Multiple regression analysis problem | Numerical analysis homework help

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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