Question 4 You are given the following model y = + 2x2 + . The predictor 2 is a categorical variable for marital status. A respondent is either married or not married. (a) Given the nature of 2; state the dummies that can be constructed from this cate- gorical variable {1 mark} (b) If n = 5 construct matrix X given the dummies in 4(a) above {2 marks] (c) Using the matrix X, identify two problems that one would experience if the variables in X were to be used as independent variables in a regression (4 marks} (d) State the three possible models that an investigator who is interested on the effect of marital status on wages would estimate to avoid the problems in 4(c) above {3 marks} (e) For one of the models with a constant find the conditional expectation of wages, married, 1 and wages, married, = 0 {2 marks} (f) Use the findings 4(e) above to provide the theoretical interpretation of 3 {1 mark} (g) After running the three models in 4(d) you obtain the following results. Use the results to answer the following questions: VARIABLES Married Not Married Constant Observations R-squared Standard errors in parentheses *** *p

You are given the following model yi=1+2x2i+i. The predictor x2i is a categorical variable for marital status. A respondent is either married or not married. (a) Given the nature of x2i state the dummies that can be constructed from this categorical variable {1 mark } (b) If n=5 construct matrix X given the dummies in 4(a) above {2 marks } (c) Using the matrix X, identify two problems that one would experience if the variables in X were to be used as independent variables in a regression {4 marks } (d) State the three possible models that an investigator who is interested on the effect of marital status on wages would estimate to avoid the problems in 4 (c) above {3 marks\} (e) For one of the models with a constant find the conditional expectation of wages i married i (f) Use the findings 4(e) above to provide the theoretical interpretation of 2{1 mark } (g) After running the three models in 4(d) you obtain the following results. Use the results to answer the following questions: 3 (i) Interpret the parameters in all the three models {3 marks } (ii) Does marriage boost earnings? \{1 mark } (h) The following results show the variance inflation factor for a given regression. What problem is this researcher experiencing? What solution would you advise this researcher to explore to deal with the problem? \{3 marks }