# 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 More About). `F` Value of the test statistic for the F test (see More About). `r` Numerator degrees of freedom for the F test (see More About). The F statistic has `r` degrees of freedom in the numerator and `mdl.DFE` degrees of freedom in the denominator.

## Examples

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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.

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## Alternatives

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