# Power of a Multiple Linear Regression

I have a set of models that are the result of a multiple linear regression. I would like to calculate the power for each of these models. I found this tutorial on calculating the power using G*Power. Since the data has already been collected, I am using the Post Hoc type of Power Analysis, and I was hoping to use the "Determine" button to automatically calculate the effect size. However, I see that one need to provide a partial R2, but I would think that for a multiple linear regression (which I think would have multiple partial R2 values), it would make more sense to provide the R2 for the resulting model. Am I misunderstanding the difference between R2 and partial R2? If so, how do I obtain the partial R2 to use in G*Power?

• It's questionable whether one should do post-hoc power analysis at all. See e.g this article. This refers to post-hoc as in after the analysis has been done, not just after the sample has been collected. Apr 14, 2013 at 18:13
• Interesting. Someone else has already done analysis on this data, where we did achieve significant results. However, someone else was questioning whether we had enough samples to validly perform a multiple linear regression. Does the presence of significance indicate that we do have enough samples, or is there another way to determine this? Apr 14, 2013 at 18:17
• Are they worried about power or over-fitting? If your result was significant, you had enough power to detect the effect size that you found. But if your N was less than about 10 times the number of variables, that can be problematic. Apr 14, 2013 at 18:40
• Our N is greater than 10 times the number of variables for some models, and less than 10 times the number of variables for other models. What does having an insufficient N indicate, even if you do get significance? Apr 14, 2013 at 18:52
• That would indicate possible overfitting of the data. To give an extreme example, if you have N-1 independent variables, you will get a perfect fit even if all the data is random. Apr 14, 2013 at 20:44