MULTIPLE REGRESSION ANALYSIS PROBLEM
MULTIPLE REGRESSION ANALYSIS
A motion picture industry analyst wants to estimate the gross earnings generated by a movie. The estimate will be based on different variables involved in the film’s production. The independent variables considered are X1 (COST) = production cost of the movie and X2 (PROM) = total costs of all promotional activities. A third variable that the analyst wants to consider is the qualitative variable of whether or not the movie is based on a book published before the release of the movie. This third qualitative variable is handled by the use of an indicator variable: X3 (BOOK) =1 if the movie is based on a book and 0 otherwise. The analyst obtains information on a random sample of 20 Hollywood movies made within the last five years. Data is give. The variable Y (EARN) is gross earnings, in millions of dollars. The two quantitative independent variables are also in millions of dollars.
Data given as under:
| EARN | COST | PROM | BOOK |
| 28 | 4.2 | 1 | 0 |
| 35 | 6 | 3 | 1 |
| 50 | 5.5 | 6 | 1 |
| 20 | 3.3 | 1 | 0 |
| 75 | 12.5 | 11 | 1 |
| 60 | 9.6 | 8 | 1 |
| 15 | 2.5 | 0.5 | 0 |
| 45 | 10.8 | 5 | 0 |
| 50 | 8.4 | 3 | 1 |
| 34 | 6.6 | 2 | 0 |
| 48 | 10.7 | 1 | 1 |
| 82 | 11 | 15 | 1 |
| 24 | 3.5 | 4 | 0 |
| 50 | 6.9 | 10 | 0 |
| 58 | 7.8 | 9 | 1 |
| 63 | 10.1 | 10 | 0 |
| 30 | 5 | 1 | 1 |
| 37 | 7.5 | 5 | 0 |
| 45 | 6.4 | 8 | 1 |
| 72 | 10 | 12 | 1 |
The applicable general regression model as given in the question is as under:
Predicted EARNings = a + b1*COST + b2*PROM + b3*BOOK + error term
As per the data fitted regression line is given as follows:
Y Hat (EARN) = 7.8362+ 2.8477 * COST + 2.2782 * PROM + 7.1661 * BOOK + 3.6895
Please answer the following:
a) How useful is the model overall?
b) Are all three independent variables relevant?
c) What gross earning does the model predict for a movie costing nothing to produce or promote, and that is not based on a book? How meaningful is this figure?
d) Explain the meaning of the estimate b1=2.85?
e) Can you reject the hypothesis that the underlying value of b1 =1?
f) What would this hypothesis imply?
g) Compare the estimated gross earnings of a movie costing $6m, with promotion cost of $3m based on a book, to that of a movie with identical costs, but not based on a book. Explain the meaning of b3?
h) An author’s association claims that the existence of a book increases gross earnings on average by at least $7.5m. Can you reject this hypothesis?
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