Chapter 13(II): Homework
5 ADAPTED. The owner of Showtime Movie Theaters, Inc. would like to estimate weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.
Weekly Gross Television Newspaper Radio
Revenue Advertising Advertising Advertising
($1000s) ($1000s) ($1000s) ($1000s)
96 5 1.5 0.3
90 2 2 0.2
95 4 1.5 0.3
92 2.5 2.5 0.1
95 3 3.3 0.4
94 3.5 2.3 0.4
94 2.5 4.2 0.3
94 3 2.5 0.3
a) Develop an estimated regression equation in Excel with the amount of television advertising as the independent variable
b) Develop an estimated regression equation in Excel with both television advertising and newspaper advertising as the independent variables
c) Develop an estimated regression equation in Excel with all three independent variables: television advertising, newspaper advertising, and radio advertising
d) Is the estimated regression equation coefficient for television advertising expenditures the same in par a), in part b) and in part c)? Interpret the coefficient in each case
e) Obtain and compare the multiple coefficient of determination and the adjusted multiple coefficient of determination for parts a), b) and c). How does the coefficient of determination changes as a result of adding more independent variables in the equation?
f) What is the estimate of the weekly gross revenue for a week when $3500 is spent on television advertising, $1800 is spent on newspaper advertising, and $350 in radio advertising?
g) Use the F test to determine the overall significance of the relationship. What is the conclusion at the .05 level of significance?
h) Use the t test to determine the significance of each independent variable. What is your conclusion at the .05 level of significance?
i) Determine the sample correlation coefficient between all possible pairs of independent variables to measure multicollinearity. Is there any value high enough to predict any potential problem in the regression model? Explain