Not sure what you're asking
Though the vector
giving you the model
I want to show that if the number of columns for my matrix of regressors is two and if the first column of my regressors matrix is full of ones then the OLS estimator of the second element of reduces to the bivariate regression formula.
How can I show such a thing? It seems obvious to me that
is the same as something like although I'm not sure that's a solid enough "proof". Help!
The exact question:
Given that is fixed and a T x k matrix...
If k=2 and the first element of is a constant, show that the expression for the OLS estimator of the second element of reduces to the familiar bivariate regression formula.
How do I do this? It's killing me.