---
title: "Confounding example"
author: "Nicholas Horton (nhorton@amherst.edu)"
date: "May 9, 2015"
output: 
  html_document:
    fig_height: 3
    fig_width: 5
  pdf_document:
    fig_height: 3
    fig_width: 5
  word_document:
    fig_height: 3
    fig_width: 5
---


```{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
)
```

```{r, include=FALSE}
# Load additional packages here.  Uncomment the line below to use Project MOSAIC data sets.
require(mosaicData)   
```

See http://www.amherst.edu/~nhorton/precursors for more papers plus commentary on this example.

```{r}
xyplot(sat ~ salary, type=c("r", "p"),
               xlab="Average teacher salary", 
               ylab="State average SAT score", data=SAT)
mod1 <- lm(sat ~ salary, data=SAT); confint(mod1)
```

What do we conclude?

```





```

```{r}
head(SAT)
SAT <- mutate(SAT, fracgrp = cut(frac, breaks=c(0, 22, 49, 81),
  labels=c("low fraction", "medium fraction", "high fraction")))
head(SAT)
bwplot(frac ~ fracgrp, data=SAT)
```

```{r}
xyplot(sat ~ salary, type=c("r", "p"), groups=fracgrp, auto.key=TRUE, 
       xlab="Average teacher salary", 
       ylab="State average SAT score", data=SAT)
mod2 <- lm(sat ~ salary + frac, data=SAT); confint(mod2)
```

```{r}
filter(SAT, salary > 45)
```

```{r}
filter(SAT, salary < 29)
```

```{r}
pairs(select(SAT, salary, sat, frac))
```