Question 2 (20 marks) The CSV file wage.csv contains 935 observations on the following variables: Wage Educ monthly earnings Years of education Years of work experience Exper Tenure Years of current employment married nonwhite =1 if married =1 if nonwhite Consider the following wage model. Download log (wage) = Bo+Beduci+Bexper;+ztenure;+4married,+B5nonwhite;+i, (1) Note that you need to use the natural logarithm for this question. (a) (4 marks) Using R, estimate the model in equation (1) and report the results in the usual way (as explained in the lectures). Intepret each coefficient estimate and comment on whether they are significantly different from zero. (b) (4 marks) Add the variable exper and tenure to the equation (1) and write out the new model. Explain why we would want to add these terms to the model above? Show that the corresponding coefficients are jointly insignificant at even the 20% level of significance. Show your reasoning. (c) (4 marks) Extend the original model in equation (1) to allow the effect of education to depend on race and write out the new model. Test whether the effect of education does actually depend on race. Show your reasoning. (d) (4 marks) Start again with the model in equation (1); now extend it to allow the effect of race depend on marital status. Rewrite the model, fit it, and use the answers to estimate the difference in wages between the following four groups: married and nonwhite, married and white, single and nonwhite, and single and white (relative to one of the groups, with all other variables kept constant). (e) (4 marks) Write a brief non-technical report to your supervisor (who does not understand any statistics) that summarises (a)-(d) (max 300 words).