I hope that I can finde someone here to help me with the following problem:

I have 11 points with x and y values. Those points are following more or less a linear trend. What I would like to do now is to choose two of those points and perform a linear regression on those two points plus three other points (choosen in a way that the residuals of those two points are minimised). I am performing this task with the solver-addIn from excel. Afterwards I am trying to minimise those residuals even further by trying different weighing factors for the regression (1/sqrt(x), 1/x,.. ).

The question is now if I can from a mathematical point of view really find the lowest residuals this way? Or would I have to test the different weighing factors for all possible combinations of points? Or is there somehow an even better way to do this?

From the beginning I would like to say that I am not a mathematician but a chemist, so pardon if I said/asked something stupid.

Thank you in advance

humic