Because we have three unknowns in the equation, linear algebra requires that we have at least three calibration stars in order to solve for the coefficients, but what happens if one of the calibration stars is mis-measured? We get the wrong coefficients!
It would be nice if we could measure several stars simultaneously and derive the coefficients from that. Fortunately there is a method called least-square fitting that permits us to do so. The mathematics behind this method will be described in the Advanced Reduction tutorial (and in a corresponding JAAVSO article from the DSLR Documentation and Reduction Team), so we will just mention that this method minimizes the chance that a outlying data point can significantly alter the coefficients.
Since advanced reduction tutorial is still not out, I am interested if somebody could explain this shortly. Should I use multiple linear regression?