I'm currently working with data contained in $Y, X_1, X_2, \ldots, X_n$ and wish to fit it to the model:
$Y = (1 + c_1X_1)(1 + c_2X_2)\ldots(1 + c_nX_n)$
where the $c_i$ are coefficients to be determined through regression. How can I do this? I've tried playing with logarithms (i.e. looking at $Y$ vs. $\log (1 + c_iX_i)$), but due to the pesky $1$, I can't figure out how to follow through.
Thanks in advance!