---
title: "IPS9 in R: Multiple regression (Chapter 11)"
author: "Nicholas Horton (nhorton@amherst.edu)"
date: "January 19, 2019"
output:
pdf_document:
fig_height: 3
fig_width: 5
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}
# knitr settings to control how R chunks work.
knitr::opts_chunk$set(
tidy = FALSE, # display code as typed
size = "small" # slightly smaller font for code
)
```
## Introduction and background
These documents are intended to help describe how to undertake analyses introduced
as examples in the Ninth Edition of \emph{Introduction to the Practice of Statistics} (2017) by Moore, McCabe, and Craig.
More information about the book can be found [here](https://macmillanlearning.com/Catalog/product/introductiontothepracticeofstatistics-ninthedition-moore).
The data used in these documents can be found under Data Sets in the [Student Site](https://www.macmillanlearning.com/catalog/studentresources/ips9e?_ga=2.29224888.526668012.1531487989-1209447309.1529940008#). This
file as well as the associated R Markdown reproducible analysis source file used to create it can be found at https://nhorton.people.amherst.edu/ips9/.
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). A paper describing the mosaic approach was published in the *R Journal*: https://journal.r-project.org/archive/2017/RJ-2017-024.
## Chapter 11: Multiple Regression
This file replicates the analyses from Chapter 11: Multiple Regression.
First, load the packages that will be needed for this document:
```{r load-packages}
library(mosaic)
library(readr)
```
### Section 11.1: Inference for multiple regression
#### Example 11.1: Predicting early success in college
```{r eg11-1, message=FALSE}
GPA <- read_csv("https://nhorton.people.amherst.edu/ips9/data/chapter11/EG11-01GPA.csv")
# Figure 11.1, page 609
head(GPA)
```
### Section 11.2: A Case Study
```{r}
# Figure 11.2, page 619
favstats(~ GPA, data = GPA)
favstats(~ HSM, data = GPA)
favstats(~ HSS, data = GPA)
favstats(~ HSE, data = GPA)
favstats(~ SATM, data = GPA)
favstats(~ SATCR, data = GPA)
favstats(~ SATW, data = GPA)
```
```{r}
# Figure 11.3, page 620
gf_histogram(~ HSM, data = GPA) %>%
gf_labs(y = "Percent")# Doesn't look great
gf_histogram(~ HSS, data = GPA) %>%
gf_labs(y = "Percent")
gf_histogram(~ HSE, data = GPA) %>%
gf_labs(y = "Percent")
```
#### Relationships between pairs of variables
```{r}
# Figure 11.4, page 621
options(digits = 2)
cor(GPA)
```
#### Example 11.13: Pairwise relationships among variables in the GPA data set
```{r message = FALSE, fig.width = 7, fig.height = 8}
GPA <- read_csv("https://nhorton.people.amherst.edu/ips9/data/chapter11/EX11-13GPA.csv")
GPA <- GPA %>%
mutate(SEX = ifelse(SEX == 1, "F", "M"))
library(GGally)
# Figure 11.5
GPA %>% select(-OBS) %>%
GGally::ggpairs()
```
#### Regression on high school grades
```{r}
# Figure 11.6, page 623
gpamultlm <- lm(GPA ~ HSM + HSE + HSS, data = GPA)
msummary(gpamultlm)
```
#### Examining the residuals
```{r}
# Figure 11.7, page 625
gf_qq(~ resid(gpamultlm)) %>%
gf_labs( x = "Normal Score", y = "Residual")
gf_histogram(~ resid(gpamultlm), binwidth = .5) %>%
gf_labs(x = "Residual", y = "Percent")
```
#### Example 11.14: Residual plots for the GPA analysis
#### Refining the model
```{r}
# Figure 11.8, page 626
gpamultlm2 <- lm(GPA ~ HSM + HSS, data = GPA)
msummary(gpamultlm2)
```
#### Regression using all variables
```{r}
# Figure 11.9
gpasatlm <- lm(GPA ~ SATM + SATCR + SATW, data = GPA)
msummary(gpasatlm)
# Figure 11.10, page 628
gpaalllm <- lm(GPA ~ SATM + SATCR + SATW + HSS + HSE + HSM, data = GPA)
msummary(gpaalllm)
# Figure 11.11, page 631
MASS::stepAIC(gpaalllm)
```