5. Let's return to the model of financial aid awards at a liberal arts college that was first introduced in Section 2.2. In that section, we estimated the following equation (standard errors in parentheses): FINAIDi=89270.36PARENTi+87.4HSRANKi(0.03)(20.7)t=11.264.22R2=.73N=50 where: FINAID i= the financial aid (measured in dollars of grant) awarded to the i th applicant PARENT i= the amount (in dollars) that the parents of the i th student are judged able to contribute to college expenses HSRANK i= the i th student's GPA rank in high school, measured as a percentage (ranging from a low of 0 to a high of 100 ) a. Create and test hypotheses for the coefficients of the independent variables. b. What econometric problems do you see in the equation? Are there any signs of an omitted variable? Of an irrelevant variable? Explain your answer. c. Suppose that you now hear a charge that financial aid awards at the school are unfairly tilted toward males, so you decide to attempt to test this charge by adding a dummy variable for gender (MALEi=1 if the i th student is a male, 0 if female) to your equation, getting the following results: INAIDINAIDi=98130.34PARENTi+83.3HSRANKi1570MALEi(0.03)t=10.88(20.1)4.13(784)R2=.75N=502.00 d. Carefully explain the real-world meaning of the estimated coefficient of MALE. What would Equation 6.21 look like if you used FEMALE ( =1 if the i th student is a female and 0 otherwise) instead of MALE in the equation? (Hint: Be specific.) e. Which equation is better, Equation 6.20 or Equation 6.21 ? Carefully use our four specification criteria to make your decision, being sure to state which criteria support which equation and why