Sample size calculation for multiple regression

Hi all!

I am struggling with sample size calculations at the minute. I have looked everywhere but all I get is formulas. I have downloaded MedCalc which gives me a number of participants I need per correlation. My supervisor keeps confusing me because she says that it is a different number for correlations and different for regression. Based on what? She said that I need 13 per correlation but for my main analysis I need 15-20 per variable. I can't figure out how she ended up with such numbers nor the logic behind it. If anyone can help me get the gist I would really appreciate it. Thanks!