The publishing company recently came up with some additional data for the 15 books in the original sample.

Two new variables, production expenditures 1x52 and number of prepublication reviewers 1x62, have been added. These additional data are as follows:

Book x5 ($) x6 1 38,000 5 2 86,000 8 3 59,000 3 4 80,000 9 5 29,500 3 6 31,000 3 7 40,000 5 8 69,000 4 9 51,000 4 10 34,000 6 11 20,000 2 12 80,000 5 13 60,000 5 14 87,000 8 15 29,000 3 Incorporating these additional data, calculate the correlation between each of these additional variables and the dependent variable, book sales.

a. Test the significance of the correlation coefficients, using a = 0.05. Comment on your results.

b. Develop a multiple regression model that includes all six independent variables. Which, if any, variables would you recommend be retained if this model is going to be used to predict book sales for the publishing company? For any statistical tests you might perform, use a significance level of 0.05.

Discuss your results.

c. Use the F-test approach to test the null hypothesis that all slope coefficients are 0. Test with a significance level of 0.05. What do these results mean? Discuss.

d. Do multicollinearity problems appear to be present in the model? Discuss the potential consequences of multicollinearity with respect to the regression model.

e. Discuss whether the standard error of the estimate is small enough to make this model useful for predicting the sales of textbooks.

f. Plot the residuals against the predicted value of y and comment on what this plot means relative to the aptness of the model.

g. Compute the standardized residuals and form these into a frequency histogram. What does this indicate about the normality assumption?

h. Comment on the overall aptness of this model and indicate what might be done to improve the model.

The following information applies to Exercises 15-70 through 15-79.

The J. J. McCracken Company has authorized its marketing research department to make a study of customers who have been issued a McCracken charge card. The marketing research department hopes to identify the significant variables that explain the variation in customer purchases. Once these variables are determined, the department intends to try to attract new customers who are predicted to make a high volume of purchases.

Twenty-five customers were selected at random, and values for the following variables are recorded in the file called McCracken:

y = Average monthly purchases 1in dollars2 at McCracken x1 = Customer age x2 = Customer family income x3 = Family size