{ "cells": [ { "cell_type": "markdown", "id": "340111bb", "metadata": {}, "source": [ "# SR2 Preface" ] }, { "cell_type": "markdown", "id": "f6461b5e-249a-4eb0-adc6-4ca643d243cc", "metadata": {}, "source": [ "Checking our installation with an example R notebook based on the SR2 preface:" ] }, { "cell_type": "code", "execution_count": 1, "id": "b109c664", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 50 × 2
speeddist
<dbl><dbl>
4 2
4 10
7 4
7 22
8 16
9 10
10 18
10 26
10 34
11 17
11 28
12 14
12 20
12 24
12 28
13 26
13 34
13 34
13 46
14 26
14 36
14 60
14 80
15 20
15 26
15 54
16 32
16 40
17 32
17 40
17 50
18 42
18 56
18 76
18 84
19 36
19 46
19 68
20 32
20 48
20 52
20 56
20 64
22 66
23 54
24 70
24 92
24 93
24120
25 85
\n" ], "text/latex": [ "A data.frame: 50 × 2\n", "\\begin{tabular}{ll}\n", " speed & dist\\\\\n", " & \\\\\n", "\\hline\n", "\t 4 & 2\\\\\n", "\t 4 & 10\\\\\n", "\t 7 & 4\\\\\n", "\t 7 & 22\\\\\n", "\t 8 & 16\\\\\n", "\t 9 & 10\\\\\n", "\t 10 & 18\\\\\n", "\t 10 & 26\\\\\n", "\t 10 & 34\\\\\n", "\t 11 & 17\\\\\n", "\t 11 & 28\\\\\n", "\t 12 & 14\\\\\n", "\t 12 & 20\\\\\n", "\t 12 & 24\\\\\n", "\t 12 & 28\\\\\n", "\t 13 & 26\\\\\n", "\t 13 & 34\\\\\n", "\t 13 & 34\\\\\n", "\t 13 & 46\\\\\n", "\t 14 & 26\\\\\n", "\t 14 & 36\\\\\n", "\t 14 & 60\\\\\n", "\t 14 & 80\\\\\n", "\t 15 & 20\\\\\n", "\t 15 & 26\\\\\n", "\t 15 & 54\\\\\n", "\t 16 & 32\\\\\n", "\t 16 & 40\\\\\n", "\t 17 & 32\\\\\n", "\t 17 & 40\\\\\n", "\t 17 & 50\\\\\n", "\t 18 & 42\\\\\n", "\t 18 & 56\\\\\n", "\t 18 & 76\\\\\n", "\t 18 & 84\\\\\n", "\t 19 & 36\\\\\n", "\t 19 & 46\\\\\n", "\t 19 & 68\\\\\n", "\t 20 & 32\\\\\n", "\t 20 & 48\\\\\n", "\t 20 & 52\\\\\n", "\t 20 & 56\\\\\n", "\t 20 & 64\\\\\n", "\t 22 & 66\\\\\n", "\t 23 & 54\\\\\n", "\t 24 & 70\\\\\n", "\t 24 & 92\\\\\n", "\t 24 & 93\\\\\n", "\t 24 & 120\\\\\n", "\t 25 & 85\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 50 × 2\n", "\n", "| speed <dbl> | dist <dbl> |\n", "|---|---|\n", "| 4 | 2 |\n", "| 4 | 10 |\n", "| 7 | 4 |\n", "| 7 | 22 |\n", "| 8 | 16 |\n", "| 9 | 10 |\n", "| 10 | 18 |\n", "| 10 | 26 |\n", "| 10 | 34 |\n", "| 11 | 17 |\n", "| 11 | 28 |\n", "| 12 | 14 |\n", "| 12 | 20 |\n", "| 12 | 24 |\n", "| 12 | 28 |\n", "| 13 | 26 |\n", "| 13 | 34 |\n", "| 13 | 34 |\n", "| 13 | 46 |\n", "| 14 | 26 |\n", "| 14 | 36 |\n", "| 14 | 60 |\n", "| 14 | 80 |\n", "| 15 | 20 |\n", "| 15 | 26 |\n", "| 15 | 54 |\n", "| 16 | 32 |\n", "| 16 | 40 |\n", "| 17 | 32 |\n", "| 17 | 40 |\n", "| 17 | 50 |\n", "| 18 | 42 |\n", "| 18 | 56 |\n", "| 18 | 76 |\n", "| 18 | 84 |\n", "| 19 | 36 |\n", "| 19 | 46 |\n", "| 19 | 68 |\n", "| 20 | 32 |\n", "| 20 | 48 |\n", "| 20 | 52 |\n", "| 20 | 56 |\n", "| 20 | 64 |\n", "| 22 | 66 |\n", "| 23 | 54 |\n", "| 24 | 70 |\n", "| 24 | 92 |\n", "| 24 | 93 |\n", "| 24 | 120 |\n", "| 25 | 85 |\n", "\n" ], "text/plain": [ " speed dist\n", "1 4 2 \n", "2 4 10 \n", "3 7 4 \n", "4 7 22 \n", "5 8 16 \n", "6 9 10 \n", "7 10 18 \n", "8 10 26 \n", "9 10 34 \n", "10 11 17 \n", "11 11 28 \n", "12 12 14 \n", "13 12 20 \n", "14 12 24 \n", "15 12 28 \n", "16 13 26 \n", "17 13 34 \n", "18 13 34 \n", "19 13 46 \n", "20 14 26 \n", "21 14 36 \n", "22 14 60 \n", "23 14 80 \n", "24 15 20 \n", "25 15 26 \n", "26 15 54 \n", "27 16 32 \n", "28 16 40 \n", "29 17 32 \n", "30 17 40 \n", "31 17 50 \n", "32 18 42 \n", "33 18 56 \n", "34 18 76 \n", "35 18 84 \n", "36 19 36 \n", "37 19 46 \n", "38 19 68 \n", "39 20 32 \n", "40 20 48 \n", "41 20 52 \n", "42 20 56 \n", "43 20 64 \n", "44 22 66 \n", "45 23 54 \n", "46 24 70 \n", "47 24 92 \n", "48 24 93 \n", "49 24 120 \n", "50 25 85 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data(cars)\n", "cars" ] }, { "cell_type": "code", "execution_count": 2, "id": "d73f45d6-598b-4402-a02c-e6bc28d88e04", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "
cars {datasets}R Documentation
\n", "\n", "

