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, + e 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 E(1,176) Prob > F R-squared Adi R-Squared Root MSE 178 0.92 0.182 0.0104 -0.0010 0.1351 We decided to run a different regression model 2 using full sample. The dependent variable is Overall Average and Polar, Disability, Household income (and its second polynomial), Bursary10 and White are independent variables. The regression output can be seen in table 2 below. OverallAverage, = do + a, Polari + a2 Disability; + a;HouseholdIncome, + a,Householdincomer + asBursary10; + aWhite, + e Table 2: output of regression 2 Overall Average Coefficient Standard Error t value P > It Polar 2.572 0.335 7.69 0.000 Disability -0.013 0.029 -0.45 0.656 Household Income 0.272 0.050 5.38 0.000 Household Income2 0.039 0. 199 -0.20 0.844 Bursary 10 -0.034 0.027 -1.26 0.209 White 0.007 0.024 0.29 0.771 cons 5.279 0.829 .29 0.000 Me of abs E(6, 1624) Prob > F R-squared Adi R-Squared Root MSE 1631 16.30 0.000 0.0568 0.0533 3.995 a) Compare regression 2 to regression 1. Is one regression better than the other? Explain why yesot. Consider all possible aspects. (10 marks)