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: 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): overallaverage; = do + a, HouseholdIncome; + &; Table 1: output of regression 1 Overall Average Coefficient Standard Error t value P> It] Household Income -9.00e-06 6.72e-06 -1.34 0.182 cons 4.287 0.095 45.12 0.000 No.of Obs F (1,176) Prob > F R-squared Adi R-Squared Root MSE 178 0.92 0. 182 0.0104 -0.0010 0.1351 a) 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