Speed and Stopping Distances of Cars

\n", "\n", "

Description

\n", "\n", "

The data give the speed of cars and the distances taken to stop.\n", "Note that the data were recorded in the 1920s.\n", "

\n", "\n", "\n", "

Usage

\n", "\n", "
cars
\n", "\n", "\n", "

Format

\n", "\n", "

A data frame with 50 observations on 2 variables.\n", "

\n", "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", "
\n", " [,1] speed numeric Speed (mph)
\n", " [,2] dist numeric Stopping distance (ft)\n", "
\n", "\n", "\n", "\n", "

Source

\n", "\n", "

Ezekiel, M. (1930)\n", "Methods of Correlation Analysis.\n", "Wiley.\n", "

\n", "\n", "\n", "

References

\n", "\n", "

McNeil, D. R. (1977)\n", "Interactive Data Analysis.\n", "Wiley.\n", "

\n", "\n", "\n", "

Examples

\n", "\n", "
require(stats); require(graphics)\n",
       "plot(cars, xlab = \"Speed (mph)\", ylab = \"Stopping distance (ft)\",\n",
       "     las = 1)\n",
       "lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = \"red\")\n",
       "title(main = \"cars data\")\n",
       "plot(cars, xlab = \"Speed (mph)\", ylab = \"Stopping distance (ft)\",\n",
       "     las = 1, log = \"xy\")\n",
       "title(main = \"cars data (logarithmic scales)\")\n",
       "lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = \"red\")\n",
       "summary(fm1 <- lm(log(dist) ~ log(speed), data = cars))\n",
       "opar <- par(mfrow = c(2, 2), oma = c(0, 0, 1.1, 0),\n",
       "            mar = c(4.1, 4.1, 2.1, 1.1))\n",
       "plot(fm1)\n",
       "par(opar)\n",
       "\n",
       "## An example of polynomial regression\n",
       "plot(cars, xlab = \"Speed (mph)\", ylab = \"Stopping distance (ft)\",\n",
       "    las = 1, xlim = c(0, 25))\n",
       "d <- seq(0, 25, length.out = 200)\n",
       "for(degree in 1:4) {\n",
       "  fm <- lm(dist ~ poly(speed, degree), data = cars)\n",
       "  assign(paste(\"cars\", degree, sep = \".\"), fm)\n",
       "  lines(d, predict(fm, data.frame(speed = d)), col = degree)\n",
       "}\n",
       "anova(cars.1, cars.2, cars.3, cars.4)\n",
       "
\n", "\n", "
[Package datasets version 4.3.3 ]
\n", "" ], "text/latex": [ "\\inputencoding{utf8}\n", "\\HeaderA{cars}{Speed and Stopping Distances of Cars}{cars}\n", "\\keyword{datasets}{cars}\n", "%\n", "\\begin{Description}\n", "The data give the speed of cars and the distances taken to stop.\n", "Note that the data were recorded in the 1920s.\n", "\\end{Description}\n", "%\n", "\\begin{Usage}\n", "\\begin{verbatim}\n", "cars\n", "\\end{verbatim}\n", "\\end{Usage}\n", "%\n", "\\begin{Format}\n", "A data frame with 50 observations on 2 variables.\n", "\n", "\\Tabular{rlll}{\n", "[,1] & speed & numeric & Speed (mph)\\\\{}\n", "[,2] & dist & numeric & Stopping distance (ft)\n", "}\n", "\\end{Format}\n", "%\n", "\\begin{Source}\n", "Ezekiel, M. (1930)\n", "\\emph{Methods of Correlation Analysis}.\n", "Wiley.\n", "\\end{Source}\n", "%\n", "\\begin{References}\n", "McNeil, D. R. (1977)\n", "\\emph{Interactive Data Analysis}.\n", "Wiley.\n", "\\end{References}\n", "%\n", "\\begin{Examples}\n", "\\begin{ExampleCode}\n", "require(stats); require(graphics)\n", "plot(cars, xlab = \"Speed (mph)\", ylab = \"Stopping distance (ft)\",\n", " las = 1)\n", "lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = \"red\")\n", "title(main = \"cars data\")\n", "plot(cars, xlab = \"Speed (mph)\", ylab = \"Stopping distance (ft)\",\n", " las = 1, log = \"xy\")\n", "title(main = \"cars data (logarithmic scales)\")\n", "lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = \"red\")\n", "summary(fm1 <- lm(log(dist) ~ log(speed), data = cars))\n", "opar <- par(mfrow = c(2, 2), oma = c(0, 0, 1.1, 0),\n", " mar = c(4.1, 4.1, 2.1, 1.1))\n", "plot(fm1)\n", "par(opar)\n", "\n", "## An example of polynomial regression\n", "plot(cars, xlab = \"Speed (mph)\", ylab = \"Stopping distance (ft)\",\n", " las = 1, xlim = c(0, 25))\n", "d <- seq(0, 25, length.out = 200)\n", "for(degree in 1:4) {\n", " fm <- lm(dist ~ poly(speed, degree), data = cars)\n", " assign(paste(\"cars\", degree, sep = \".