Problem 1: The following table shows the regression output of a multiple regression model relating the beginning salaries in dollars of employees in a given company to the following predictor variables:
Sex: An indicator variable (1 = man 0 = woman)
Education: Years of schooling at the time of hire
Experience: Number of months of previous work experience
Months: Number of months with company
ANOVA Table:
|
Source
|
Sum of squares
|
d.f.
|
Mean Square
|
F-test
|
|
Regression
|
23665352
|
4
|
5916338
|
22.98
|
|
Residuals
|
22657938
|
88
|
257477
|
|
Coefficients table:
|
Variable
|
Coefficients
|
s.e.
|
t-test
|
p-value
|
|
Constant
|
3526.4
|
327.7
|
10.76
|
0.000
|
|
Sex
|
722.5
|
117.8
|
6.13
|
0.000
|
|
Education
|
90.02
|
24.69
|
3.65
|
0.000
|
|
Experience
|
1.2690
|
0.5877
|
2.16
|
0.034
|
|
Months
|
23.406
|
5.201
|
4.50
|
0.000
|
|
N = 93
|
R2 = 0.515
|
Ra2 = 0.489
|
S = 507.4
|
|
1. Conduct an F-test for the overall fit of the regression?
2. Is there a positive linear relationship between Salary and Experience, after accounting for the effect of the variable Sex, Education and Months?
3. What salary would you forecast for a man with 12 years of education, 10 months of experience and 15 months with company?
Problem 2: Now consider a reduced model in which Salary is regressed on Education only. The ANOVA table obtained when fitting this model is shown below. Conduct a single test to compare the full and reduced models at α = 0.05 level. What conclusion can be drawn from the result of the test?
ANOVA Table:
|
Source
|
Sum of squares
|
d.f.
|
Mean Square
|
F-Test
|
|
Regression
|
7862535
|
1
|
7862535
|
18.6
|
|
Residuals
|
38460756
|
91
|
422646
|
|