How to find optimal weight for explanatory variables in a regression?

Hello all, I have the following regression model: Y = b0 + b1*w1*X1 + b2*w2*X2 where w1+w2=1. These are weights on the X variables. I need to find w1 and w2 that would create the best fit for this regression model. I need help on how to create a Matlab code that would estimate the optimal weights on these X variables. Thanks a lot. Mai

[Sargondjani]

it seems your system is not properly identified.

if you would run the regression":

Y=c0+c1*X1+c2*X2

with c1=b1*w1 and c2=b2*w2, and w1+w2=1

it seems to me that there are infinitely many solutions for w1 and w2. for examply: set w1 to 0.5 then w2 is 0.5 and the values for b1 and b2 would adjust. and if you set w1=0.25 then you just get different results for b1 and b2... so there is no unique solution.

i suspect that you want the weights to hold for every observation, but you would have to adjust the formulation for that.

anyway, i suspect you will have to use "lsqlin" or fmincon (which requires you to specify your own objective function)