Linear hypothesis test on nonlinear regression model coefficients
p = coefTest(mdl)
p = coefTest(mdl,H)
p = coefTest(mdl,H,C)
[p,F] = coefTest(mdl,...)
[p,F,r] = coefTest(mdl,...)
Nonlinear regression model, constructed by fitnlm.
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.
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.
p-value of the F test (see Definitions).
Value of the test statistic for the F test (see Definitions).
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.
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 Hβ = 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.
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.
The values of commonly used test statistics are available in the mdl.Coefficients table.