Some Interpretations of the Multiple Correlation Coefficient

The multiple correlation coefficient, R (or r, in the simple case), is frequently used in evaluating regression models.Statistical significance is the usual criterion for judging R.Various views of its practical significance should also be considered.One practical measure is the percent reduction in the standard deviation of the response variable achieved by the model.A graph giving this as a function of R and percent loss in degrees of freedom is presented.This measure is compared with others which are sometimes appropriate.