hills R Documentation

## Scottish Hill Races Data

### Description

The record times in 1984 (hills) for 35 Scottish hill races, or in 2000 (hills2000) for 56 hill races. The hills2000 dataset is the subset of races2000 for which type is hill.

### Usage

  data(hills)
data(hills2000)


### Format

dist

distance, in miles (on the map)

climb

total height gained during the route, in feet

time

record time in hours

timef

record time in hours for females, in the hills2000 dataset.

### Source

A.C. Atkinson (1986) Comment: Aspects of diagnostic regression analysis. Statistical Science 1, 397-402.

Also, in MASS library, with time in minutes.

The Scottish Running Resource, http://www.hillrunning.co.uk

### References

A.C. Atkinson (1988) Transformations unmasked. Technometrics 30, 311-318. [ "corrects" the time for Knock Hill, in the hills dataset, from 78.65 to 18.65. It is unclear if this based on the original records.]

### Examples

print("Transformation - Example 6.4.3")
pairs(hills, labels=c("dist\n\n(miles)", "climb\n\n(feet)",
"time\n\n(hours)"))
pause()

pairs(log(hills), labels=c("dist\n\n(log(miles))", "climb\n\n(log(feet))",
"time\n\n(log(hours))"))
pause()

hills0.loglm <- lm(log(time) ~ log(dist) + log(climb), data = hills)
oldpar <- par(mfrow=c(2,2))
plot(hills0.loglm)
pause()

hills.loglm <- lm(log(time) ~ log(dist) + log(climb), data = hills[-18,])
summary(hills.loglm)
plot(hills.loglm)
pause()

hills2.loglm <- lm(log(time) ~ log(dist)+log(climb)+log(dist):log(climb),
data=hills[-18,])
anova(hills.loglm, hills2.loglm)
pause()

step(hills2.loglm)
pause()

summary(hills.loglm, corr=TRUE)$coef pause() summary(hills2.loglm, corr=TRUE)$coef
par(oldpar)
pause()

print("Nonlinear - Example 6.9.4")
hills.nls0 <- nls(time ~ (dist^alpha)*(climb^beta), start =
c(alpha = .909, beta = .260), data = hills[-18,])
summary(hills.nls0)
plot(residuals(hills.nls0) ~ predict(hills.nls0)) # residual plot
pause()

hills$climb.mi <- hills$climb/5280
hills.nls <- nls(time ~ alpha + beta*dist + gamma*(climb.mi^delta),
start=c(alpha = 1, beta = 1, gamma = 1, delta = 1), data=hills[-18,])
summary(hills.nls)
plot(residuals(hills.nls) ~ predict(hills.nls)) # residual plot