You have access to a UK university dataset of 1632 students who recently completed their studies. For each student, the dataset reports information on the following variables: 1. Overall Average: This represents the overall degree average mark at the end of the student's study 2. Household income: Student's average family household income 3. Polar: Represents whether the student lives in a deprived area (i.e., an area with low higher education participation rate). This is a dummy variable (1=yes lives in a deprived area; 0=Does not live in a deprived area). 4. Gender: This is a dummy variable (1-female;0=male) 5. EconDegree: This is a dummy variable (1-student studied an Economics degree; 0=Student did not study an Economics degree) 6. Disability: Whether the student has a disability or not. This is a dummy variable (1=declared disability;0=No declared disability) 7. Bursary10: Whether the student received a bursary during their studies. A bursary is awarded to a student from a low-income family. This is a dummy variable (1=Bursary; 0=No Bursary) 8. White: A dummy variable representing ethnic background of student (1-white; 0=other ethnic background) You are interested in studying whether household income is an important determinant of students performance. To this end, you run the following regression 1 on a smaller subsample of 178 people (out of total 1632): (1) overallaverage, = a + a, HouseholdIncome, + & Look at the regression output in Table 1 and answer the following questions: a) Comment on the R-squared and Adjusted R-squared displayed in the regression output. How can the value of the R-squared be increased? (5 marks) b) Write down the estimated form of your regression. Carefully interpret the estimated coefficients and comment on their significance. Are they in line with your expectations? Explain why. (5 marks) c) Comment on the F-test. Describe what it measures and what it tells you about your regression model. Do you think you need to adjust the model? If yes, what would you suggest? If no, why not? (5 marks) Table 1: output of regression 1 Overall Average Household Income cons No.of Obs 178 Coefficient F(1,176) 0.92 -9.00-06 4.287 Standard Error 6.72e-06 Prob > F 0.402 0.095 R-squared 0.0104 t value P>It -1.34 45.12 Adi R-Squared -0.0010 0.182 0.000 Root MSE 0.1351