Question

Fran’s Convenience Marts are located throughout a metropolitan area. Fran, the owner, would like to expand into other communities. As part of her presentation to the local bank, she would like to better understand the factors that make a particular outlet profitable. She must do all the work herself, so she will not be able to study all her outlets. She selects a random sample of 15 marts and records the average daily sales (Y ), the floor space (area), the number of parking spaces, and the median income of families in each region. The sample information is reported below:

Sampled Mart	Daily Sales ($)	Store Area	Parking Spaces	Income ($000)
1	$1727	500	3	$45
2	1784	523	4	45
3	1841	548	7	46
4	1735	472	4	44
5	1713	472	4	46
6	1805	556	6	52
7	1796	515	5	46
8	1725	487	4	43
9	1772	512	5	47
10	1834	533	6	49
11	1825	547	7	52
12	1723	484	4	47
13	1841	542	7	49
14	1836	531	7	51
15	1754	526	5	46

a. Determine the regression equation. (Round the final answers to 4 decimal places. Negative answer should be indicated by a minus sign.)

Y′ =  +  Store Area +  Parking Spaces +  Income ($000)

b. What is the value of R²? (Round the final answer to 1 decimal place.)

R² = ? %

Conduct a global hypothesis test to determine if any of the independent variables are different from zero. Test at a significance level of 0.05.

H₀: β₁ = β₂ = β₃ = 0

H₁: Not all β_i's = 0

c. State the decision rule. (Round the final answer to 2 decimal places.)

Reject H₀ if F > ? .

c-1. Compute the value of the test statistic. (Round the final answer to 2 decimal places.)

F =             .

Conduct individual hypothesis tests to determine if any of the independent variables can be dropped. Test at a significance level of 0.05.

For Store Area	For Parking Spaces	For Income
H0: β1 = 0	H0: β2 = 0	H0: β3 = 0
H1: β1 ≠ 0	H1: β2 ≠ 0	H1: β3 ≠ 0

d. State the decision rule. (Round the final answers to 3 decimal places. Negative answer should be indicated by a minus sign.)

Reject H₀ if t < ? or t >  .?

e. If variables are dropped, recompute the regression equation and R2R2 . (Round the final answers to 3 decimal places. If variable is dropped, enter 0 as a coefficient. Negative answer should be indicated by a minus sign.)

Y′ = ? + ? Store Area + ? Parking Spaces + ? Income ($000)

R2R2 = ?

Answer 1