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DesignMatrix[{{x11,x12,…,y1},{x21,x22,…,y2},…},{f1,f2,…},{x1,x2,…}]

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

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
IncludeConstantBasis  
NominalVariables  
Properties & Relations  
See Also
Related Guides
History
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DesignMatrix

DesignMatrix[{{x11,x12,…,y1},{x21,x22,…,y2},…},{f1,f2,…},{x1,x2,…}]

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. »

Examples

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Basic Examples  (3)

Design matrix for a linear model:

Wolfram Language code: data = Table[{i, i ^ (3 / 2) + RandomReal[]}, {i, 5}]
Wolfram Language code: DesignMatrix[data, x, x]//MatrixForm

Add a quadratic term:

Wolfram Language code: DesignMatrix[data, {x, x ^ 2}, x]//MatrixForm

Leave out the constant term:

Wolfram Language code: DesignMatrix[data, {x, x ^ 2}, x, IncludeConstantBasis -> False]//MatrixForm

Design matrix with two predictor variables:

Wolfram Language code: data2 = Table[{RandomInteger[10], RandomInteger[10], RandomReal[]}, {10}]
Wolfram Language code: DesignMatrix[data2, {x, y}, {x, y}]//MatrixForm

Include a product term:

Wolfram Language code: DesignMatrix[data2, {x, y, x * y}, {x, y}]//MatrixForm

Assume predictor values 1, 2, …:

Wolfram Language code: DesignMatrix[RandomReal[10, 5], x, x]//MatrixForm

Scope  (2)

Use any numeric functions of the predictors:

Wolfram Language code: data = Table[{i, RandomReal[]}, {i, 5}]
Wolfram Language code: DesignMatrix[data, {Sin[x], Sqrt[x]}, x]//MatrixForm

Get the design matrix using exact arithmetic:

Wolfram Language code: data = RandomInteger[99, {5, 2}]
Wolfram Language code: DesignMatrix[data, {x, Sin[x]}, x] //MatrixForm

Use machine arithmetic:

Wolfram Language code: DesignMatrix[N[data], {x, Sin[x]}, x] //MatrixForm

Use arbitrary-precision arithmetic:

Wolfram Language code: DesignMatrix[N[data, 24], {x, Sin[x]}, x] //MatrixForm

Use fixed 24-digit precision arithmetic:

Wolfram Language code: DesignMatrix[data, {x, Sin[x]}, x, WorkingPrecision -> 24] //MatrixForm

Options  (3)

IncludeConstantBasis  (1)

A constant term is included by default:

Wolfram Language code: data = Table[{i, RandomReal[]}, {i, 10}]
Wolfram Language code: DesignMatrix[data, x, x]//MatrixForm

Construct a design matrix without a constant term:

Wolfram Language code: DesignMatrix[data, x, x, IncludeConstantBasis -> False]//MatrixForm

NominalVariables  (2)

Treat x as a numeric variable:

Wolfram Language code: data = {{0, 1.5}, {2, 2.3}, {2, 1.8}, {0, 2.5}};
Wolfram Language code: DesignMatrix[data, x, x]//MatrixForm

Treat x as nominal:

Wolfram Language code: DesignMatrix[data, x, x, NominalVariables -> x]//MatrixForm

Use nominal variables that are not numeric:

Wolfram Language code: DesignMatrix[{{a, 1.5}, {b, 2.3}, {b, 1.8}, {a, 2.5}}, x, x, NominalVariables -> x]//MatrixForm

Treat only x as nominal:

Wolfram Language code: DesignMatrix[{{a, 0, 1.5}, {b, 2, 2.3}, {a, 2, 1.8}, {b, 0, 2.5}}, {x, y}, {x, y}, NominalVariables -> x]//MatrixForm

Treat all predictors as nominal:

Wolfram Language code: DesignMatrix[{{a, 0, 1.5}, {b, 2, 2.3}, {a, 2, 1.8}, {b, 0, 2.5}}, {x, y}, {x, y}, NominalVariables -> All]//MatrixForm

Properties & Relations  (1)

DesignMatrix constructs the design matrix used by LinearModelFit:

Wolfram Language code: data = Table[{i, RandomReal[]}, {i, 5}]
Wolfram Language code: DesignMatrix[data, x, x]//MatrixForm
Wolfram Language code: lm = LinearModelFit[data, x, x];
Wolfram Language code: lm["DesignMatrix"]//MatrixForm

The matrix is the same for GeneralizedLinearModelFit:

Wolfram Language code: glm = GeneralizedLinearModelFit[data, x, x];
Wolfram Language code: glm["DesignMatrix"]//MatrixForm
Wolfram Research (2008), DesignMatrix, Wolfram Language function, https://reference.wolfram.com/language/ref/DesignMatrix.html.

Text

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

CMS

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

APA

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

BibTeX

@misc{reference.wolfram_2026_designmatrix, author="Wolfram Research", title="{DesignMatrix}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/DesignMatrix.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_designmatrix, organization={Wolfram Research}, title={DesignMatrix}, year={2008}, url={https://reference.wolfram.com/language/ref/DesignMatrix.html}, note=[Accessed: 13-June-2026]}