QR-R.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "suppressMessages(library(pracma))\n",
    "suppressMessages(library(tidyverse))\n",
    "suppressMessages(library(ggplot2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "QR.regression <- function(y, X)\n",
    "{\n",
    "  nr <- length(y)\n",
    "  nc <- NCOL(X)\n",
    "  \n",
    "  for (j in seq_len(nc))\n",
    "  {\n",
    "    id <- seq.int(j, nr) \n",
    "    sigma <- sum(X[id,j]^2) \n",
    "    s <- sqrt(sigma) \n",
    "    diag_ej <- X[j,j] \n",
    "    gamma <- 1.0 / (sigma + abs(s * diag_ej)) \n",
    "    kappa <- if (diag_ej < 0) s else -s \n",
    "    X[j,j] <- X[j,j] - kappa\n",
    "    if (j < nc)\n",
    "      for (k in seq.int(j+1, nc))\n",
    "      {\n",
    "        yPrime <- sum(X[id,j] * X[id,k]) * gamma\n",
    "        X[id,k] <- X[id,k] - X[id,j] * yPrime\n",
    "      }\n",
    "    yPrime <- sum(X[id,j] * y[id]) * gamma\n",
    "    y[id] <- y[id] - X[id,j] * yPrime\n",
    "    X[j,j] <- kappa\n",
    "  } # end Householder\n",
    "  \n",
    "  # residual sum of squares\n",
    "  rss <- sum(y[seq.int(nc+1, nr)]^2)\n",
    "  \n",
    "  # Backsolve\n",
    "  beta <- rep(NA, nc)\n",
    "  for (j in seq.int(nc, 1))\n",
    "  {\n",
    "    beta[j] <- y[j]\n",
    "    if (j < nc)\n",
    "      for (i in seq.int(j+1, nc))\n",
    "        beta[j] <- beta[j] - X[j,i] * beta[i]\n",
    "      beta[j] <- beta[j] / X[j,j]\n",
    "  }\n",
    "  \n",
    "  # set zeros in the lower triangular side of X (which stores) \n",
    "  # not really necessary, this is just to return R for illustration\n",
    "  for (i in seq_len(ncol(X)))\n",
    "    X[seq.int(i+1, nr),i] <- 0\n",
    "    list(R=X[1:nc,1:nc], y=y, beta=beta, rss=rss)\n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>(Intercept)</dt>\n",
       "\t\t<dd>3.5</dd>\n",
       "\t<dt>X1</dt>\n",
       "\t\t<dd>1.4</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] 3.5\n",
       "\\item[X1] 1.4\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   3.5X1\n",
       ":   1.4\n",
       "\n"
      ],
      "text/plain": [
       "(Intercept)          X1 \n",
       "        3.5         1.4 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>3.5</li>\n",
       "\t<li>1.4</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 3.5\n",
       "\\item 1.4\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 3.5\n",
       "2. 1.4\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 3.5 1.4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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Q4lJAPoHOq9J24ZqQ6AEpIBdAb1/pPr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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# --------- 1 variable model -------------------------------#\n",
    "\n",
    "mydata <- read.csv(file=\"Ex1LS2.csv\", header=TRUE, sep=\",\")\n",
    "model <- lm( Y ~ X1 ,mydata)\n",
    "model$coefficients\n",
    "\n",
    "p <- ggplot(data = mydata, aes(x= X1, y= Y)) + geom_point() + geom_smooth(method = 'lm', se = FALSE)\n",
    "p\n",
    "\n",
    "Y <- mydata$Y\n",
    "X <- mydata$X1\n",
    "X <- as.matrix(cbind(1, X))\n",
    "\n",
    "res <- QR.regression(Y, X)\n",
    "\n",
    "res$beta\n",
    "\n",
    "library(pracma)\n",
    "\n",
    "R <- round(res$R,2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>(Intercept)</dt>\n",
       "\t\t<dd>2.79850746268657</dd>\n",
       "\t<dt>X1</dt>\n",
       "\t\t<dd>0.0671641791044776</dd>\n",
       "\t<dt>X2</dt>\n",
       "\t\t<dd>0.701492537313433</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] 2.79850746268657\n",
       "\\item[X1] 0.0671641791044776\n",
       "\\item[X2] 0.701492537313433\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   2.79850746268657X1\n",
       ":   0.0671641791044776X2\n",
       ":   0.701492537313433\n",
       "\n"
      ],
      "text/plain": [
       "(Intercept)          X1          X2 \n",
       " 2.79850746  0.06716418  0.70149254 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>2.79850746268657</li>\n",
       "\t<li>0.0671641791044773</li>\n",
       "\t<li>0.701492537313433</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 2.79850746268657\n",
       "\\item 0.0671641791044773\n",
       "\\item 0.701492537313433\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 2.79850746268657\n",
       "2. 0.0671641791044773\n",
       "3. 0.701492537313433\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 2.79850746 0.06716418 0.70149254"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<table>\n",
       "<thead><tr><th scope=col></th><th scope=col>X1</th><th scope=col>X2</th></tr></thead>\n",
       "<tbody>\n",
       "\t<tr><td>-2        </td><td>-5.000000 </td><td>-11.500000</td></tr>\n",
