Geometrical representation of two methods of linear least squares multiple correlation

Geometrical properties and relationships of the Doolittle and square root methods of multiple correlation, as represented in the variable subspace of an orthogonal person space, are shown. The method of representation is also useful for depicting zero-order and partial correlations, as well as for the more general problem of the combination of variables.     

Adaptation and repulsion in the figural after-effect

An experiment is reported which shows the effect of inspection of a curved line on the apparent curvature of a curved test line for a range of curvatures of both I and T lines. A second experiment extends the range of I curvatures, using only one T line, a straight line. The experiments showed both adaptation and repulsion components in the FAE.

An experiment by Kohler and Wallach which could not be reconciled with these results was repeated in the relevant part; the results were in agreement with the first experiment here and did not agree with those obtained by Kohler and Wallach.

An argument is presented that both adaptation and repulsion effects could be produced by a cell adaptation mechanism.     

Some multiple correlation and predictor selection methods

The Doolittle, Wherry-Doolittle, and Summerfield-Lubin methods of multiple correlation are compared theoretically as well as by an application in which a set of predictors is selected. Wherry's method and the Summerfield-Lubin method are shown to be equivalent; the relationship of these methods to the Doolittle method is indicated. The Summerfield-Lubin method, because of its compactness and ease of computation, and because of the meaningfulness of the interim computational values, is recommended as a convenient least squares method of multiple correlation and predictor selection.