---
title: "Duncan's Occupational Prestige Regression"
author: "John Fox"
date: "`r Sys.Date() # generates today's date`"
output: html_document
---


```{r echo=FALSE}
# include this code chunk as-is to set options
knitr::opts_chunk$set(comment=NA, prompt=TRUE, fig.height=8, fig.width=8) 
#    use fig.height=6.5, fig.width=6.5 for word output
```

Duncan's Occupational Prestige Regression
-----------------------------------------

* Reading and examining the data:

```{r}
Duncan <- read.table("data/Duncan.txt", header=TRUE) 
  # assumes the file is in data subdirectory of current directory
summary(Duncan)
library(car)
scatterplotMatrix(~ prestige + income + education, id=list(n=3), data=Duncan)
```

* Duncan's regression:

```{r}
duncan.mod <- lm(prestige ~ income + education, data=Duncan)
summary(duncan.mod)
```

* Some diagnostics for Duncan's regression:

```{r fig.width=6, fig.height=6}
qqPlot(duncan.mod, id=list(n=2), reps=1000)
influencePlot(duncan.mod, id=list(n=2))
```

```{r fig.height=4}
avPlots(duncan.mod, id=list(n=3, method="mahal"))
crPlots(duncan.mod, smooth=list(span=0.9))
```

The residual QQ plot is unremarkable, as are the component+residual plots, but the influence plot, and especially the added-variable plots suggest that minister and railroad conductor might be an influential pair of cases, decreasing the magnitude of the income coefficient and increasing the magnitude of the education coefficient.

* Try refitting the model removing conductors and ministers:

```{r}
duncan.mod.2 <- update(duncan.mod, subset= 
                           - whichNames(c("minister", "conductor"), Duncan))
summary(duncan.mod.2)
compareCoefs(duncan.mod, duncan.mod.2)
```

The income coefficient is now more than twice the education coefficient.
