constructs the design matrix for the linear model β0+β1 f1+β2 f2+.

Details and Options

  • DesignMatrix[{y1,y2,},{f1,f2,},x] assumes data of the form {{1,y1},{2,y2},}. »
  • With data in the form {{x_(11),x_(12),...,y_(1)},{x_(21),x_(22),...,y_(2)},...}, the number of coordinates xi1, xi2, should equal the number of variables xi.
  • The design matrix m is formed from the values of basis functions fi at data points in the form
  • DesignMatrix takes the following options:
  • IncludeConstantBasis Truewhether to include a constant basis function
    NominalVariables Nonevariables considered as nominal or categorical
    WorkingPrecisionAutomaticprecision used in internal computations
  • With the setting IncludeConstantBasis->False, the design matrix for a model of form β1 f1+β2 f2+ is constructed. »


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Basic Examples  (3)

Design matrix for a linear model:

Add a quadratic term:

Leave out the constant term:

Design matrix with two predictor variables:

Include a product term:

Assume predictor values 1, 2, :

Scope  (2)

Use any numeric functions of the predictors:

Get the design matrix using exact arithmetic:

Use machine arithmetic:

Use arbitrary-precision arithmetic:

Use fixed 24-digit precision arithmetic:

Options  (3)

IncludeConstantBasis  (1)

A constant term is included by default:

Construct a design matrix without a constant term:

NominalVariables  (2)

Treat x as a numeric variable:

Treat x as nominal:

Use nominal variables that are not numeric:

Treat only x as nominal:

Treat all predictors as nominal:

Properties & Relations  (1)

DesignMatrix constructs the design matrix used by LinearModelFit:

The matrix is the same for GeneralizedLinearModelFit:

Wolfram Research (2008), DesignMatrix, Wolfram Language function,


Wolfram Research (2008), DesignMatrix, Wolfram Language function,


Wolfram Language. 2008. "DesignMatrix." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2008). DesignMatrix. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2023_designmatrix, author="Wolfram Research", title="{DesignMatrix}", year="2008", howpublished="\url{}", note=[Accessed: 17-April-2024 ]}


@online{reference.wolfram_2023_designmatrix, organization={Wolfram Research}, title={DesignMatrix}, year={2008}, url={}, note=[Accessed: 17-April-2024 ]}