4. Wage variation by age—modeling age as a polynomial term. [20 marks] a. Run the following regression: wage = f (age, age2 , education, sex, part-time status, year) report and discuss regression results. b. Compare the fit of the linear model (3.a) and the quadratic model (4.a) by comparing the residual plots. Do you see any differences? c. Add a cubic term for age to the regression above (4.a), run, report, discuss, and note any differences from the quadratic model. d. Add a quartic (fourth-order) term for age to the regression above (4.c), run, report, discuss, and note any differences from the quadratic or cubic models e. Rerun the above two regressions with cubic and quartic age terms (4.c and 4.d), but now use a scaled version of the numeric age variable. Create the new scaled age variable, age—mean(age) ages, defined as Report results and comment, and compare to unscaled estimates. f. Estimate the basic regression from question 3.a but use a fractional polynomial model on age. Compare regression results to the quadratic, cubic and quartic models (4.a, 4.c, and 4.d). g. To put all the models to a more practical test, generate four sets of predicted wages (emmeans) by age using quadratic, cubic, quartic and fractional polynomial models of age. Comment on results, and comment on how much explanation is provided by adding in the higher-order polynomial terms.
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