Multiple regression with betas constrained to be equal

I would like to fit a multiple regression with beta constrained to be the same across variables.

Y = alpha + b1*X1 + b2*X2 +...+ b10*X10 where b1-b10 are equal, alpha unconstrained.

I have seen a number of examples where constraints are to keep beta in a certain range, but does not seem to be appropriate here.

[Jon]

Can you not just follow one of the examples you cite but restrict the beta to be in a very tiny range?

[John D'Errico]

Actually, trying to fix a variable by setting the bounds to a VERY narrow range tends to produce nastiness in the solution. It can cause problems. Anyway, this would not solve the problem as apparently asked, because the question was not to fix the b_i to a given value, but to make them all the same, while still estimating them.

Answer 1

[John D'Errico]

So you REALLY want to fit the model...

Y = alpha + b1*(X1 + X2 +...+ X10)

Hint. Hint. Hint. Does this look like a simple, linear regression in ONE variable? Could polyfit solve your problem?

[James Moreland]

Now I feel dumb. This does look like the solution to the question I posed. Now I just need to work out if the question was the right one for my data. Thanks John.

[John D'Errico]

:) Sometimes we just have a mental block, and need to view a problem from a different perspective.