Home > OA_JOURNALS > JMASM > Vol. 7 (2008) > Iss. 2

#### 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 τ^{2} (*Y*) be some measure of variation. Explanatory power is η^{2} = τ^{2} (*Υ̂*) /τ^{2}(*Y*) . When *γ*(*X*) = *β_{0} + β_{1}X and τ^{2}(Y) is the variance of Y , η^{2} = ρ^{2} , 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.*

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*#### Recommended Citation

Wilcox, Rand R.
(2008)
"Estimating Explanatory Power in a Simple Regression Model Via Smoothers,"
*Journal of Modern Applied Statistical Methods*:
Vol. 7:
Iss.
2, Article 2.

Available at:
http://digitalcommons.wayne.edu/jmasm/vol7/iss2/2