# 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 , 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 True whether to include a constant basis function NominalVariables None variables considered as nominal or categorical WorkingPrecision Automatic precision used in internal computations
• With the setting , the design matrix for a model of form β1 f1+β2 f2+ is constructed. »

# Examples

open allclose all

## Basic Examples(3)

Design matrix for a linear model:

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, 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_2024_designmatrix, author="Wolfram Research", title="{DesignMatrix}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/DesignMatrix.html}", note=[Accessed: 14-September-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_designmatrix, organization={Wolfram Research}, title={DesignMatrix}, year={2008}, url={https://reference.wolfram.com/language/ref/DesignMatrix.html}, note=[Accessed: 14-September-2024 ]}