The per-store daily customer count (i.e., the mean number of customers in a store in one day) for a nationwide convenience store chain that operates nearly 10,000 stores has been steady, at 900, for some time. To increase the customer count, the chain is considering cutting prices for coffee beverages. The question to be determined is how much prices should be cut to increase the daily customer count without reducing the gross margin on coffee sales too much.You decide to carry out an experiment in a sample of 24 stores where customer counts have been running almost exactly at the national average of 900. In 6 of the stores, the price of a small coffee will now be $0.59, in 6 stores the price of a small coffee will now be $0.69, in 6 stores, the price of a small coffee will now be $0.79, and in 6 stores, the price of a small coffee will now be $0.89. After four weeks at the new prices, the daily customer count in the stores is determined and is stored in CoffeeSales2.
a. Construct a scatter plot for price and sales.
b. Fit a quadratic regression model and state the quadratic regression equation.
c. Predict the weekly sales for a small coffee priced at 79 cents.
d. Perform a residual analysis on the results and determine whether the regression model is valid.
e. At the 0.05 level of significance, is there a significant quadratic relationship between weekly sales and price?
f. At the 0.05 level of significance, determine whether the quadratic model is a better fit than the linear model.
g. Interpret the meaning of the coefficient of multiple determination.
h. Compute the adjusted r2.
i. Compare the results of (a) through (h) to those of Problem 11.11 on page 428.