The MBA program at a large university is facing a pleasant problem-too many applicants. The current admissions policy requires students to have completed at least 3 years of work experience and an undergraduate degree with a B-average or better. Until 3 years ago, the school admitted any applicant who met these requirements. However, because the program recently converted from a 2-years program (four semesters) to a 1-year program (three semesters), the number of applicants has increased substantially. The dean, wants to raise the admissions standards by developing a method that more accurately predicts how well an applicant will perform in the MBA program. She believes that the primary determinants of success are the following: Undergraduate grade point average (GPA) Graduate Management Admissions Test (GMAT) She randomly sampled students who completed the MBA and recorded their MBA program GPA, as well as the two variables listed here. a. Estimate the relationship between mba_GPA, ug_GPA and GMAT using OLS; that is, obtain the intercept and slope estimates in the equation (Note: use Matrix approach) mba_GPA=^0+^1ugGPA+^2GMAT Comment on the direction of the relationship between the variables. Does the intercept have a useful interpretation here? Explain. How much higher is the mba_GPA predicted to be if the GMAT score is increased by five points? Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero. What is the predicted value of mba_GPA when GMAT =500 and ug_GPA =10.5 1. How much of the variation in mba_GPA for these six students is explained by ug_GPA and GMAT? Explain