5. You are asked by the US Department of Education to provide an analysis of what influences education levels across the country. You use data from the 1980HighSchool and Beyond Surveywhich consists a random sample of students who graduated 10 years ago from 1100 high schools, totaling 3,796 respondents.

You obtain one dependent variable: years of education completed (Educ)

You have the following explanatory variables:

1. A binary variable indicating gender where 1=female and 0=male (Female),
2. A variable indicating the distance from the closest 4-year college in miles (Distance)
3. A categorical variable for the education level of parents, with 4 options (Parentcoll):
   1. Both father and mother are college graduates (Bothcoll)
   2. Only the father is a college graduate (Fathercoll)
   3. Only the mother is a college graduate (Mothercoll)
   4. Both father and mother are not college graduates (Notcoll)

(a) Write down the equation for the multivariate regression you would run given the information above. Notate your true coefficients associated with X variables (label them clearly) as b1, b2,... and so on. Notate your constant as b0.

Answer the following questions using the regression results.

Regression results:

Regression Statistics Multiple R 0.3212 R Square 0.1032 Adjusted R Square 0.1020 Standard Error 1.7190 Observations 3796 Coefficients SE t Stat P-value Lower 95% Upper 95% Intercept 13.57 0.05 265.104 0.0000 13.467 13.667 Female 0.03 0.06 a 0.6091 -0.081 0.139 Distance -0.04 0.01 -3.169 b -0.068 -0.016 Bothcoll 1.60 0.10 16.163 0.0000 d Fathercoll 1.16 0.09 C 0.0000 0.985 1.337 Mothercoll 0.91 0.13 6.974 0.0000 0.651 1.160