Transform the variable mother_educ so that it can be included in a regression. Generate the variable ln_birth_weight as the natural logarithm of birth_weight. Generate the variable age_mothersq as the square of age_mother.
Append means, standard deviations, minima and maxima of these new variables that you generated to your table of descriptive statistics from (a).
Estimate a multiple linear regression model of score on black, siblings, age_mother, age_mothersq, female, ln_birth_weight, age_child and mother’s education, remembering to avoid the dummy variable trap.
Provide the results of your estimation in the second column of your regression results table.
How do you interpret the estimated coefficient on ln_birth_weight?
Based on the signs of the second order polynomial in mother_age, how does the effect of mother_age on predicted score change with increasing age of the mother?
Test whether the effect of age_mother on score is in fact nonlinear (5% level). Do the six steps and state all your assumptions.
Test whether there is a relationship between mother’s education and score (5% level). Report the results of the auxiliary regression that you need to run in the third column of your table. Do the six steps and state all your assumptions.
Answer the following questions using the third column of your regression results table.
Interpret the coefficient on black.
Conduct a hypothesis test of whether black infants have lower mental ability scores than white infants, holding the other independent variables in your model fixed. Do the six steps and state all your assumptions.
Compare your findings from part (b)(i) and (b)(iii) with your findings from part (d)(i) and d(ii). Explain any potential differences by making reference to what you have learned about omitted variables bias.
