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
The record times in 1984 for 35 Scottish hill races.
This data frame contains the following columns:
distance, in miles (on the map)
total height gained during the route, in feet
record time in hours
A.C. Atkinson (1986) Comment: Aspects of diagnostic regression
analysis. Statistical Science 1, 397-402.
Also, in MASS library, with time in minutes.
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.]
print("Transformation - Example 6.4.3")
pairs(hills, labels=c("dist\n\n(miles)", "climb\n\n(feet)",
pause()pairs(log(hills), labels=c("dist\n\n(log(miles))", "climb\n\n(log(feet))",
pause()hills0.loglm <- lm(log(time) ~ log(dist) + log(climb), data = hills)
oldpar <- par(mfrow=c(2,2))
hills.loglm <- lm(log(time) ~ log(dist) + log(climb), data = hills[-18,])
pause()hills2.loglm <- lm(log(time) ~ log(dist)+log(climb)+log(dist):log(climb),
pause()print("Nonlinear - Example 6.9.4")
hills.nls0 <- nls(time ~ (dist^alpha)*(climb^beta), start =
c(alpha = .909, beta = .260), data = hills[-18,])
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,])
plot(residuals(hills.nls) ~ predict(hills.nls)) # residual plot
Dataset imported from https://www.r-project.org.