coefTest

Class:NonLinearModel

Linear hypothesis test on nonlinear regression model coefficients

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Syntax

p = coefTest(mdl) p = coefTest(mdl,H) p = coefTest(mdl,H,C) [p,F] = coefTest(mdl,...) [p,F,r] = coefTest(mdl,...)

Description

p= coefTest(mdl)computes thep价值的Ftest that all coefficient estimates inmdlare zero.

p= coefTest(mdl,H)performs anFtest thatH*B = 0, whereBrepresents the coefficient vector.

p= coefTest(mdl,H,C)performs anFtest thatH*B = C.

[p,F] = coefTest(mdl,...)returns theFtest statistic.

[p,F,r] = coefTest(mdl,...)returns the numerator degrees of freedom for the test.

Input Arguments

`mdl`	Nonlinear regression model, constructed by`fitnlm`.
`H`	Numeric matrix having one column for each coefficient in the model. When`H`is an input, the output`p`是p价值的Ftest that`H*B = 0`, where`B`represents the coefficient vector.
`C`	Numeric vector with the same number of rows as`H`. When`C`is an input, the output`p`是p价值的Ftest that`H*B = C`, where`B`represents the coefficient vector.

Output Arguments

`p`	p-value of theFtest (seeMore About).
`F`	Value of the test statistic for theFtest (seeMore About).
`r`	Numerator degrees of freedom for theFtest (seeMore About). TheFstatistic has`r`degrees of freedom in the numerator and`mdl.DFE`degrees of freedom in the denominator.

Examples

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Test Nonlinear Regression Model Coefficients

Open Live Script

Make a nonlinear model of mileage as a function of the weight from thecarsmalldata set. Test the coefficients to see if all should be zero.

Create an exponential model of car mileage as a function of weight from thecarsmalldata. Scale the weight by a factor of 1000 so all the variables are roughly equal in size.

loadcarsmallX = Weight; y = MPG; modelfun ='y ~ b1 + b2*exp(-b3*x/1000)'; beta0 = [1 1 1]; mdl = fitnlm(X,y,modelfun,beta0);

Test the model for significant differences from a constant model.

p = coefTest(mdl)

p = 1.3708e-36

There is no doubt that the model contains nonzero terms.

More About

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Test Statistics

Thep-value,Fstatistic, and numerator degrees of freedom are valid under these assumptions:

The data comes from a normal distribution.
The entries are independent.

Suppose these assumptions hold. Letβ代表的未知系数向量near regression. SupposeHis a full-rank matrix of sizer-by-s, wheres是number of terms inβ. Letcbe a vector the same size asβ. The following is a test statistic for the hypothesis thatHβ=c:

$F = {(H \hat{β} - c)}^{'} {(H V H^{'})}^{- 1} (H \hat{β} - c) .$

Here $\hat{β}$ 是estimate of the coefficient vectorβinmdl.Coefs, andV是estimated covariance of the coefficient estimates inmdl.CoefCov. When the hypothesis is true, the test statisticFhas anF Distributionwithrandudegrees of freedom.