Comparing effects y1 ON x vs. y2 ON x in different regressions

Let's assume we have predictors $$x_1-x_5$$ and dependent variables $$y_1-y_9$$ in one dataset. We have a certain hypothesis about $$x_1$$: it should have differently strong effects on our 9 dependent variables $$y_1-y_9$$.

We perform 9 regressions, and find that $$x_1$$ 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.

• Is that $y_1 \lt -x_1$ or $y_1 \leftarrow x_1$ or possibly the R code y1 <- x1? Nov 15 '12 at 7:15
• With y <- x I mean the regression effect of x on y. y ON x, as MPLUS puts it. Nov 15 '12 at 15:09
• Torvon, are you asking whether there is a way to compare which of the three outcomes, $y_1,y_2,y_3$ that $x_1$ has the greatest effect on? Also: do $y_1,y_2,$ and $y_3$ all have the same units? Nov 20 '21 at 17:44