Let's assume we have predictors x1-x5 and dependent variables y1-y9 in one dataset. We have a certain hypothesis about x1: it should have differently strong effects on our 9 dependent variables y1-y9.
We perform 9 regressions, and find that x1 significantly predicts all y with p<.001. Now we want to find out whether these (highly significant) effects are different from each other (just because they are significant effects does not mean they are equally strong). Two questions:
(1) What information that a regression provides us with would give us insight into this question? Unstandardized beta? Standardized beta? t?
(2) Is there a statistical test we can perform to find out whether the strengths of predictions are different between (y1 ON x1) and (y2 ON x1) and (y3 ON x1)?
Software I can use is R and SPSS; field is psychology/medicine.