On this Picostat.com statistics page, you will find information about the hills data set which pertains to Scottish Hill Races Data. The hills data set is found in the DAAG R package. You can load the hills data set in R by issuing the following command at the console data("hills"). This will load the data into a variable called hills. If R says the hills data set is not found, you can try installing the package by issuing this command install.packages("DAAG") and then attempt to reload the data. If you need to download R, you can go to the R project website. You can download a CSV (comma separated values) version of the hills R data set. The size of this file is about 883 bytes.

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

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Dataset imported from https://www.r-project.org.