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, X₁. Using a separate plot symbol or color, add daily gross sales and items sold for credit card purchases, X₂. Visually compare the relationship between sales and number of items sold for cash with that for credit card purchases.

b. Define the dummy variable

and fit the regression

Y = β₀ + β₁X₁ + β₂X₂ + ε

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.

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