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.
a. The "novel" variable is a categorical variable.
b. To find the multiple linear regression equation, we need to use the given data and perform a regression analysis. This analysis will help us estimate the equation that relates the Gross Earnings to Production Costs, Promotion Costs, and whether the movie is based on a bestseller novel. The equation will have the form:
Gross Earnings = β0 + β1 * Production Cost + β2 * Promotion Cost + β3 * Novel
c. To find the regression coefficients for each X variable, we can use statistical software or Excel. These coefficients are estimates of the impact of each independent variable on the dependent variable.
Interpretation of regression coefficients:
- β1: This coefficient represents the estimated change in Gross Earnings for a one-unit increase in Production Cost, holding all other variables constant.
- β2: This coefficient represents the estimated change in Gross Earnings for a one-unit increase in Promotion Cost, holding all other variables constant.
- β3: This coefficient represents the estimated difference in Gross Earnings between movies based on a bestseller novel and movies not based on a bestseller novel, holding all other variables constant.
d. We cannot determine whether Jean will be pleased with the results without additional information. It depends on the significance and strength of the regression coefficients, the overall fit of the model, and the purpose or criteria for the analysis.
e. The intercept value is denoted as β0 in the linear regression equation. It represents the estimated Gross Earnings when all independent variables (Production Cost, Promotion Cost, and Novel) are zero or not applicable. In this case, it could represent the baseline or minimum expected Gross Earnings.