Estimating Explanatory Power in a Simple Regression Model Via Smoothers

Authors

Rand R. Wilcox, University of Southern CaliforniaFollow

Abstract

Consider the regression model Y = γ(X) + ε , where γ(X) is some conditional measure of location associated with Y , given X. Let Υ̂ be some estimate of Y, given X, and let τ² (Y) be some measure of variation. Explanatory power is η² = τ² (Υ̂) /τ²(Y) . When γ(X) = β₀ + β₁X and τ²(Y) is the variance of Y , η² = ρ² , where ρ is Pearson's correlation. The small-sample properties of some methods for estimating a robust analog of explanatory power via smoothers is investigated. The robust version of a smoother proposed by Cleveland is found to be best in most cases.