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.
Wilcox, Rand R.
"Estimating Explanatory Power in a Simple Regression Model Via Smoothers,"
Journal of Modern Applied Statistical Methods:
2, Article 2.
Available at: http://digitalcommons.wayne.edu/jmasm/vol7/iss2/2