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:
  • IncludeConstantBasisTruewhether to include a constant basis function
    NominalVariablesNonevariables 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:

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:

Introduced in 2008
 (7.0)