---
title: "SDM4 in R: Regression Wisdom (Chapter 8)"
author: "Nicholas Horton (nhorton@amherst.edu)"
date: "January 2, 2017"
output: 
  pdf_document:
    fig_height: 3
    fig_width: 6
  html_document:
    fig_height: 3
    fig_width: 5
  word_document:
    fig_height: 4
    fig_width: 6
---


```{r, include=FALSE}
# Don't delete this chunk if you are using the mosaic package
# This loads the mosaic and dplyr packages
require(mosaic)
```

```{r, include=FALSE}
# Some customization.  You can alter or delete as desired (if you know what you are doing).

# This changes the default colors in lattice plots.
trellis.par.set(theme=theme.mosaic())  

# knitr settings to control how R chunks work.
require(knitr)
opts_chunk$set(
  tidy=FALSE,     # display code as typed
  size="small"    # slightly smaller font for code
)
```

## Introduction and background 

This document is intended to help describe how to undertake analyses introduced 
as examples in the Fourth Edition of \emph{Stats: Data and Models} (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).

```{r message=FALSE}
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.

```{r}
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.

```{r message=FALSE}
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.

```{r}
xyplot(resid(Cerealmod) ~ fitted(Cerealmod))
```

By adding some random noise we can more easily observe values that are shared by more than one cereal.

```{r}
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.

```{r}
tally(~ shelf, data=Cereals)
Cereals <- mutate(Cereals, shelfgrp = derivedFactor(
  bottomshelf = shelf==1,
  middleshelf = shelf==2,
  topshelf = shelf==3
))
tally(~ shelfgrp, data=Cereals)
xyplot(calories ~ sugars, group=shelfgrp, auto.key=TRUE, 
  lwd=2, type=c("p", "r"), data=Cereals)
```


### Section 8.2: Extrapolation and reaching beyond the data

### Section 8.3: Outliers, leverage, and influence

### Section 8.4: Lurking variables and causation

### Section 8.5: Working with summary values