In Mplus 5.2 I regressed 1 continuous observed variable on 3 continuous observed predictors. No latent variables. The output lists R-square and the Two-Tailed P-value.
Is the reported p-value truly for a two-tailed test or is it really for a one-tailed test? I am trying to understand why one would ever want a two-tailed test for R-square, since the traditional R-square in OLS regression can only vary from 0 to 1. (A two-tailed test would seem to imply that one is considering the possibility that R-square is significantly less than 0.) If the R-square Mplus provides is something different from the traditional value (explained sum of squares divided by total sum of squares which is tested using 1 tail of the F distribution), could you please describe how your R-square value is calculated and why/when a 2-tailed test is appropriate? Thanks!