Introduction and background
This document is intended to help describe how to undertake analyses introduced as examples in the Fourth Edition of (2014) by De Veaux, Velleman, and Bock. More information about the book can be found at http://wps.aw.com/aw_deveaux_stats_series. This file as well as the associated R Markdown reproducible analysis source file used to create it can be found at http://nhorton.people.amherst.edu/sdm4.
This work leverages initiatives undertaken by Project MOSAIC (http://www.mosaic-web.org), an NSF-funded effort to improve the teaching of statistics, calculus, science and computing in the undergraduate curriculum. In particular, we utilize the mosaic package, which was written to simplify the use of R for introductory statistics courses. A short summary of the R needed to teach introductory statistics can be found in the mosaic package vignettes (http://cran.r-project.org/web/packages/mosaic).
Chapter 8: Regression Wisdom
Section 8.1: Examining residuals
Figure 8.1 (page 220) displays the scatterplot of heart rate vs duration for the Penguins dataset (along with a superimposed regression line and a smoother).
library(mosaic); library(readr)
options(digits=3)
Penguins <- read_csv("http://nhorton.people.amherst.edu/sdm4/data/Penguins.csv")
xyplot(DiveHeartRate ~ Duration, ylab="Dive Heart Rate (bpm)",
xlab="Duration (mins)", type=c("p", "r", "smooth"), data=Penguins)
Figure 8.2 (page 220) displays the residuals from a linear regression model as a function of duration.
Penguinmod <- lm(DiveHeartRate ~ Duration, data=Penguins)
xyplot(resid(Penguinmod) ~ Duration, type=c("p", "r", "smooth"), data=Penguins)
Figure 8.3 (page 221) displays the histogram of residuals for the cereal data from Chapter 7.
Cereals <- read_csv("http://nhorton.people.amherst.edu/sdm4/data/Cereals.csv")
Cerealmod <- lm(calories ~ sugars, data=Cereals)
histogram(~ resid(Cerealmod), width=7.5, center=3.75)
Figure 8.4 (page 221) displays a scatterplot of the residuals vs predicted values. Without jittering, the display has an odd pattern.
xyplot(resid(Cerealmod) ~ fitted(Cerealmod))
By adding some random noise we can more easily observe values that are shared by more than one cereal.
xyplot(jitter(resid(Cerealmod)) ~ jitter(fitted(Cerealmod)))
Figure 8.5 (page 222) displays the scatterplot stratified by what shelf it is displayed on at the store.
tally(~ shelf, data=Cereals)## shelf
## 1 2 3
## 20 21 36Cereals <- mutate(Cereals, shelfgrp = derivedFactor(
bottomshelf = shelf==1,
middleshelf = shelf==2,
topshelf = shelf==3
))
tally(~ shelfgrp, data=Cereals)## shelfgrp
## bottomshelf middleshelf topshelf
## 20 21 36xyplot(calories ~ sugars, group=shelfgrp, auto.key=TRUE,
lwd=2, type=c("p", "r"), data=Cereals)