15. We might expect credit card purchases to differ from cash purchases at the same store. Table P-15 contains daily gross sales and items sold for cash purchases and daily gross sales and items sold for credit card purchases at the same consignment store for 25 consecutive days.

a. Make a scatter diagram of daily gross sales, Y, versus items sold for cash purchases, . Using a separate plot symbol or color, add daily gross sales and items sold for credit card purchases, . Visually compare the relationship between sales and number of items sold for cash with that for credit card purchases.

TABLE P-15 Day Gross Cash ($) Number of Items Gross Credit Card ($) Number of Items 1 348 55 148 4 2 42 8 111 6 3 61 9 62 7 4 94 16 0 0 5 60 11 39 5 6 165 26 7 1 7 126 27 143 26 8 111 19 27 5 9 26 5 14 2 10 109 18 71 12 11 180 27 116 21 12 212 36 50 9 13 58 10 13 2 14 115 20 105 16 15 15 8 19 3 16 97 15 44 14 17 61 10 0 0 18 85 15 24 3 19 157 24 144 10 20 88 15 63 11 21 96 19 0 0 22 202 33 14 3 23 108 23 0 0 24 158 21 24 4 25 176 43 253 28

b. Define the dummy variable and fit the regression model

c. Analyze the fit in part

b. Be sure to include an analysis of the residuals. Are you happy with your model?

d. Using the fitted model from part

b, generate a forecast of daily sales for an individual that purchases 25 items and pays cash. Construct a large-sample 95% prediction interval for daily sales.

e. Describe the nature of the fitted function in part

b. Do you think it is better to fit two separate straight lines, one for the cash sales and another for the credit card sales, to the data in Table P-15? Discuss.