Pelican Stores, a division of National Clothing, is a chain of women's apparel stores operating throughout the country. The chain recently ran a promotion in which discount coupons were sent to customers of other National Clothing stores. Data collected for a sample of 100 in-store credit card transactions at Pelican Stores during one day while the promotion was running are below.

The Proprietary Card method of payment refers to charges made using a National Clothing charge card. Customers who made a purchase using a discount coupon are referred to as promotional customers and customers who made a purchase but did not use a discount coupon are referred to as regular customers. Because the promotional coupons were not sent to regular Pelican Stores customers, management considers the sales made to people presenting the promotional coupons as sales it would not otherwise make. Of course, Pelican also hopes that promotional customers will continue to shop at its stores.

Most of the variables in the worksheet are self-explanatory, but two of the variables require some clarification. "Items" is the total number of items purchased. "Net Sales" is the total amount of dollars charged to the credit card.

Pelican's management would like to use these sample data to learn about its customer base and to evaluate the promotion involving discount coupons.

Run a regression using Net Sales as the dependent variable and all of the other variables as independent variables. Assume that males, single customers, regular customers and those using a Proprietary Card represent the base cases.

A. What do you estimate the net sales to be for the case where the customer is a 35-year old single female who is a promotional customer and uses a MasterCard to buy 4 items? Give your answer to 2 decimal places.

B. Is the overall model significant at the .05 level of significance?

C. What is the p-value that you used to test the hypothesis in the previous question? Use 3 significant figures to enter your answer. (Because the answer to this question requires scientific notation, use the following example to guide how you report your answer. If the answer were 1.2286x10^-5, you would enter your answer as 1.23E-05. So enter 3 numbers before the letter E and 2 numbers after the negative sign.)

D. All other things being equal, what do you estimate the change in Net Sales is for a Promotional customer compared to a Regular customer? Be sure to include the sign of your estimate. (You don't need to enter "+" if the number is positive, but do add the minus sign if it is negative.) Give your answer to 2 decimal places.

E. Is the difference in Net Sales between a promotional and a regular customer significant at the .05 level of significance?

F. What is the p-value you used to answer the previous question? Use 3 significant figures to enter your answer. (Because the answer to this question requires scientific notation, use the following example to guide how you report your answer. If the answer were 1.2286x10-5, you would enter your answer as 1.23E-05. So enter 3 numbers before the letter E and 2 numbers after the negative sign.)

G. Give the lower end of a 95% interval estimate of the change in net sales for a customer using MasterCard vs. one using a Proprietary Card. Assume that all other independent variables remain constant. Be sure to include the sign of your estimate. (You don't need to enter "+" if the number is positive, but do add the minus sign if it is negative.) Give your answer to 2 decimal places.

H. Give the upper end of a 95% interval estimate of the change in net sales for a customer using MasterCard vs. one using a Proprietary Card. Assume that all other independent variables remain constant. Be sure to include the sign of your estimate. (You don't need to enter "+" if the number is positive, but do add the minus sign if it is negative.) Give your answer to 2 decimal places.

I. Use your regression output from the previous question to answer this one. Using the appropriate plot(s), check the linearity and equal variance assumptions. What do you conclude?

1. The plot shows a curved pattern, so the linearity assumption is broken. The spread in the data points appears to remain constant, however, so the equal variance assumption is met.

2. The plot shows a curved pattern, so the linearity assumption is broken. The spread in the data points is changing also, so the equal variance assumption is broken.

3. The plot shows no curved pattern, so the linearity assumption is met. The spread in the data points appears to change as we move across the x-axis, however, so the equal variance assumption is broken.

4. There is no discernible curvature or change in spread, so both the linearity and the equal variance assumptions are met.

J. Use Excel to do an informal check on the normality assumption. What is the frequency of the highest bar in your histogram?

K. Based on your informal check from the previous question, say whether you believe the following conclusion is true or false. "The normality assumption is met."