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) What percent of the variation in box office receipts can be attributed to the corresponding variation in production costs? (Use 1 decimal place.) _____ % b) Perform a regression analysis with x1 as the response variable. Use x2, x3, and x4 as explanatory variables. Look at the coefficient of multiple determination. What percentage of the variation in x1 can be explained by the corresponding variations in x2, x3, and x4 taken together? (Use 1 decimal place.) ______% c) Write out the regression equation. (Use 2 decimal places.) x1 = _____+ _____x2 + _____x3 + _____x4
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) What percent of the variation in box office receipts can be attributed to the corresponding variation in production costs? (Use 1 decimal place.)
_____ %
b) Perform a
c) Write out the regression equation. (Use 2 decimal places.)
x1 = _____+ _____x2 + _____x3 + _____x4
a.
The percent of variation in box office receipts can be attributed to the corresponding variation in production costs
R2(x1, x2)
84.2%
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