Comparing polynomial and local regression:

(a) The local-linear regression of prestige on income with span s ¼ 0:6 (in Figure 18.7 on page 543) has 5:006 equivalent degrees of freedom, very close to the number of degrees of freedom for a global fourth-order polynomial. Fit a fourth-order polynomial to these data and compare the resulting regression curve with the local-linear regression.

(b) Now, consider the local-linear regression of infant mortality on GDP per capita for 193 nations shown in Figure 3.14 (page 45), which is for a span of s ¼ 0:5 and which has 5.9 equivalent degrees of freedom. Fit a fifth-order polynomial to these data and compare the fitted regression curve to the local-linear regression.

(c) What do you conclude from these two examples?