This paper considers the problem of estimating the overall strength of an association, including situations where there is curvature. The general strategy is to fit a robust regression line, or some type of smoother that allows curvature, and then use a robust analogue of explanatory power, say η2. When the regression surface is a plane, an estimate of η2 via the Theil–Sen estimator is found to perform well, relative to some other robust regression estimators, in terms of mean squared error and bias. When there is curvature, a generalization of a kernel estimator derived by Fan performs relatively well, but two alternative smoothers have certain practical advantages. When η2 is approximately equal to zero, estimation using smoothers has relatively high bias. A variation of η2 is suggested for dealing with this problem. Methods for testing H0: η2=0 are examined that are based in part on smoothers. Two methods are found that control Type I error probabilities reasonably well in simulations. Software for applying the more successful methods is provided.