# Sample size formula for multiple regression between binomial variables?

Let's say we have k binomial variables, and a sample size of n observations per variable, where each variable occurs (positive case) at a given frequency/probability f. We would like to check if there is a correlation between these variables, so the null hypothesis assumes that they are all independent (no correlation).

Is there a formula to calculate the minimum sample size n required to identify a "significant" correlation (p <= alpha) between these variables?

That is, how are n, k, f and alpha linked to each other mathematically?

Are any other parameters involved in the formula, e.g., beta, $$R^2$$, etc.?

I have a feeling that this relates to power and/or sample size calculations for multiple logistic regression, but I'm really not sure. Could the Wald test or likelihood-ratio test be used here?

• What exactly is involved in your "multiple regression," given you have assumed these variables are independent? Why do you need to identify a correlation when you have explicitly assumed there is none? – whuber Mar 22 '16 at 21:37
• Sorry, I should clarify that the null hypothesis assumes there is no correlation, but that is what we are trying to test. (original post now edited). – Kelvin Mar 22 '16 at 21:38
• Thank you. Since it's a little strange to be analyzing vectors of binomial variables using correlation, could you explain the purpose of this and perhaps describe what these variables represent? – whuber Mar 22 '16 at 21:42
• Yes, for example, how many individual human genomes (n) do we need to study to see if there is a correlation between k genetic mutations, where each mutation occurs at the same frequency f? – Kelvin Mar 22 '16 at 21:45