Scottish hill races 2008. In Chapter 30, Exercises 4 and 6, we considered data on hill races in Scotland. These are overland races that climb and descend hills—sometimes several hills in the course of one race. Here is a regression analysis to predict the Women’s Record times from the Distance and total vertical Climb of the races:

 

Here is the scatterplot of externally Studentized residuals against predicted values, as well as a histogram of leverages for this regression:

a) Comment on what these diagnostic displays indicate.

b) The two races with the largest Studentized residuals are the Arochar Alps race and the Glenshee 9. Both are relatively new races, having been run only one or two times with relatively few participants. What effects can you be reasonably sure they have had on the regression? What displays would you want to see to investigate other effects? Explain.

c) If you have access to a suitable statistics package, make the diagnostic plots you would like to see and discuss what you find.

Exercises 4

Scottish hill races 2008. Hill running—races up and down hills—has a written history in Scotland dating back to the year 1040. Races are held throughout the year at different locations around Scotland. A recent compilation of information for 91 races (for which full information was available and omitting two unusual races) includes the Distance (km), the Climb (m), and the Record Time (minutes). A regression to predict the men’s records as of 2008 looks like this:

a) Write the regression equation. Give a brief report on what it says about men’s record times in hill races.

b) Interpret the value of in this regression.

c) What does the coefficient of Climb mean in this regression?

Exercises 6

More hill races 2008. Here is the regression for the women’s records for the same Scottish hill races we considered in Exercise 4:

a) Compare the regression model for the women’s records with that found for the men’s records in Exercise 4. Here’s a scatterplot of the residuals for this regression:

b) Discuss the residuals and what they say about the assumptions and conditions for this regression.

Exercise 4

Scottish hill races 2008. Hill running—races up and down hills—has a written history in Scotland dating back to the year 1040. Races are held throughout the year at different locations around Scotland. A recent compilation of information for 91 races (for which full information was available and omitting two unusual races) includes the Distance (km), the Climb (m), and the Record Time (minutes). A regression to predict the men’s records as of 2008 looks like this:

a) Write the regression equation. Give a brief report on what it says about men’s record times in hill races.

b) Interpret the value of in this regression.

c) What does the coefficient of Climb mean in this regression?

 

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