How should we know if our regression have enough power? I believe my question is very basic. I was presenting my work in a seminar explaining that my coefficients are not significant. A professor objected, saying that might be due to the low power of my regression. What is a convincing response to such a question?
Generally, suppose that I have a sample size of n (which I am not able to increase) and aim to estimate m parameters. I run a simple OLS, and some of the coefficients turn out to be statistically insignificant. By just looking at the regression table, how can I argue whether I have enough power or not? What are the signs and symptoms of an underpowered analysis?
As I am testing H0:b=0 against H1:b!=0, and thus my H1 is not equality but rather simply the negation of H0, then even conceptually, I think the power cannot be calculated unless we assign a particular value to H1.

You never have enough power, if you have non-significant results.
To misquote Cohen (1992) from the book "Statistical Power Analaysis": All (non-trivial) null hypotheses are false, at least in their two tailed form."
This is a problem with hypothesis testing. Failing to find a significant effect does not mean that there's no effect. It just means that you didn't find one. A non-significant result is (fairly) uninformative, but people treat it as if it is informative. A significant result is also not informative - it tells you that the null hypothesis is unlikely to be true. But you already know that all (non-trivial) null hypotheses are unlikely to be true.
If you have large effects that are not statistically significant, you probably want to have more power.
