Question

Answer the below questions, rounding to two decimal places where necessary.

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?

Answer 1

Solution:

First of all we have to find the regression model for the prediction of dependent variable average finish time in seconds based on the independent variable average amount of food in lbs. Required regression model by using excel is given as below:

Regression Statistics
Multiple R	0.680562712
R Square	0.463165605
Adjusted R Square	0.284220807
Standard Error	1.932607466
Observations	5
ANOVA
	df	SS	MS	F	Significance F
Regression	1	9.667285144	9.667285144	2.588315556	0.206025803
Residual	3	11.20491486	3.734971619
Total	4	20.8722
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	119.6558786	12.39688453	9.652092697	0.00236088	80.20345924	159.1082979
Average amount of food in lbs. (X)	-1.111501597	0.690878185	-1.608824278	0.206025803	-3.310184325	1.087181131

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?

The correlation coefficient between the two variable average amount eaten the night before and time is taken to reach the finish line is given as -0.68056. This means there is considerable high negative linear relationship exists between the average amount eaten the night before and time taken to reach the finish line. The strength of relationship is considerably high and direction of the relationship is negative or inverse.

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?

From the above regression model, the required regression equation for the prediction of finish time is given as below:

Average finish time = 119.6559 – 1.1115*Average amount of food

Y = 119.6559 – 1.1115*X

We are given an average amount of food = 19 lbs

Average finish time = 119.6559 - 1.1115*19

Average finish time = 98.5374

Average finish time = 98.54 seconds approximately

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

For horse 2’s average amount of food is given as X = 17.25 lbs and average finish time = Y = 103.3 seconds

Predicted average finish time when X = 17.25 is given as below:

Average finish time = 119.6559 – 1.1115* Average amount of food

Average finish time = 119.6559 - 1.1115*17.25

Average finish time = 100.483

Observed finish time = 103.3 seconds

Predicted finish time = 100.5 seconds approximately

Error = Observed finish time – Predicted finish time

Error = 103.3 - 100.5 = 2.8 seconds

Answer = 2.8 seconds approximately

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

The standard error of the estimate of this data is given as 1.9326 approximately.

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?

The coefficient of determination or the value for R square is given as 0.4632, which means about 46.32% 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.