A motion picture industry analyst is studying movies based on epic novels. The following data were obtained for 10 Hollywood movies made in the past five years. Each movie was based on an epic novel. For these data, x1 = first-year box office receipts of the movie, x2 = total production costs of the movie, x3 = total promotional costs of the movie, and x4 = total book sales prior to movie release. All units are in millions of dollars. x1 x2 x3 x4 85.1 8.5 5.1 4.7 106.3 12.9 5.8 8.8 50.2 5.2 2.1 15.1 130.6 10.7 8.4 12.2 54.8 3.1 2.9 10.6 30.3 3.5 1.2 3.5 79.4 9.2 3.7 9.7 91.0 9.0 7.6 5.9 135.4 15.1 7.7 20.8 89.3 10.2 4.5 7.9   a) Suppose Hollywood is planning a new epic movie with projected box office sales x1 = 100 million and production costs x2 = 12 million. The book on which the movie is based had sales of x4 = 9.2 million. Forecast the dollar amount (in millions) that should be budgeted for promotion costs x3 and find an 80% confidence interval for your prediction. prediction   lower limit   upper limit     b) Construct a new regression model with x3 as the response variable and x1, x2, and x4 as explanatory variables. (Use 2 decimal places.) x3 =  ___+  ____x1 +  ____x2 + ____x4

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 65P
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A motion picture industry analyst is studying movies based on epic novels. The following data were obtained for 10 Hollywood movies made in the past five years. Each movie was based on an epic novel. For these data, x1 = first-year box office receipts of the movie, x2 = total production costs of the movie, x3 = total promotional costs of the movie, and x4 = total book sales prior to movie release. All units are in millions of dollars.

x1 x2 x3 x4
85.1 8.5 5.1 4.7
106.3 12.9 5.8 8.8
50.2 5.2 2.1 15.1
130.6 10.7 8.4 12.2
54.8 3.1 2.9 10.6
30.3 3.5 1.2 3.5
79.4 9.2 3.7 9.7
91.0 9.0 7.6 5.9
135.4 15.1 7.7 20.8
89.3 10.2 4.5 7.9

 

a) Suppose Hollywood is planning a new epic movie with projected box office sales x1 = 100 million and production costs x2 = 12 million. The book on which the movie is based had sales of x4 = 9.2 million. Forecast the dollar amount (in millions) that should be budgeted for promotion costs x3 and find an 80% confidence interval for your prediction.

prediction  
lower limit  
upper limit  

 

b) Construct a new regression model with x3 as the response variable and x1x2, and x4 as explanatory variables. (Use 2 decimal places.)


x3 =  ___+  ____x1 +  ____x2 + ____x4

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