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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 the leverage values.

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

h = plotDiagnostics(___) returns handles to the lines in the plot, using any of the previous syntaxes.

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

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Full, fitted linear regression model, specified as a LinearModel object constructed using fitlm or stepwiselm.

Type of plot, specified as one of the following:

'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.

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).

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Color of the line or marker, specified as the comma-separated pair consisting of 'Color' and a ColorSpec specification. For details, see linespec.

Line style, specified as the comma-separated pair consisting of 'LineStyle' and a Chart Line Properties specification. For details, see linespec.

Width of the line or edges of filled area, in points, specified as the comma-separated pair consisting of 'LineWidth' and a positive numeric value. One point is equal to 1/72 inch.

Color of the marker or edge color for filled markers, specified as the comma-separated pair consisting of 'MarkerEdgeColor' and a ColorSpec specification. For details, see linespec.

Color of the marker face for filled markers, specified as the comma-separated pair consisting of 'MarkerFaceColor' and a ColorSpec specification. For details, see linespec.

Size of the marker in points, specified as the comma-separated pair consisting of 'MarkerSize' and a positive numeric value. One point is 1/72 inch.

Output Arguments

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Graphics handles, returned as a vector of graphics handles corresponding to the 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

0hii1i=1nhii=p,

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

Di=j=1n(y^jy^j(i))2pMSE,

where

  • y^j is the jth fitted response value.

  • y^j(i) 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:

Di=ri2pMSE(hii(1hii)2),

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

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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
tbl = table(MPG,Weight);
tbl.Year = categorical(Model_Year);
mdl = fitlm(tbl,'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.

Related Examples

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.

See Also

More About

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