3. The data file "MBA" (posted on Canvas) includes information from a sample of MBA students. MBAGPA refers to the GPA after the first semester of classes. GMAT refers to the entrance exam score at the time of admission. WORK refers to the number of years of work experience at the time of admission. GENDER is either male or female. DEGREE refers to the field in which the student holds an undergraduate degree. (a) Estimate a multiple regression model where GPA is the dependent variable and GMAT, WORK, GENDER and DEGREE are independent variables. Let "male" and "arts" represent the reference categories. Write down the estimated regression equation(s). (b) Construct and conduct appropriate hypothesis tests to determine which slope coefficients are statistically significant. Use a 5% level of significance. (c) Suppose two otherwise identical students had GMAT scores that differed by 50 points. What is the expected difference in their first-semester GPAs? (d) Construct a point estimate and 95% prediction interval for the predicted first-semester GPA of a female student with an undergraduate arts degree, GMAT of 500 and 6 years of work experience. (e) Is there a significant difference in GPA between business and engineering majors, all else equal? Adjust your regression model as needed to answer this question and use statistical reasoning