# Comparing effect sizes across univariate regressions with identical independent variable but different dependent variables

I have done several univariate regressions with investor sentiment as independent variable (identical across regressions) and different sector portfolio returns as dependent variable.

Can I infer that the effect sizes are larger/smaller by just looking at the regression coefficients or do I have to perform tests to evaluate if there are significant differences?

N.B. the coefficients are standardized.

Thanks!

## 1 Answer

No you cannot. As a human being, you can make a judgment that a statistically significant $\beta$ of 0.9 is most likely greater than a non-statistically significant $\beta$ of 0.1. However, your analysis does not permit you to make this conclusion, as you would have to compare both $\beta's$ within the same model. You don't know if the difference between .1 and .9 is statistically different from zero.

You can do this by running a single moderated regression. Investor sentiment would be the independent variable, the sectors would be the moderator, and the returns would be the dependent variable. By using plots to interpret your moderation analysis, you can see how the relationship between sentiment and returns changes from sector, if it does.

• How would the model look like mathematically? – Christoffer Janson May 29 '17 at 8:44