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. The following results are shown
Store Size (Sq. Ft)Average Monthly Sales
17400…………………………..$581,241.00
15920…………………………..$538,275.00
17440…………………………..$636,059.00
17320…………………………..$574,477.00
15760…………………………..$558,043.00
20200…………………………..$689,256.00
15280…………………………..$552,569.00
17000…………………………..$584,737.00
11920…………………………..$470,551.00
12400…………………………..$520,798.00
15640…………………………..$619,703.00
12560…………………………..$465,416.00
21680…………………………..$730,863.00
14120…………………………..$501,501.00
16680…………………………..$624,255.00
14920…………………………..$567,043.00
18360…………………………..$612,974.00
18440…………………………..$618,122.00
16720…………………………..$691,403.00
19880…………………………..$719,275.00
17880…………………………..$536,592.00
a. Develop a simple linear regression model to explain the variation in average monthly sales based on the size of the store.
b. Construct and interpret a 95% confidence interval estimate for the regression slope coefficient.
c. Provide a 90% confidence interval for the average value of monthly sales when xp = 15,000.
d. Provide a 90% prediction interval for a particular month’s average sales when the store size is 15,000 square feet.