Documentation Center

  • Trial Software
  • Product Updates

coefTest

Class: NonLinearModel

Linear hypothesis test on nonlinear regression model coefficients

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 the p-value for an F test that all coefficient estimates in mdl are zero.

p = coefTest(mdl,H) performs an F test that H*B = 0, where B represents the coefficient vector.

p = coefTest(mdl,H,C) performs an F test that H*B = C.

[p,F] = coefTest(mdl,...) returns the F test 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 is the p-value for an F test 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 is the p-value for an F test that H*B = C, where B represents the coefficient vector.

Output Arguments

p

p-value of the F test (see Definitions).

F

Value of the test statistic for the F test (see Definitions).

r

Numerator degrees of freedom for the F test (see Definitions). The F statistic has r degrees of freedom in the numerator and mdl.DFE degrees of freedom in the denominator.

Definitions

Test Statistics

The p-value, F statistic, 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. Let β represent the unknown coefficient vector of the linear regression. Suppose H is a full-rank matrix of size r-by-s, where s is the number of terms in β. Let v be a vector the same size as β. The following is a test statistic for the hypothesis that  = v:

Here is the estimate of the coefficient vector β in mdl.Coefs, and C is the estimated covariance of the coefficient estimates in mdl.CoefCov. When the hypothesis is true, the test statistic F has an F Distribution with r and u degrees of freedom.

Examples

expand all

Test Nonlinear Regression Model Coefficients

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

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

load carsmall
X = 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.

Alternatives

The values of commonly used test statistics are available in the mdl.Coefficients table.

See Also

More About

Was this topic helpful?