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Weights

is an option for various fitting and other functions which specifies weights to associate with data elements.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Applications  
Properties & Relations  
See Also
Related Guides
History
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Weights

Weights

is an option for various fitting and other functions which specifies weights to associate with data elements.

Details

  • Weights->Automatic associates weight 1 with all data elements.
  • Weights->{w1,w2,…} associates weight wi with the i^(th) data element.
  • Weights->func associates weight func[xi1,xi2,…,yi] with the i^(th) data element.
  • Using VarianceEstimatorFunction->(1&) and Weights->{1/Δy12,1/Δy22,…}, Δyi is treated as the known uncertainty of measurement yi and parameter standard errors are effectively computed only from the weights. »

Examples

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Basic Examples  (1)

Fit a model using equal weights:

Give explicit weights to the data points:

Compute weights from values:

Compute weights from the response values:

Scope  (2)

Use weights in a nonlinear model:

Give explicit weights to the data points:

A generalized linear model:

Logit model:

Probit model:

Weight by a function of multiple variables:

Use default equal weights:

Compute weights from the response values:

Applications  (1)

Fit a nonlinear model using measurement errors as weights:

Obtain standard errors for the parameters:

Compare to estimates with weights not assumed to be from measurement errors:

Properties & Relations  (2)

Weights impact the relative importance of data points on the fitting:

Scaling by a constant does not change the parameter estimates:

Obtain parameter estimates from a weighted linear fitting:

LeastSquares gives the equivalent result when weights are incorporated:

Wolfram Research (2008), Weights, Wolfram Language function, https://reference.wolfram.com/language/ref/Weights.html.

Text

Wolfram Research (2008), Weights, Wolfram Language function, https://reference.wolfram.com/language/ref/Weights.html.

CMS

Wolfram Language. 2008. "Weights." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Weights.html.

APA

Wolfram Language. (2008). Weights. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Weights.html

BibTeX

@misc{reference.wolfram_2025_weights, author="Wolfram Research", title="{Weights}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Weights.html}", note=[Accessed: 16-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_weights, organization={Wolfram Research}, title={Weights}, year={2008}, url={https://reference.wolfram.com/language/ref/Weights.html}, note=[Accessed: 16-August-2025]}