mathematics

ULTIPLE 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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