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.

`plotDiagnostics(mdl)`

plotDiagnostics(mdl,plottype)

h = plotDiagnostics(___)

h = plotDiagnostics(mdl,plottype,Name,Value)

`plotDiagnostics(`

plots
diagnostics from the `mdl`

)`mdl`

linear model using the
leverage values.

`plotDiagnostics(`

plots
diagnostics in a plot of type `mdl`

,`plottype`

)`plottype`

.

returns
handles to the lines in the plot, using any of the previous syntaxes.`h`

= plotDiagnostics(___)

plots
with additional options specified by one or more `h`

= plotDiagnostics(`mdl`

,`plottype`

,`Name,Value`

)`Name,Value`

pair
arguments.

For many plots, the Data Cursor tool in the figure window displays the

*x*and*y*values for any data point, along with the observation name or number.

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

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

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.

Cook's distance is the scaled change in fitted values.
Each element in `CooksDistance`

is the normalized
change in the vector of coefficients due to the deletion of an observation.
The Cook's distance, *D*_{i},
of observation *i* is

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

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 *r*_{i} is
the *i*th residual, and *h*_{ii} is
the *i*th leverage value.

`CooksDistance`

is an *n*-by-1
column vector in the `Diagnostics`

table of the `LinearModel`

object.

[1] Neter, J., M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. *Applied
Linear Statistical Models*, Fourth Edition. Irwin, Chicago,
1996.

The `mdl.Diagnostics`

property contains the
information that `plotDiagnostics`

uses to create
plots.

Was this topic helpful?