Selecting the span by smoothing residuals: A complementary visual approach to selecting the span in local-polynomial regression is to find the residuals from the fit from the local regression, E i = Y...

Selecting the span by smoothing residuals: A complementary visual approach to selecting the span in local-polynomial regression is to find the residuals from the fit from the local regression, E_i
= Y_i
- Y_i, and to smooth the residuals against the xi. If the data have been over smoothed, then there will be a systematic relationship between the average residual and X; if the fit does not over smooth the data, then the average residual will be approximately 0 regardless of the value of X. We seek the largest value of s that yields residuals that are unrelated to X. Apply this approach to the regression of prestige on income in the Canadian occupational prestige data by smoothing the residuals from local-linear regressions with various spans. An examination of the scatter plots in Figure 18.4 suggested picking s » 0:6. Is this choice supported by smoothing the residuals?