Question

2. A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0 =female, 1 = male) and job type (0 =clerical, 1 = technical). The following ANOVA summarizes the regression results:

1. Based on the ANOVA and a 0.05 significance level, the global null hypothesis test of the multiple regression model
A. Will be rejected and conclude that monthly salary is related to all of the independent variables
B. Will be rejected and conclude that monthly salary is related to at least one of the independent variables.
C. Will not be rejected.
D. Will show a high multiple coefficient of determination.

2. Based on the ANOVA, the multiple coefficient of determination is:
A. 5.957%
B. 59.3%
C. 40.7%
D. cannot be computed

3. Based on the hypothesis tests for the individual regression coefficients,
A. All the regression coefficients are not equal to zero.
B. "job" is the only significant variable in the model.
C. Only months of service and gender are significantly related to monthly salary.
D. "service" is the only significant variable in the model

4. In the regression model, which of the following are dummy variables?
A. Intercept
B. Service
C. Service and gender
D. Gender and jobE. Service, gender, and job

5. The results for the variable gender show that
A. males average $222.78 more than females in monthly salary
B. females average $222.78 more than males in monthly salary
C. gender is not related to monthly salary
D. Gender and months of service are correlated

6. Based on the hypothesis tests for individual regression coefficients,
A. All regression coefficients should remain in the regression equation
B. Based on the standard errors, the variable, service, should not be included in the regression equation.
C. Based on the p-values, the variable, job, should not be included in the regression equation.
D. The relationship between monthly salary and gender is linear.

Answer 1

1. By using excel function \(=\operatorname{FDIST}(5.96,3,26),\) the \(\mathrm{p}\) -value \(=0.0031 .\) Since p-value \(<0.05,\)reject the null hypothesis. The correct option is: B. Will be rejected and conclude that monthly salary is related to at least one of the independent variables.

2. \(R^{2}=\frac{S S R}{S S T}=\frac{1004346.771}{2465481.367}=0.407=40.7 \%\)

The correct option is: C. \(40.7 \%\)

3. P-value for Job is greater than 0.05. In contrast, p-values for service and gender are less than \(0.05 .\) Therefore, the job is not significantly related to a monthly salary. The correct option is C. Only months of service and gender are significantly related to a monthly salary.

4. In the regression model, gender and job are categorical variables and coded as 0 and \(1 .\) The correct option is: D. Gender and job

5. The coefficient for gender is 222.78, and males are coded as gender \(=1 .\) Therefore, males' average salary is \(\$ 222.78\) more than the female's average salary. The correct option is: A. males average \(\$ 222.78\) more than females in monthly salary

6. P-value for Job is greater than 0.05 while p-values for service and gender are less than \(0.05 .\) Therefore, the job is not significantly related to a monthly salary. The correct option is: C. Based on the p-values, the variable, job, should not be included in the regression equation.