4. (i) Develop the explicit formula for df in smooth.spline() and r in spans() so that the smoothing of these smoothers is about the same as lowess() with f = ????∕√n, where 0.5 < ???? < 2.

(ii) Smooth the NYC temperature data with all three smoothers

(spans, smooth.spline, lowess) and three levels of smoothing f =

0.25∕√n, 0.5∕√n, 1∕√n for lowess() and the equivalent level smoothing for the other smoothers.

(iii) Plot each smoothed periodogram (there are nine). Which seems best, which seems worst?