Take the cps09mar dataset (full sample).

(a) Estimate quadratic spline regressions of log(wage) on education. Estimate four models: (1) no knots (a quadratic); (2) one knot at 10 years; (3) three knots at 5, 10, and 15; (4) four knots at 4, 8, 12, & 16. Plot the four estimates. Intrepret your findings.

(b) Compare the four splines models using either cross-validation or AIC. Which is the preferred specification?

(c) For your selected specification plot the estimated regression function along with 95% pointwise confidence intervals. Intrepret your findings.

(d) If you also estimated a polynomial specification do you prefer the polynomial or the quadratic spline estimates?