This problem uses the trade.union data in the SemiPar package. (a) Plot the wage as a function of age using a dierent plotting symbol for the...

5. This problem uses the trade.union data in the SemiPar package.

(a) Plot the wage as a function of age using a different plotting symbol for the different union membership of the world.

(b) Determine a transformation on the response wage to facilitate linear modeling with age and union membership as predictors.

(c) Fit a linear model regressing transformed wage on age and union membership. What is the relationship of age and union membership to wage?

(d) State the null and alternative hypotheses for the overall F-test for the model in (c). Perform the test and summarize results.

(e) Explain the practical meaning of the hypothesis H0 : βunion.member = βage×union.member = 0, where βage×union.member is the slope parameter for the interaction term of age and union membership