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).

```

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