If I have two sets of noisy data, with same number of points in each set and measured at the same set of x positions, then carry out a polynomial least squares fits on each set of data, are the resulting coefficients such that if I repeated the least squares fit on the union of the two data sets - then the resulting coefficients would be the average of the equivalent coefficients for the first two sets?
And more generally, if you have sets, {a}, {b}, {c}..., measured from the same data source, but with differing numbers of data points and measurement at randomly distributed x positions, would the least squares coefficients of the combined data be related to a weighted sum of the coefficients of the individual sets?