NonLinearRegression Weights

*To*: mathgroup at smc.vnet.net*Subject*: [mg73584] NonLinearRegression Weights*From*: pershan at seas.harvard.edu*Date*: Thu, 22 Feb 2007 04:37:26 -0500 (EST)

I am trying to add Weights to NonlinearRegression Fit. The relevant section of Mathematica Help (Statistics `NonlinearFit` ) is as follows The Weights option allows you to implement weighted least squares by specifying a list of weights, one for each data point; the default Weights -> Automatic implies a weight of unity for each data point. When Weights -> {a, ... , a}, the parameter estimates are chosen to minimize the weighted sum of squared residuals a. The command I am using is: fitting[x_] = NonlinearFit[data, f[x], {x}, { {Background, {0, 1000}}, {Amplitude, {10, 0}}, {Wid, {10, 25}}}, Weights -> wt] where wt is a column vector that has precisely the same length as the data file. This command works perfectly if I use either Weights->Automatic or something like Weights -> (Sqrt[#] &) On the other hand, when the weights are from a list {....} I get the following error. NonlinearFit::bdwghts: Warning: Value of option Weights -> {{0.00322435}, \ {0.00359912}, \[LeftSkeleton]8\[RightSkeleton], \[LeftSkeleton]31\ \[RightSkeleton]} is not Automatic, a pure function mapping a response to a \ non-negative numerical weight, or a non-negative numerical vector having the \ same length as the data. Setting all weights to 1 (Weights -> Automatic).

**Follow-Ups**:**Re: NonLinearRegression Weights***From:*Darren Glosemeyer <darreng@wolfram.com>