Chapter Review Problems
13.73 Can you use movie critics’ opinions to forecast box office receipts on the opening weekend? The following data, stored in Tomatometer, indicate the Tomatometer rating, the percentage of professional critic reviews that are positive, and the receipts per theater ($thousands) on the weekend a movie opened for 10 movies:
Movie Tomatometer Rating Receipts
The Mummy 16 7.8
Zookeeper’s Wife 61 6.1
Beatriz at Dinner 80 28.4
The Hero 76 11.3
Wonder Woman 93 24.8
Baby Boss 52 13.3
The Circle 15 2.9
Dean 61 4.0
Baywatch 20 5.1
Churchill 38 1.9
Source:
“Top Box Office Movies – Rotten Tomatoes,” and “The Numbers – Weekend Box Office Chart for May 26th 2017,” bit.ly/2t0tqS6.
Use
Use
A. Use the least-squares method to compute the regression coefficients b0 and b1
B. Interpret the meaning of b0 and b1 in this problem.
C. Predict the mean receipts for a movie that has a Tomatometer rating of 55%.
D. Should you use the model to predict the receipts for a movie that has a Tomatometer rating of 5%? Why or why not?
E. Determine the coefficient of determination, and explain its meaning in this problem.
F. Perform a residual analysis. Is there any evidence of a pattern in the residuals? Explain.
At the 0.05 level of significance, is there evidence of a linear relationship between Tomatometer rating and receipts?
At the 0.05 level of significance, is there evidence of a linear relationship between Tomatometer rating and receipts?
H. Construct a 95% confidence interval estimate of the mean receipts for a movie that has a Tomatometer rating of 55% and a 95% prediction interval of the receipts for a single movie that has a Tomatometer rating of 55%.
I. Based on the results of (a)–(h), do you think that Tomatometer rating is a useful predictor of receipts on the first weekend a movie opens? What issues about these data might make you hesitant to use Tomatometer rating to predict receipts?
13.75 Measuring the height of a California redwood tree is very difficult because these trees grow to heights of more than 300 feet. People familiar with these trees understand that the height of a California redwood tree is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person. The data in Redwood represent the height (in feet) and diameter (in inches) at the breast height of a person for a sample of 21 California redwood trees.
A. Assuming a linear relationship, use the least-squares method to compute the regression coefficients and State the regression equation that predicts the height of a tree based on the tree’s diameter at breast height of a person.
B. Interpret the meaning of the slope in this equation.
C. Predict the mean height for a tree that has a breast height diameter of 25 inches.
D. Interpret the meaning of the coefficient of determination in this problem.
E. Perform a residual analysis on the results and determine the adequacy of the model.
F. Determine whether there is a significant relationship between the height of redwood trees and the breast height diameter at the 0.05 level of significance.
G. Construct a 95% confidence interval estimate of the population slope between the height of the redwood trees and breast height diameter.
H. What conclusions can you reach about the relationship of the diameter of the tree and its height?
Chapter Review Problems
14.71 Increasing customer satisfaction typically results in increased purchase behavior. For many products, there is more than one measure of customer satisfaction. In many, purchase behavior can increase dramatically with an increase in just one of the customer satisfaction measures. Gunst and Barry (“One Way to Moderate Ceiling Effects,” Quality Progress, October 2003, pp. 83–85) consider a product with two satisfaction measures, and , that range from the lowest level of satisfaction, 1, to the highest level of satisfaction, 7. The dependent variable, Y, is a measure of purchase behavior, with the highest value generating the most sales. Consider the regression equation:
14.71 Increasing customer satisfaction typically results in increased purchase behavior. For many products, there is more than one measure of customer satisfaction. In many, purchase behavior can increase dramatically with an increase in just one of the customer satisfaction measures. Gunst and Barry (“One Way to Moderate Ceiling Effects,” Quality Progress, October 2003, pp. 83–85) consider a product with two satisfaction measures, and , that range from the lowest level of satisfaction, 1, to the highest level of satisfaction, 7. The dependent variable, Y, is a measure of purchase behavior, with the highest value generating the most sales. Consider the regression equation:
Y i =-3.888+1.449x1i + 1.462x21i- 0.190x1i x2i
Suppose that is the perceived quality of the product and is the perceived value of the product. (Note: If the customer thinks the product is overpriced, he or she perceives it to be of low value and vice versa.)
A. What is the predicted purchase behavior when x1=2and X2=2
B. What is the predicted purchase behavior when x1=2 and x2=7
C. What is the predicted purchase behavior when x1=7 and x2=2
D. What is the predicted purchase behavior when x1=7 and x2 =7
E. What is the regression equation when x2=2 What is the slope x1 for now?
F. What is the regression equation when x2=7 What is the slope for x1 now?
G. What is the regression equation when x1=2 What is the slope for x2 now?
H. What is the regression equation when x1=7What is the slope for x2 now?
I. Discuss the implications of (a) through (h) in the context of increasing sales for this product with two customer satisfaction measures.
14.72 The owner of a moving company typically has his most experienced manager predict the total number of labor hours that will be required to complete an upcoming move. This approach has proved useful in the past, but the owner has the business objective of developing a more accurate method of predicting labor hours. In a preliminary effort to provide a more accurate method, the owner has decided to use the number of cubic feet moved and the number of pieces of large furniture as the independent variables and has collected data for 36 moves in which the origin and destination were within the borough of Manhattan in New York City and the travel time was an insignificant portion of the hours worked. The data are organized and stored in Moving.
A. State the multiple regression equation.
B. mnterpret the meaning of the slopes in this equation.
C. Predict the mean labor hours for moving 500 cubic feet with two large pieces of furniture.
D. Perform a residual analysis on your model and determine whether the regression assumptions are valid.
E. Determine whether there is a significant relationship between labor hours and the two independent variables (the number of cubic feet moved and the number of pieces of large furniture) at the 0.05 level of significance.
F. Determine the p-value in (e) and interpret its meaning.
G. Interpret the meaning of the coefficient of multiple determination in this problem.
H. Determine the adjusted r2
I. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.
J. Determine the p-values in (i) and interpret their meaning.
K. Construct a 95% confidence interval estimate of the population slope between labor hours and the number of cubic feet moved.
L. Compute and interpret the coefficients of partial determination.
M. What conclusions can you reach concerning labor hours?