rms2-5.Rmd

---
title: "RMS Chapter 2 Problem 5"
author: "your name"
date: "`r Sys.Date()`"
output:
  html_document:
    highlight: pygments
    toc: yes
major: regression modeling; rms
minor: curve fitting
---
```{r setup}
require(Hmisc)
knitrSet(lang='markdown')
```
# SAT Data
```{r define-data}
pct <- c( 4,  5,  5,  6,  6,  7,  9,  9, 10, 10, 10, 10, 12, 12, 13, 13, 
         14, 14, 14, 16, 17, 18, 20, 22, 23,
         24, 29, 37, 43, 44, 45, 49, 50, 52, 55, 57, 58, 59, 60,      
         62, 63, 63, 63, 64, 64, 68, 69,
         72, 73, 81)
score <-
c(482,498,513,498,511,479,480,483,475,476,487,494,474,478,457,
  485,451,471,473,467,470,464,471,455,452,440,460,448,441,424,
  417,422,441,408,412,400,401,430,433,433,404,424,430,
  431,437,446,424,420,432,436)

# Prepare rms so that it will use good limits for plotting
require(rms)
dd <- datadist(pct); options(datadist='dd')
```
# Linear Spline Fit
```{r linear-spline}
f <- ols(score ~ lsp(pct, 50))
f
ap <- geom_point(aes(x=pct, y=score), data.frame(pct, score))
# Take charge of x-axis limits for plotting predicted values so will
# show entire range of data
pcts <- seq(0,80,length=150)
ggplot(Predict(f, pct=pcts)) + ap
```

# Restricted Cubic Spline Fit
```{r rcs}
f <- ols(score ~ rcs(pct, c(6, 12, 58, 68)))
f
ggplot(Predict(f, pct=pcts)) + ap
f.linear <- ols(score ~ pct)
# Retrieve R^2 from the cubic spline fit and from the reduced model (linear)
R2 <- f$stats['R2']
R2red <- f.linear$stats['R2']
# Compute F statistic using difference in R^2 and R^2 of full model
# df.num <- ...
# df.denom <- ...
# Fstat <- ...
# pvalue <- 1 - pf(Fstat, df.num, df.denom)
# c(df.num=df.num, df.denom=df.denom, Fstat=Fstat, P=pvalue)  # prints all stats

```

# Computing Environment
```{r rsession,echo=FALSE}
si <- sessionInfo(); si$loadedOnly <- NULL
print(si, locale=FALSE)
```
```{r cite,results='asis',echo=FALSE}
print(citation(), style='text')
```