Operating under the requirement that the parameters must be linear, I have the following question:

Y = B0 + B1X (simple linear regression equation.)

Let's assume B0 = 1 and B1 = 9.

Then we have Y = 1 + 9X (Still a simple linear regression equation.)

However, we could also write this as

Y = 1 + (3^2) X

(i.e., Y = 1 + (B1^2) X which would NOT be deemed a linear regression.)

What am I missing here? (Its probably something that is a bit abstract and related to B1-hat being an estimate and the difference between a population regression equation and a sample regression equation....not sure.)

Thanks,

Brian