Ex2.Rmd

---
title: 'Statistics 692, exercises #2'
author: "Douglas Bates"
date: "2014-10-14"
output: 
    pdf_document:
        keep_tex: true
        fig_caption: true
---
```{r initial,echo=FALSE,print=FALSE,cache=FALSE}
library(knitr)
library(ggplot2)
classroom <- read.csv("http://www-personal.umich.edu/~bwest/classroom.csv")
opts_chunk$set(cache=TRUE)
options(width=76, show.signif.stars = FALSE, str = strOptions(strict.width = "cut"))
set.seed(123454321)
``` 
Your answers should be submitted as an _R Markdown_ (`Rmd`) document providing both the code you use and a brief description of each step.  The description should be written as if intended for the "client".

Submit only the `.Rmd` file.  The file will be run through `knitr::knit` to verify that it produces the desired results.  Use `pdf_document` as the output format.  Allow them to float to the top or the bottom of the page.  Provide figure captions.

Load the `classroom` data frame that you saved in the previous set of exercises and attach the `ggplot2` package.

1. Provide a histogram of the `mathkind` (mathematics score in kindergarten) variable.  For this and all other plots in this assignment provide informative axis labels where appropriate.  An example of this plot is shown in Figure (#fig:hist1)

```{r hist1,echo=FALSE,fig.cap="Histogram of the kindergarten mathematics score",fig.height=3,fig.width=6.5,fig.pos="tb"}
p <- ggplot(classroom,aes(x=mathkind)) + xlab("Kindergarten Mathematics Score")
p + geom_histogram()
```

2. Provide an empirical density plot of `mathkind`, as shown in Figure (#fig:dens1)

```{r dens1,echo=FALSE,fig.cap="Empirical density plot of the kindergarten mathematics score",fig.height=2.5,fig.width=6.5,fig.pos="tb"}
p + geom_density()
```

3. Provide an empirical density plot of `mathkind` by `sex`.  Do this in two ways: One panel with two lines and two panels.

4. Provide an empirical density plot of `mathkind` by `minority`.

5. Provide a scatter-plot of `mathgain` versus the kindergarten score.  Include a scatterplot smoother curve with the band of pointwise confidence intervals.
    a. The negative correlation between `mathgain` and `mathkind` is not surprising.  Explain.
    b. Does it make sense to include `mathkind` as a covariate in a model for `mathgain`?  Explain.

6. Repeat this plot with a simple linear regression line instead of a scatterplot smoother.
    a. Include the estimated coefficients of the regression line in the caption for the plot

7. Create a new variable called `mathone` which is the sum of `mathkind` and `mathgain`.  Repeat the plot with the scatterplot smoother for `mathone` versus `mathkind`.  Because both variables are measured on the same scale use a unit aspect ratio for the plot.

8. Create a dotplot of the mathgain by classroom for students in school 11 only.