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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?