Question

Bowie State University athletic department wants to develop its budget for the coming year, using a forecast for football attendance. Football attendance accounts for the largest portion of the University revenues. The new President of the university who is also a football fan has asked the athletic director to come up with strategies in promoting the university football team. The athletic director believes that attendance is directly related to the number of wins by the team. Instead of attempting to predict attendance based on only one variable (wins), the athletic department has included a second variable for advertising and promotional expenditures as well. The university president is anxious to know the result of this forecast to determine strategies that improve attendance and boost revenues for the University. The business manager of the BSU football team has accumulated total annual attendance figures for the past 8 years:  

Wins	Promotion	Attendance
4	$14500	21300
6	40700	25100
6	56300	26200
8	72000	38000
6	60000	29000
7	57000	30600
5	40300	24000
7	66600	32500

Given the number of returning starters and the strength of the schedule, the athletic director believes the team will win at least seven games next year. He wants to develop a multiple regression equation for these data to forecast attendance for this level of success.

Discussion questions

1 Given that Attendance as the dependent variable and Wins and Promotion as independent variables, use excel to estimate the relationship between attendance and promotion and wins. (Copy results and paste).

2 What is the strength of this relationship? Use the coefficient of determination R squared from the excel output to describe this relationship.

3 Is the relationship significant? Use the “Fisher significance” from the excel output to determine this. Begin by stating the null and the alternate hypotheses

Answer 1

1) Using Excel output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.949280683
R Square	0.901133815
Adjusted R Square	0.861587341
Standard Error	1986.59925
Observations	8
ANOVA
	df	SS	MS	F	Significance F
Regression	2	179858948	89929473.99	22.78670442	0.003073403
Residual	5	19732882.9	3946576.579
Total	7	199591830.9
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	4656.401319	4965.428663	0.937764216	0.39141762	-8107.639405	17420.44
Wins	3558.133271	1498.406214	2.374611929	0.063588076	-293.642524	7409.909
Promotion	0.037091947	0.101239944	0.366376603	0.729076396	-0.223153615	0.297338

Regression equation: Y'= 4656.401319 + 3558.133271*Wins + 0.037091947*Promotion

2) Coefficient of determination( R-sqaured value) = 0.901133815

The R-sqaured value defines, the relationship is trong becasue it is greater than 0.8. The percentage estimated variance explained by regression equation is 90.1133815%.

3) using ANOVA table:

The test statistic: F= MSReg/ MS Res= 22.7867

P-value= 0.00307

The test statistic is significant and rejects H0 at 0.05 significant level. There is sufficient evidence to support the claim that there is significant relstionship between variables.