Imagine that we have a regression of y on x1, x2, ..., xk where b1, b2, ..., bk are the corresponding slope coefficients and we do not have access to the data. What we do have is the kxk matrix, C, of variances and covariances between the regressor variables, and a vector, q, containing the covariance of each of the k regressors with y. We can obtain the estimated vector of slope coefficients, B, like so:
B=C^-1*q'
And the intercept is then easy to derive if I know the means of the regressors and y (assume that I do). For the k estimated slope coefficients, a kxk variance-covariance matrix, V, can be derived like so:
V=Var(e)/N*C^-1
Where Var(e) is the (estimated) variance of the residuals and N is the sample size. Assuming that I know nothing other than C, q, Var(e) and N (i.e. I do not have access to the underlying data), how then do I derive the standard error for the intercept?
