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.

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