Take the DDK2011 dataset (full sample). Use a quadratic spline to estimate the regression of testscore on percentile.

(a) Estimate five models: (1) no knots (a quadratic); (2) one knot at 50; (3) two knots at 33 and 66;

(4) three knots at 25, 50 & 75; (5) knots at 20, 40, 60, & 80. Plot the five estimates. Intrepret your findings.

(b) Select a model. Consider using leave-cluster-one CV.

(c) For your selected specification plot the estimated regression function along with 95% pointwise confidence intervals. [Use cluster-robust standard errors.] Intrepret your findings.