Linear regression with weighted data?

Question

LinearModelFit doesn't seem to support WeightedData objects. Is there anything I can do smarter than repeating the data proportionally to the weights?

MWE: The following code,

data = WeightedData[{{1, 1}, {3, 2}, {2, 3}}, {1, 2, 3}];
LinearModelFit[data, x, x]

gives the following error message:

Answer 1

You're right in that it's strange that WeightedData doesn't work here, but LinearModelFit has the Weights options that you can use to specify the weights. This example is from the documentation of LinearModelFit (specifically the Weights section under Options):

LinearModelFit[Range[10]^2, x, x] // Normal
LinearModelFit[Range[10]^2, x, x, Weights -> 1/Range[10]] // Normal

Out[1]= -22. + 11. x

Out[2]= -13.5039 + 9.45526 x

As a general tip for finding these kinds of options, it's always worthwhile to browse the Options section in the documentation of a function if you think some logical functionality of a function is missing. Many option symbols have their own documentation page as well. Furthermore, some functions have hidden options that aren't shown in the documentation. You can see all of them by simply typing:

Options[LinearModelFit]

{ConfidenceLevel -> 19/20, IncludeConstantBasis -> True, LinearOffsetFunction -> None, NominalVariables -> None, Tolerance -> Automatic, VarianceEstimatorFunction -> Automatic, Weights -> Automatic, WorkingPrecision -> Automatic}