diff_var\""
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# comparison of analytic variance and that of the simulated prediction\n",
    "diff_var<-numeric(N)\n",
    "for (i in 1:N){\n",
    "  diff_var[i]=var(Y.hat[,i])-sd.w^2*(t(X[i,])%*%ginv(t(X)%*%X)%*%X[i,])\n",
    "}\n",
    "hist(diff_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.3.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}