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9.20 (III). Kentucky Derby.Display 9.20 is a partial listing of data in file ex0920 on Kentucky Derby horse race winners from 1896 to 2011. In all those years the race was 1.25 miles in length so that winning time and speed are exactly inversely related. Nevertheless, a simple regression model for changes over time—such as a straight line model that includes Yearor a quadratic curve that includes Yearand Year2—might work better for one of these response variables than the other.
a) Find a model for describing the mean of either winning time or winning speed as a function of year, whichever works better.
b) Quantify the amount (in seconds or miles per hour) by which the mean winning time or speed on fast tracks exceeds the mean on slow tracks(using the two-category variable Conditions), after accounting for the effect of year.
c) After accounting for the effects of year and track conditions, is there any evidence that the mean winning time or speed depends on number of horses in the race (Starters)? Is there any evidence of an interactive effect of Startersand Conditions; that is, does the effect of number of horses on the response depend on whether the track was fast or slow? Describe the effect of number of horses on mean winning time or speed. (Data from Kentucky Derby: Kentucky Derby Racing Results, http://www.kentuckyderby.info/kentuckyderby-results.php (July 21, 2011).)