hw2p2-reading-test-scores.Rmd

---
title: "Reading Test Scores"
author: "Terrel Shumway"
date: "04/29/2015"
output: html_document
---

This document presents answers for homework 2 part 2.

## Getting and Cleaning the Data
```{r}
baseurl = "https://courses.edx.org/c4x/MITx/15.071x_2/asset/"

getdata = function(local){
  if(!file.exists(local)){
    library(downloader)
    remote = paste0(baseurl,local)
    print(remote)
    download(remote,local)
  }
  read.csv(local)
}

train = getdata("pisa2009train.csv")
test = getdata("pisa2009test.csv")
```

problem 1.1:
```{r}
nrow(train)
```

problem 1.2:
```{r}
tapply(train$readingScore,train$male,mean)
```

problem 1.3: This may not be elegant, but it works better than manually searching through the untidy summary output
```{r}
s = summary(train)
colnames(s)[!is.na(s[7,])] # at least 1 NA
colnames(s)[is.na(s[7,])] # no NA's
```

problem 1.3: This, however, *is* elegant.
```{r}
sapply(train,function(x){sum(is.na(x))})
```

problem 1.4:
```{r}
train = na.omit(train)
test = na.omit(test)
nrow(train)
nrow(test)
```

problem 3.1:
```{r}
library(plyr)
l_ply(list(train,test),function(d){
  d$raceeth = relevel(d$raceeth,"White")
})

m1.form = readingScore ~ .
m1 = lm(m1.form,data=train)
```

problem 3.2: `r sqrt(mean(m1$residuals^2))`

problem 3.3: `r (11-9)*m1$coefficients[["grade"]]`

problem 3.5:
```{r}
sc = summary(m1)$coefficients
rownames(sc)[sc[,4]>.05]
```

## Predicting on Unseen Data
```{r}
m1.pred = predict(m1,newdata=test)
r = range(m1.pred,na.rm=T)
```

problem 4.1: `r r[2]-r[1]`

```{r}
m1.resid = m1.pred - test$readingScore
sse = sum((m1.resid)^2)
rmse = sqrt(mean(m1.resid^2))
```
problem 4.2: 

 * sse = `r sse` 
 * rmse = `r rmse`

```{r}
baseline = mean(train$readingScore)
sst = sum((test$readingScore - baseline)^2)
```
problem 4.3:

 * baseline=`r baseline` 
 * sst=`r sst`

problem 4.4: 

 * R-squared = `r 1-sse/sst`

## Bonus

```{r}
m2 = step(m1)
sqrt(mean((predict(m2,newdata=test)-test$readingScore)^2))
```