Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Nonlinear regression model class

An object comprising training data, model description, diagnostic
information, and fitted coefficients for a nonlinear regression. Predict
model responses with the `predict`

or `feval`

methods.

or `nlm`

=
fitnlm(`tbl`

,`modelfun`

,`beta0`

)

create
a nonlinear model of a table or dataset array `nlm`

=
fitnlm(`X`

,`y`

,`modelfun`

,`beta0`

)`tbl`

,
or of the responses `y`

to a data matrix `X`

.
For details, see `fitnlm`

.

coefCI | Confidence intervals of coefficient estimates of nonlinear regression model |

coefTest | Linear hypothesis test on nonlinear regression model coefficients |

disp | Display nonlinear regression model |

feval | Evaluate nonlinear regression model prediction |

fit | Fit nonlinear regression model |

plotDiagnostics | Plot diagnostics of nonlinear regression model |

plotResiduals | Plot residuals of nonlinear regression model |

plotSlice | Plot of slices through fitted nonlinear regression surface |

predict | Predict response of nonlinear regression model |

random | Simulate responses for nonlinear regression model |

The *hat matrix* *H* is
defined in terms of the data matrix *X* and the Jacobian
matrix *J*:

$${J}_{i,j}={\frac{\partial f}{\partial {\beta}_{j}}|}_{{x}_{i},\beta}$$

Here *f* is the nonlinear model function, and *β* is
the vector of model coefficients.

The Hat Matrix *H* is

*H* = *J*(*J ^{T}J*)

The diagonal elements *H _{ii}* satisfy

$$\begin{array}{l}0\le {h}_{ii}\le 1\\ {\displaystyle \sum _{i=1}^{n}{h}_{ii}}=p,\end{array}$$

where *n* is the number of observations (rows
of *X*), and *p* is the number of
coefficients in the regression model.

The *leverage* of observation *i* is
the value of the *i*th diagonal term, *h*_{ii},
of the hat matrix *H*. Because the sum of the leverage
values is *p* (the number of coefficients in the
regression model), an observation *i* can be considered
to be an outlier if its leverage substantially exceeds *p*/*n*,
where *n* is the number of observations.

The Cook's distance *D _{i}* of
observation

$${D}_{i}=\frac{{\displaystyle \sum _{j=1}^{n}{\left({\widehat{y}}_{j}-{\widehat{y}}_{j(i)}\right)}^{2}}}{p\text{\hspace{0.17em}}MSE},$$

where

$${\widehat{y}}_{j}$$ is the

*j*th fitted response value.$${\widehat{y}}_{j(i)}$$ is the

*j*th fitted response value, where the fit does not include observation*i*.*MSE*is the mean squared error.*p*is the number of coefficients in the regression model.

Cook's distance is algebraically equivalent to the following expression:

$${D}_{i}=\frac{{r}_{i}^{2}}{p\text{\hspace{0.17em}}MSE}\left(\frac{{h}_{ii}}{{\left(1-{h}_{ii}\right)}^{2}}\right),$$

where *e _{i}* is the

Value. To learn how value classes affect
copy operations, see Copying Objects in
the MATLAB^{®} documentation.

Was this topic helpful?