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!