How to calculate the expected beta values in multiple regression?

#1
We wish to carry out multiple regression of the type y= x0 + (beta1*x1 + beta2*x2) / (beta3*x3 + beta4*x4), where y is the response variable, x0 is the interecept, x1-x4 are the four independent variables, and beta1 - beta4 are the four corresponding beta coefficients. Our only a priori assumption about the betas is that their *absolute* values are all equal.

How do we estimate the *expected* values of the four betas? Or equivalently for our purposes, how does one test (say, in R) if one or more of the independent variables have a disproportionate effect on y?

Any help you can provide (including references) you can provide would be extremely useful to us. Thank you very much in advance.
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Is this for a multiple linear regression model? Are all IVs on the same scale?

Not quite sure what you want to do with the division on the right hand side?

You may want to look into the concept of partial R^2 values.
 

noetsi

Fortran must die
#3
"Our only a priori assumption about the betas is that their *absolute* values are all equal." Why would you assume that? It does not make a lot of sense to me. And if you do assume it, why do regression.