---
title: "SDM4 in R: Scatterplots, Association, and Correlation (Chapter 6)"
author: "Nicholas Horton (nhorton@amherst.edu)"
date: "January 2, 2017"
output: 
  html_document:
    fig_height: 5
    fig_width: 7
  pdf_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}
# 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
)
```

## Introduction and background 

This document is intended to help describe how to undertake analyses introduced 
as examples in the Fourth Edition of \emph{Stats: Data and Models} (2014) by De Veaux, Velleman, and Bock.
More information about the book can be found at http://wps.aw.com/aw_deveaux_stats_series.  This
file as well as the associated R Markdown reproducible analysis source file used to create it can be found at http://nhorton.people.amherst.edu/sdm4.

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).

## Chapter 6: Scatterplots, Association, and Correlation

### Section 6.1: Scatterplots

Figure 6.1 (page 152) displays the scatterplot of the average tracking error over time.

```{r message=FALSE}
library(mosaic); library(readr)
options(digits=3)
Hurricanes <- 
  read_csv("http://nhorton.people.amherst.edu/sdm4/data/Tracking_hurricanes_2012.csv")
xyplot(Error72h ~ Year, ylab="Prediction error (nautical miles)", data=Hurricanes)
```

 
### Section 6.2: Correlation

Figure 6.2 (page 155) displays the scatterplot of weight vs. height for a sample of students from statistics classes.

```{r message=FALSE}
HtWt <- read_csv("http://nhorton.people.amherst.edu/sdm4/data/Heights_and_Weights.csv")
xyplot(Weight ~ Height, ylab="Weight (lbs)", xlab="Height (in)", data=HtWt)
cor(Weight ~ Height, data=HtWt)
```

#### Kendall's Tau and Spearman's Rho

```{r}
cor(Weight ~ Height, method="kendall", data=HtWt)
cor(Weight ~ Height, method="spearman", data=HtWt)
```
       
### Section 6.3: Warning: Correlation does not always equal Causation

### Section 6.4: Straightening scatterplots

Since the dataset is so small for Figure 6.10 (page 165) we can enter it by hand.
```{r}
fstop <- c(2.8, 4, 5.6, 8, 11, 16, 22, 32)
shutter <- c(1/1000, 1/500, 1/250, 1/125, 1/60, 1/30, 1/15, 1/8)
lenses <- data.frame(fstop, shutter)
xyplot(fstop ~ shutter, ylab="f/stop", xlab="Shutter Speed (sec)", data=lenses)
```

A new transformed variable can be added using the `mutate` function.
```{r}
lenses <- mutate(lenses, fstopsq = fstop*fstop)
xyplot(fstopsq ~ shutter, ylab="f/stop (squared)", xlab="Shutter Speed (sec)", data=lenses)
```