Question
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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