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A multiple regression model was developed to predict initial salary after graduation (in thousands of dollars ($K)) based on two independent variables Gender (Dummy/Categorical Variable;

A multiple regression model was developed to predict initial salary after graduation (in thousands of dollars ($K)) based on two independent variables Gender (Dummy/Categorical Variable; Female student '0'; Male Student '1') and Cumulative GPA (on a scale of 4.0)of 13 graduating students. Part of the regression results is shown below. Based on the partial Excel regression output provided below answer the following questions.

Regression Statistics

Multiple R

R Square

Adjusted R Square

Standard Error

1.53

Observations

13

ANOVA

df

SS

MS

F

Significance F

Regression

704.74

Residual

Total

728

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

38.01

1.23

30.80

0.00

35.26

40.76

Gender

0.39

0.85

GPA

8.31

0.48

A. Use the above results and write the multiple regression equation that can be used to predict initial salary and interpret the statical meaning of the estimated slope coefficient b2 (forGPA).

B. Based on the multiple regression equation, estimate the initial salary for a male student with a cumulative GPA of 3.0. Give your answer in dollars. Please show all the relevant calculations.

C. At = 0.05, test to determine through an F-test if the fitted regression equation represents a significant relationship between the independent variables and the dependent variable. Please show all the relevant calculations.

D. At = 0.05, test to see through a t-test if 2( for GPA) is significantly different from zero. Please show all the relevant calculations.

E. Construct a 95% confidence interval for 1 (Gender). Based on the confidence interval indicate whether the independent variable Gender is statistically significant and explain why. Please show all the relevant calculations.

F. Compute the adjusted coefficient of determination (Adj R^2). Please show all the relevant calculations.

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