A regional retailer would like to determine if the variation in average monthly store sales can, in part, be explained by the size of the store measured in square feet. A random sample of 21 stores was selected and the store size and average monthly sales were computed. Complete parts a through c. Use a significance level of 0.10 where needed.
a. Compute the simple linear regression model using the sample data to determine whether variation in average monthly sales can be explained by store size. What is the linear regression model based on the sample data? ModifyingAbove y with caretequals 182150plus(24.72)x (Type integers or decimals rounded to two decimal places as needed.)
Interpret the slope coefficient. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.)
A. For each additional square foot of store size, the average increase in monthly sales is $24.72.
B. For each additional dollar of monthly sales, the average increase in store size is nothing square feet.
Interpret the intercept coefficient. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal rounded to two decimal places as needed.)
A. The average monthly sales of a store with 0 square feet is $182150.
B. The size of a store with average monthly sales of $0 is nothing square feet.
C. A store with no floor space cannot occur; therefore, the y intercept does not have a meaningful interpretation.
b. Test the significance of the slope coefficient of the regression model. Use a significance level of 0.10. What are the appropriate hypotheses to test?
A. H0: beta1equals0 HA: beta1not equals0
B. H0: beta1less than or equals0 HA: beta1greater than0
C. H0: beta1less than0 HA: beta1greater than or equals0
D. H0: beta1greater than0 HA: beta1less than or equals0
E. H0: beta1greater than or equals0 HA: beta1less than0
F. H0: beta1not equals0 HA: beta1equals0
Determine the rejection region for the test statistic t. Select the correct choice below and fill in any answer boxes to complete your choice. (Type integers or decimals rounded to three decimal places as needed.)
A. tless than negative 1.729 or tgreater than 1.729
B. tgreater than nothing
C. tless than nothing
Calculate the simple linear regression test statistic t. tequals 6.752 (Type an integer or decimal rounded to three decimal places as needed.) Since the test statistic is not in the rejection region, do not reject the null hypothesis. Conclude that the regression model is not significant. This means that knowing x does not provide useful help in predicting y.
c. Based on the estimated regression model, what percentage of the total variation in average monthly sales can be explained by store size? 70.6% (Type an integer or decimal rounded to one decimal place as needed.)
Store_Size_(Sq._Ft)
Average_Monthly_Sales
17520 582528.00
16030 534061.00
17530 637858.00
17210 572052.00
15660 559158.00
20310 693884.00
15310 555547.00
17110 586163.00
11910 470810.00
12470 523593.00
15660 619349.00
12500 467161.00
21740 728663.00
14180 505080.00
16720 626402.00
15030 593527.00
18440 613840.00
18520 617692.00
16680 694570.00
20030 719866.00
17750 534973.00