       "\t<tr><td> 0        </td><td>-2.236068 </td><td> -4.248529</td></tr>\n",
       "\t<tr><td> 0        </td><td> 0.000000 </td><td>  2.588436</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "\\begin{tabular}{lll}\n",
       "  & X1 & X2\\\\\n",
       "\\hline\n",
       "\t -2         & -5.000000  & -11.500000\\\\\n",
       "\t  0         & -2.236068  &  -4.248529\\\\\n",
       "\t  0         &  0.000000  &   2.588436\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "|  | X1 | X2 |\n",
       "|---|---|---|\n",
       "| -2         | -5.000000  | -11.500000 |\n",
       "|  0         | -2.236068  |  -4.248529 |\n",
       "|  0         |  0.000000  |   2.588436 |\n",
       "\n"
      ],
      "text/plain": [
       "        X1        X2        \n",
       "[1,] -2 -5.000000 -11.500000\n",
       "[2,]  0 -2.236068  -4.248529\n",
       "[3,]  0  0.000000   2.588436"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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hcqqsWSyJBmZqS75S5UVIslgSHN7Uh2y12oqBZL4kKa3JHslrtQUS2WhIU0uyPZ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\nZXh29VrSHOgAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "# ----------------- 2 variable model ---------------------- #\n",
    "\n",
    "mydata <- read.csv(file=\"Ex1LS2.csv\", header=TRUE, sep=\",\")\n",
    "\n",
    "model <- lm( Y ~ ., mydata)\n",
    "model$coefficients\n",
    "\n",
    "\n",
    "X <- mydata[1:2]\n",
    "\n",
    "p <- ggplot(data = mydata, aes(x= X2, y= Y)) + geom_point() + geom_smooth(method = 'lm', se = FALSE) \n",
    "p\n",
    "\n",
    "Y <- mydata$Y\n",
    "X <- mydata[1:2]\n",
    "X <- as.matrix(X)\n",
    "X <- as.matrix(cbind(1, X))\n",
    "\n",
    "res <- QR.regression(Y, X)\n",
    "res$beta\n",
    "res$R\n",
    "\n",
    "house <- householder(X)\n",
    "Q2 <- round(as.matrix(house$Q),5)\n",
    "R2 <- round(as.matrix(house$R),5)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>(Intercept)</dt>\n",
       "\t\t<dd>-32094.2919872874</dd>\n",
       "\t<dt>wheel.base</dt>\n",
       "\t\t<dd>230.893120047467</dd>\n",
       "\t<dt>engine.size</dt>\n",
       "\t\t<dd>109.395903116209</dd>\n",
       "\t<dt>horsepower</dt>\n",
       "\t\t<dd>65.8101106048046</dd>\n",
       "\t<dt>highway.mpg</dt>\n",
       "\t\t<dd>55.6085857299627</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[(Intercept)] -32094.2919872874\n",
       "\\item[wheel.base] 230.893120047467\n",
       "\\item[engine.size] 109.395903116209\n",
       "\\item[horsepower] 65.8101106048046\n",
       "\\item[highway.mpg] 55.6085857299627\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "(Intercept)\n",
       ":   -32094.2919872874wheel.base\n",
       ":   230.893120047467engine.size\n",
       ":   109.395903116209horsepower\n",
       ":   65.8101106048046highway.mpg\n",
       ":   55.6085857299627\n",
       "\n"
      ],
      "text/plain": [
       " (Intercept)   wheel.base  engine.size   horsepower  highway.mpg \n",
       "-32094.29199    230.89312    109.39590     65.81011     55.60859 "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>-32094.2919872873</li>\n",
       "\t<li>230.893120047467</li>\n",
       "\t<li>109.395903116209</li>\n",
       "\t<li>65.8101106048045</li>\n",
       "\t<li>55.6085857299625</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item -32094.2919872873\n",
       "\\item 230.893120047467\n",
       "\\item 109.395903116209\n",
       "\\item 65.8101106048045\n",
       "\\item 55.6085857299625\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. -32094.2919872873\n",
       "2. 230.893120047467\n",
       "3. 109.395903116209\n",
       "4. 65.8101106048045\n",
       "5. 55.6085857299625\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] -32094.29199    230.89312    109.39590     65.81011     55.60859"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Vpd/u46PdNE0cCbL1nd5/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\nAa/uKt+D8ZqbAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      },
      "text/plain": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ------------------ auto regression ---------------#\n",
    "\n",
    "Autos <- read.csv(file=\"Automobile Price Prediction.csv\")\n",
    "Autos <- select(Autos, wheel.base, engine.size, horsepower, highway.mpg, price )\n",
    "\n",
    "model <- lm( price ~ ., Autos)\n",
    "\n",
    "model$coefficients\n",
    "\n",
    "p <- ggplot(data = Autos, aes(x= horsepower, y= price)) + geom_point() + geom_smooth(method = 'lm', se = FALSE) \n",
    "p\n",
    "\n",
    "Y <- Autos$price\n",
    "X <- Autos[1:4]\n",
    "X <- as.matrix(X)\n",
    "X <- as.matrix(cbind(1, X))\n",
    "\n",
    "res <- QR.regression(Y, X)\n",
    "res$beta\n",
    "\n",
    "R <- res$R\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}