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# plotDiagnostics

Class: LinearModel

Plot diagnostics of linear regression model

## Syntax

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

## Description

plotDiagnostics(mdl) plots diagnostics from the mdl linear model using scaled delete-1 fitted values.

plotDiagnostics(mdl,plottype) plots diagnostics in a plot of type plottype.

h = plotDiagnostics(...) returns handles to the lines in the plot.

h = plotDiagnostics(mdl,plottype,Name,Value) plots with additional options specified by one or more Name,Value pair arguments.

## Tips

• 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.

## Input Arguments

mdl

Linear model, as constructed by fitlm or stepwiselm.

plottype

String specifying the type of plot:

 'contour' Residual vs. leverage with overlayed Cook's contours 'cookd' Cook's distance 'covratio' Delete-1 ratio of determinant of covariance 'dfbetas' Scaled delete-1 coefficient estimates 'dffits' Scaled delete-1 fitted values 'leverage' Leverage 's2_i' Delete-1 variance estimate

Delete-1 means compute a new model without the current observation. If the delete-1 calculation differs significantly from the model using all observations, then the observation is influential.

Default: 'leverage'

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

 Note:   The plot property name-value pairs apply to the first returned handle h(1).
 'Color' Color of the line or marker, a string or ColorSpec specification. For details, see linespec. 'LineStyle' Type of line, a string or Chart Line Properties specification. For details, see linespec. 'LineWidth' Width of the line or edges of filled area, in points, a positive scalar. One point is 1/72 inch. Default: 0.5 'MarkerEdgeColor' Color of the marker or edge color for filled markers, a string or ColorSpec specification. For details, see linespec. 'MarkerFaceColor' Color of the marker face for filled markers, a string or ColorSpec specification. For details, see linespec. 'MarkerSize' Size of the marker in points, a strictly positive scalar. One point is 1/72 inch.

## Output Arguments

 h Vector of handles to lines or patches in the plot.

## Definitions

### Hat Matrix

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

H = X(XTX)–1XT.

The diagonal elements Hii satisfy

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

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

### Leverage

The leverage of observation i is the value of the ith diagonal term, hii, 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

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, Di, of observation i is

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

where

• ${\stackrel{^}{y}}_{j}$ is the jth fitted response value.

• ${\stackrel{^}{y}}_{j\left(i\right)}$ is the jth 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 ri is the ith residual, and hii is the ith leverage value.

CooksDistance is an n-by-1 column vector in the Diagnostics table of the LinearModel object.

## Examples

expand all

### Leverage Plot of Linear Model

Plot the leverage values of observations in a fitted model.

Load the carsmall data and fit a linear model of the mileage as a function of model year, weight, and weight squared.

```load carsmall
ds = dataset(MPG,Weight);
ds.Year = ordinal(Model_Year);
mdl = fitlm(ds,'MPG ~ Year + Weight^2');```

Plot the leverage values.

`plotDiagnostics(mdl)`

Plot the Cook's distance.

`plotDiagnostics(mdl,'cookd')`

The two diagnostic plots give different results.

## References

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

## Alternatives

The mdl.Diagnostics property contains the information that plotDiagnostics uses to create plots.