1. Perform a similar analysis comparing the high- and low-elevation groups.

(i) Fit a Fourier series to each watershed and find the estimated AR(m) order of the residuals.

(ii) Plot the averaged watershed value for the high-elevation groups and discuss how this plot compares to the other watersheds. Is there any sense in which the shapes of the three groups form a natural progression from low to high elevations?

(iii) Form a plot similar to Figure 19.4 using Frenchman Creek.

(iv) Form a table as in the chapter, but comparing the low to the high elevations.

(a) Perform the analysis without filtering the data.

(b) Perform the analysis filtering the data [parts (iii) and (iv) will be different].

Observe that the patterns are the same in both tables (filtered and unfiltered), although the R2 values are consistently higher for the unfiltered analysis. Explain why this pattern occurs.