Constant SE from covariance matrix on Multiple Regression


I'm currently developing a Statistical package on Ruby, called statsample (, and I'm now working on improvements on Multiple Regression Module, using covariance matrix. To obtain raw coefficients, the user could input the means for every variable.

Is almost complete, but I can't find a way to obtain SE of constant without the original data. With the original data, I know I can obtain it with MSE*(XX')^-1, but I'm searching in several books and Google and I can't find a way.

Thanks in advance.
I found the solution

The key is in the traditional fast way to calculate variance and covariance

If X'X is for diagonal equal to \sum{x_i^2} and for else \sum{x_iy_i}, i can obtain for each cell the value using

for later inverse the matrix, multiply by MSE and take the square root of diagonals.