I am assuming you know how to do a normal regression.
For a weighted regression, you would need to compute the correlation or covariance matrix in a weighted fashion and then do the regression .
I did this in Matlab a long time ago, but have not had a need to do so in MathNet Numerics. If the rest is Greek to you this could be too, but it really is just a bunch of weighted sums. There might be higher level statistical libraries that can do weighted regression already.
For a weighted regression, you would need to compute the correlation or covariance matrix in a weighted fashion and then do the regression .
I did this in Matlab a long time ago, but have not had a need to do so in MathNet Numerics. If the rest is Greek to you this could be too, but it really is just a bunch of weighted sums. There might be higher level statistical libraries that can do weighted regression already.