\"), fm)\n", " lines(d, predict(fm, data.frame(speed = d)), col = degree)\n", "}\n", "anova(cars.1, cars.2, cars.3, cars.4)\n", "\\end{ExampleCode}\n", "\\end{Examples}" ], "text/plain": [ "cars package:datasets R Documentation\n", "\n", "_\bS_\bp_\be_\be_\bd _\ba_\bn_\bd _\bS_\bt_\bo_\bp_\bp_\bi_\bn_\bg _\bD_\bi_\bs_\bt_\ba_\bn_\bc_\be_\bs _\bo_\bf _\bC_\ba_\br_\bs\n", "\n", "_\bD_\be_\bs_\bc_\br_\bi_\bp_\bt_\bi_\bo_\bn:\n", "\n", " The data give the speed of cars and the distances taken to stop.\n", " Note that the data were recorded in the 1920s.\n", "\n", "_\bU_\bs_\ba_\bg_\be:\n", "\n", " cars\n", " \n", "_\bF_\bo_\br_\bm_\ba_\bt:\n", "\n", " A data frame with 50 observations on 2 variables.\n", "\n", " [,1] speed numeric Speed (mph) \n", " [,2] dist numeric Stopping distance (ft) \n", " \n", "_\bS_\bo_\bu_\br_\bc_\be:\n", "\n", " Ezekiel, M. (1930) _Methods of Correlation Analysis_. Wiley.\n", "\n", "_\bR_\be_\bf_\be_\br_\be_\bn_\bc_\be_\bs:\n", "\n", " McNeil, D. R. (1977) _Interactive Data Analysis_. Wiley.\n", "\n", "_\bE_\bx_\ba_\bm_\bp_\bl_\be_\bs:\n", "\n", " require(stats); require(graphics)\n", " plot(cars, xlab = \"Speed (mph)\", ylab = \"Stopping distance (ft)\",\n", " las = 1)\n", " lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = \"red\")\n", " title(main = \"cars data\")\n", " plot(cars, xlab = \"Speed (mph)\", ylab = \"Stopping distance (ft)\",\n", " las = 1, log = \"xy\")\n", " title(main = \"cars data (logarithmic scales)\")\n", " lines(lowess(cars$speed, cars$dist, f = 2/3, iter = 3), col = \"red\")\n", " summary(fm1 <- lm(log(dist) ~ log(speed), data = cars))\n", " opar <- par(mfrow = c(2, 2), oma = c(0, 0, 1.1, 0),\n", " mar = c(4.1, 4.1, 2.1, 1.1))\n", " plot(fm1)\n", " par(opar)\n", " \n", " ## An example of polynomial regression\n", " plot(cars, xlab = \"Speed (mph)\", ylab = \"Stopping distance (ft)\",\n", " las = 1, xlim = c(0, 25))\n", " d <- seq(0, 25, length.out = 200)\n", " for(degree in 1:4) {\n", " fm <- lm(dist ~ poly(speed, degree), data = cars)\n", " assign(paste(\"cars\", degree, sep = \".\"), fm)\n", " lines(d, predict(fm, data.frame(speed = d)), col = degree)\n", " }\n", " anova(cars.1, cars.2, cars.3, cars.4)\n", " " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "?cars" ] }, { "cell_type": "markdown", "id": "009e85ea-9b82-45ec-b6ab-f0a52567e051", "metadata": { "tags": [] }, "source": [ "Fit a linear regression of distance on speed:" ] }, { "cell_type": "code", "execution_count": 3, "id": "765c6ef2-225d-4345-9392-8e09188c4177", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/plain": [ "\n", "Call:\n", "lm(formula = dist ~ speed, data = cars)\n", "\n", "Coefficients:\n", "(Intercept) speed \n", " -17.579 3.932 \n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m <- lm(dist ~ speed, data=cars)\n", "m" ] }, { "cell_type": "markdown", "id": "8db6432d-ba5b-45ad-9f94-e1b88707e2aa", "metadata": { "tags": [] }, "source": [ "Estimated coefficients from the model:" ] }, { "cell_type": "code", "execution_count": 4, "id": "0f1e158b-510f-4877-a23d-6e6190baa919", "metadata": { "tags": [] }, "outputs": [ { "data": { "text/html": [ "
(Intercept)
-17.5790948905109
speed
3.93240875912409
\n" ], "text/latex": [ "\\begin{description*}\n", "\\item[(Intercept)] -17.5790948905109\n", "\\item[speed] 3.93240875912409\n", "\\end{description*}\n" ], "text/markdown": [ "(Intercept)\n", ": -17.5790948905109speed\n", ": 3.93240875912409\n", "\n" ], "text/plain": [ "(Intercept) speed \n", " -17.579095 3.932409 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "coef(m)" ] }, { "cell_type": "markdown", "id": "fad7f57e-23e4-47a5-947e-50c5fda74fac", "metadata": {}, "source": [ "Plot residuals against speed:" ] }, { "cell_type": "code", "execution_count": 5, "id": "a863b30d-f61f-418c-a3a3-4ff008de54fd", "metadata": {}, "outputs": [ { "data": { "application/pdf": 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