How to compare three dependent correlation coefficients?

Question

I have done some data collection on Hermit crabs. I have recorded the shell aperture, the shell slope length, and then calculated the volume of the shell using formula for a a cone. I have collected the distance each crab travelled in a given period of time. From this, I have obtained 3 correlation coefficients. Obviously, they are dependent, as they all use the same crabs and distance. I am thinking, and have asked here about using Fisher’s Z-test. Is there anything better or more suitable?

Answer 1

What are you trying to figure out about the variables exactly? If you're trying to find the variable with the largest effect on the distance I would do multiple linear regression and compare the standardized betas

Answer 2

Howdy! No need for anything complicated.

Use excel to estimate a multi variable regression. Note: this assumes normality, homoskedasticity, linearity, independence of errors, etc in the dataset. However, I would assume given the dataset you have, these conditions are present.

For statistical significance, use the p-value. Less than or equal to .05 is usually the standard.