Nike Co. wants to estimate the sales revenue of its stores to determine which stores to be shut down. They collected a sample of 25 stores with the following variables:

l Y = the Nike stores sales revenue (in million dollars);

l X₁ = the Nike stores size (in square foot);

l X₂ = the Nike stores advertising expenditure (in million dollars);

l X₃ = the Nike stores location: S for Seoul, C for cities, and T for towns;

l X₄ = the competitors promotional expenditure (in million dollars);

You are given the following two computer outputs:

Output I

Regression Statistics
Multiple R	0.3914
R Square	0.1532
Adjusted R Square	0.1164
Standard Error	100.6035
Observations	25
ANOVA
	df	SS	MS	F	P-value
Regression	1	42130.64	42130.65	4.1626	0.05296
Residual	23	232784.71	10121.07
Total	24	274915.36
	Coefficients	Standard Error	t Stat	P-value
Intercept	91.67	100.14	0.915	0.3694
X2	7.29	3.57	2.040	0.0529

Output II

Regression Statistics
Multiple R	0.5141
R Square	?
Adjusted R Square	0.2324
Standard Error	93.772
Observations	25
ANOVA
	df	SS	MS	F	P-value
Regression	1	72670.9	72670.9	8.2644	0.0085
Residual	23	202244.5	8793.237
Total	24	274915.4
	Coefficients	Standard Error	t Stat	P-value
Intercept	407.78	44.47	9.168	3.83E-09
X4	-11.47	3.99	-2.874	0.0085

Output III

Groups	Count	Sum	Average	Variance
C	10	3141	314.1	3819.211
S	7	2580	368.5714	4775.619
T	8	1575	196.875	13367.55
ANOVA
Source of Variation	SS	df	MS	F	P-value
Between Groups	118315.9	2	59157.94	8.3108	0.0020
Within Groups	156599.5	22	7118.159
Total	274915.4	24

Answer the following questions.

1. Can we be reasonably confident that Nikes advertising expenditure has a positive effect on the Nike stores sales revenue (a = 5%)?

(1) Ho and Ha can be set up in two different ways. State both cases.

Ho (symbolically):

(in words):

Ha (symbolically):

(in words):

Or alternatively,

Ho (symbolically):

(in words):

Ha (symbolically):

(in words):

(2) Define test, show test statistic, p-value, and alpha in the diagram:

(3) conclusion:

2. In the above model (Question 1), find and interpret the coefficient of determination?

3. Interpret the meaning of standard error of estimate in the problem.

4. Predict the sales revenue if a store spends 100 million dollars for advertising.

5. Can we be reasonably confident that the stores sales revenue differs by the stores location (a = 5%)?

(1) Ho (symbolically):

(in words):

Ha (symbolically):

(in words):

(2) Define test, show test statistic, p-value, and alpha in the diagram:

(3) conclusion: