Scottish Hill Races Data

Description

The record times in 1984 for 35 Scottish hill races.

Usage

hills

Format

This data frame contains the following columns:

dist

distance, in miles (on the map)

climb

total height gained during the route, in feet

time

record time in hours

Source

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

Also, in MASS library, with time in minutes.

References

A.C. Atkinson (1988) Transformations unmasked. Technometrics 30, 311-318. [ "corrects" the time for Knock Hill 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