compare two Beta coefficience between two different model.

I am running two regressions,
each with the one independent variables (Y) but with two different dependent variables (X1, X2).

examply: Y is central obesity, X1 is waist circumference, X2 is waist / hip ratio.
I think the waist/hip ratio more good indicator than waist for central obesity.

Y = I1 + b11*X1 (1)

Y = I2 + b21*X2 (2)

I need to find if the difference between the coefficients for X 1 v.s. X2 (b11 v.s. b21) with statistically significant.

I already calculated the Beta coefficiend using Z score, and b11 is greater than b21. b11 >> b21 is meaning that X1 is better than X2 for prediciting Y ?
If not, is there any test for that?

Many thanks.

Jin-Ha Yoon.


Ambassador to the humans
Note that an 'independent variable' is a predictor in a model and a dependent variable is the response.

Why exactly do you want to compare the two coefficients?