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11.9 Measuring the Strength of an Associ... > 11.9 Measuring the Strength of an As... - Pg. 599

Chapter 11 More Regression Methods 599 described that report the explanatory strength of association include lplot (lowess) and tsreg (the Theil­sen estimator). In principle, explanatory power can be estimated when using any regression method or smoother. First, compute the percentage bend midvariance based on predicted y values, say 2 ( y ), compute the percentage bend midvariance based on the observed y values, 2 (y), in ^ ^ ^ which case the estimate of 2 is 2 ( y ) ^ 2 = 2 . ^ (11.24) (y) ^ But a fundamental issue is whether the choice of method for obtaining the predicted y values make a practical difference when estimating 2 . For small to moderate sample sizes, it has been found that it does (e.g., Wilcox, 2010b). Two regression estimators that seem to perform relatively well, given the goal of estimating 2 , are the Theil­Sen estimator when the regression surface is a plane, and Cleveland's smoother (LOWESS), described in Section 11.5.2, when there is curvature. Section 11.5.3 described an R function, lplot, for plotting Cleveland's nonparametric regression line (LOESS). One of the arguments is varfun, which can now be explained. It indicates the measure of variation used when estimating explanatory power and defaults to the