Question #3 [40 Points] a. [6 Points] Suppose now that you suspect nonlinearity in the wage and tenure relationship as well as in the wage and exper relationship. So, i) how would you check for nonlinearity, both informally and formally (you do not need to actually perform the test), in the relationship between wage and tenure, and using the same approaches, in the relationship between wage and exper, ii) Plot the two way scatter plot between wage and tenure as well as between wage and exper, and iii) Report your observations based on these plots. b. [6 Points] Creating variables that you might need along the way, i) run a regression of wage on educ exper, tenure, expersq, expercube (i.e., the cubic term of years of experience), tenuresq, and tenurecube (i.e., the cubic term of years with current employer); and ii) run a similar regression without the cubic terms. Conduct a formal test for linearity between wage and tenure as well as wage and exper using both (i) and (ii) regressions. Report your findings. c. [10 Points] Suppose now you want to estimate percentage changes given your dataset. One way of estimating elasticities is by using logarithmic functions/models. Run the following three versions of logarithmic models and interpret the slope parameters. i. Log - linear model: Run a regression of log(wage) on educ exper, tenure, nonwhite, female, married, smsa, south, and west. Interpret the coefficients on educ, exper, and tenure. ii. Linear - log model: Run a regression of wage on log (educ), log(exper), log(tenure), nonwhite, female, married, smsa, south, and west. Interpret the coefficient on log(educ), log(exper), and log(tenure). iii. Log - log model: Run a regression of log (wage) on log (educ), log(exper), log(tenure), nonwhite, female, married, smsa, south, and west. Interpret the coefficient on log(educ), log(exper), and log(tenure). Why do you think that the sample size decreases between (i) and (ii) or (ii)