10-06-2014 09:15 AM
I Am working on a multiple linear regression project for my econometrics class and I was asked by my professor to find any difference in the coefficients using different models (log). My professor wants to make up a mathematical formula for a derivative where the dependent variable is differentiable with respect to one of the independent variables using the means for each model. Any hints about how can I tackle this question?
10-06-2014 09:31 AM
If you assume that
Y = b0 + b1*x1 + b2*x2 + ... + bn*xn + epsilon
then the mean model is just
Y = b0 + b1*x1 + b2*x2 + ... + bn*xn
dY/dx1 = b1
dY/dx2 = b2
dY/dxn = bn
In other words, the regression coefficients ARE the partial derivatives of Y w.r.t. the independent variables.