Question

Background: Jesse frequently bets on horse races at Dover Downs in Delaware. As an aspiring handicapper, Jesse is looking for reliable ways to predict the winning horse. He thinks that the amount of food eaten by the horse on the night before the race might predict how fast the horse will finish. To test this, Jesse tracks 5 horses over 5 1-mile races on dirt, recording the amount of food (in lbs.) they ate the night before and the time (in seconds) it took them to reach the finish line. Below is the average amount eaten the night before and time taken to reach the finish line for each horse:
Horse   Average amount of food in lbs. (X)   Average finish time in seconds (Y)
1   18   99.33
2   17.25   103.32
3   18.5   98.04
4   19.75   97.63
5   16   100.48

What is the strength and direction of the relationship between the average amount eaten the night before and time taken to reach the finish line?

Using the appropriate regression equation, what is the predicted finish time for a horse that eats 19 lbs. of food the night before a 1-mile race on dirt?

Based on the appropriate regression equation, what is the error of horse 2’s finish time?

What is the standard error of the estimate of this data?

How much of the variance in the average time taken to reach the finish line for a 1-mile race on dirt is accounted for by variance in the average amount eaten the night before?

Jesse’s friend, Marty, thinks that another good predictor of time taken to reach the finish line for a 1-mile race on dirt would be the difference between the jockey (rider) and horse’s weight. Therefore, Marty tracks 5 horses over 5 1-mile races on dirt, recording the average difference between the weight of the horse and jockey (horse weight – jockey weight) and the time (in seconds) it took the horse to reach the finish line. His data is summarized below:
Horse   Average weight difference in lbs. (X)   Average finish time in seconds (Y)
1   891.69   104.33
2   889.92   102.32
3   891.32   97.04
4   892.04   95.63
5   884.2   104.48

What is the strength and direction of the relationship between the average weight difference and time taken to reach the finish line?

Using the appropriate regression equation, what is the predicted finish time for a horse that weighs 893 lbs. more than its jockey?

What is the standard error of the estimate of Marty’s data?

How much of the variance in the average time taken to reach the finish line for a 1-mile race on dirt is accounted for by variance in weight difference?

Which data better predicts the time taken to reach the finish line for a 1-mile race on dirt? Explain your reasoning.

Answer 1