Class: GeneralizedLinearModel
Linear hypothesis test on generalized linear regression model coefficients
p = coefTest(mdl)
p = coefTest(mdl,H)
p = coefTest(mdl,H,C)
[p,F] =
coefTest(mdl,...)
[p,F,r]
= coefTest(mdl,...)
computes
the pvalue for an F test that
all coefficient estimates in p
= coefTest(mdl
)mdl
are zero, except
for the intercept term.
performs
an F test that p
= coefTest(mdl
,H
)H*B = 0
, where B
represents the
coefficient vector.
performs
an F test that p
= coefTest(mdl
,H
,C
)H*B = C
.
[
returns the F test
statistic.p
,F
] =
coefTest(mdl
,...)
[
returns the numerator
degrees of freedom for the test.p
,F
,r
]
= coefTest(mdl
,...)

Generalized linear model, as constructed by 

Numeric matrix having one column for each coefficient in the
model. When 

Numeric vector with the same number of rows as 

pvalue 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 
The pvalue, F statistic, and numerator degrees of freedom are valid under these assumptions:
The data comes from a model represented by the formula mdl
.Formula
.
The observations are independent conditional on the predictor values.
Suppose these assumptions hold. Let β represent the (unknown) coefficient vector of the linear regression. Suppose H is a fullrank matrix of size rbys, 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:
$$F={\left(H\widehat{\beta}v\right)}^{\prime}{\left(HC{H}^{\prime}\right)}^{1}\left(H\widehat{\beta}v\right).$$
Here $$\widehat{\beta}$$ 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.
The values of commonly used test statistics are available in
the
table.mdl
.Coefficients