Comparing the kernel and local-linear estimators: To illustrate the reduced bias of the local-linear estimator in comparison to the kernel estimator, generate n ¼ 100 observations of artificial data according to the cubic regression equation Y ¼ 100 & 5 x

10 & 5

( ) þ

x 10 & 5

( )3

þ ε ð18:15Þ

where the X-values are sampled from the uniform distribution X ; Uð0; 100Þ, and the errors are sampled from the normal distribution ε ; Nð0; 202Þ. Draw a scatterplot of the data showing the true regression line EðYÞ ¼ 100 & 5ð Þþ x=10 & 5 ð Þ x=10 & 5 3

. Then, use both kernel regression and local-linear regression to estimate the regression of Y on X, in each case adjusting the span to produce a smooth regression curve. Which estimator has less bias? Why?67 Save the data from this exercise, or generate the data in a manner that can be replicated.