Comparing regression equations


I have a question about how to compare regression equations and regression coefficients. I have data set A with n data points, and two possible predictor data sets, X and Y, that cannot be combined in one equation, i.e., X is one way of explaining A, and Y is a different way. My purpose is to find two regression equations, one using X, and the other using Y, and to compare them and the coefficients.

So I get these two equations:
1) A = aX
2) A = bY

I use Minitab, because I can get it for free, and get values for a and b, each with with an associated standard error (SE).

I am trying to determine if a and b can be considered identical with their given SE.

I thought I need to use a hypothesis test, where the null hypothesis is that a and b are equal. But I don't know whether to use a two sample t-test, a two sample Z-test, or something else entirely.

I also have access to Montgomery's "Design and Analysis of Experiments" (7th ed.), so referencing specific equations in that book would be extremely helpful. I would be so grateful for any advice! :) Thanks for your time!