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plotDiagnostics

Plot observation diagnostics of linear regression model

Description

plotDiagnostics creates a plot of observation diagnostics such as leverage, Cook's distance, and delete-1 statistics to identify outliers and influential observations.

plotDiagnostics(mdl) creates a leverage plot of the linear regression model (mdl) observations. A dotted line in the plot represents the recommended threshold values.

example

plotDiagnostics(mdl,plottype) specifies the type of observation diagnostics plottype.

plotDiagnostics(___,Name,Value) specifies additional options using one or more name-value arguments in addition to any of the input argument combinations in the previous syntaxes. For example, you can specify the marker symbol and size for the data points.

plotDiagnostics(ax,___) plots into the axes specified by ax instead of the current axes (gca). (since R2024a)

h = plotDiagnostics(___) returns graphics objects for the lines or contour in the plot. Use h to modify the properties of a specific line or contour after you create the plot. For a list of properties, see Line Properties and Contour Properties.

Examples

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Plot the leverage values and Cook's distances of observations and find the outliers.

Load the carsmall data set and fit a linear regression 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)
legend('show') % Show the legend

Figure contains an axes object. The axes object with title Case order plot of leverage, xlabel Row number, ylabel Leverage contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Leverage, Reference Line.

The dotted line represents the recommended threshold value 2*p/n, where p is the number of coefficients, and n is the number of observations. Find the threshold value using the NumCoefficients and NumObservations properties.

t_leverage = 2*mdl.NumCoefficients/mdl.NumObservations
t_leverage = 
0.1064

Find the observations with leverage values that exceed the threshold value.

find(mdl.Diagnostics.Leverage > t_leverage)
ans = 3×1

    26
    32
    35

You can also find an observation number by using a data tip. Select the data points above the threshold line to display their data tips. The data tip includes the x-axis and y-axis values for the selected point, along with the observation number.

Plot the Cook's distance values.

plotDiagnostics(mdl,'cookd')

Figure contains an axes object. The axes object with title Case order plot of Cook's distance, xlabel Row number, ylabel Cook's distance contains 2 objects of type line. One or more of the lines displays its values using only markers These objects represent Cook's distance, Reference Line.

The dotted line represents the recommended threshold value. Compute the threshold value t_cookd.

t_cookd = 3*mean(mdl.Diagnostics.CooksDistance,'omitnan')
t_cookd = 
0.0320

Find the observations with the Cook's distance values that exceed the threshold value.

find(mdl.Diagnostics.CooksDistance > t_cookd)
ans = 6×1

    26
    35
    80
    90
    92
    97

Two observations (26 and 35) are outliers by both measures, but some points (32, 80, 90, 92, and 97) are outliers by only one measure.

Input Arguments

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Linear regression model, specified as a LinearModel object created using fitlm or stepwiselm.

Type of plot, specified as one of the values in this table.

ValuePlot TypeDotted Reference Line in Plot Purpose
'contour'Residual vs. leverage with overlaid contours of Cook's distanceContours of Cook's distanceIdentify observations with large residual values, high leverage, and large Cook's distance values.
'cookd'Cook's distanceRecommended threshold, computed by 3*mean(mdl.Diagnostics.CooksDistance)Identify observations with large Cook's distance values.
'covratio'Delete-1 ratio of determinant of covarianceRecommended thresholds, computed by 1±3*p/n, where p is the number of coefficients (mdl.NumCoefficients) and n is the number of observations (mdl.NumObservations)Identify observations where the delete-1 statistic value is not in the range of the recommended thresholds.
'dfbetas'Delete-1 scaled differences in coefficient estimatesRecommended threshold, computed by 3/sqrt(n)Identify observations with large delete-1 statistic values.
'dffits'Delete-1 scaled differences in fitted valuesRecommended threshold, computed by 2*sqrt(p/n) in an absolute valueIdentify observations with large delete-1 statistic values in an absolute value.
'leverage'LeverageRecommended threshold, computed by 2*p/nIdentify high leverage observations.
's2_i'Delete-1 varianceMean squared error (mdl.MSE)Compare the delete-1 variance with the mean squared error.

For all plot types except 'contour', the x-axis is the row number (case order) of observations.

The Diagnostics property of mdl contains the diagnostic values used by plotDiagnostics to create plots.

For more information about observation diagnostics, see Cook’s Distance, Delete-1 Statistics, and Leverage.

Since R2024a

Target axes, specified as an Axes object. If you do not specify the axes, then plotDiagnostics uses the current axes (gca).

Name-Value Arguments

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Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'Color','blue','Marker','o'

Note

The graphical properties listed here are only a subset. For a complete list, see Line Properties. The specified properties determine the appearance of diagnostic data points.

Line color, specified an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the following table.

The Color name-value argument also determines marker outline color and marker fill color if MarkerEdgeColor is "auto" (default) and MarkerFaceColor is "auto".

For a custom color, specify an RGB triplet or a hexadecimal color code.

  • An RGB triplet is a three-element row vector whose elements specify the intensities of the red, green, and blue components of the color. The intensities must be in the range [0,1], for example, [0.4 0.6 0.7].

  • A hexadecimal color code is a string scalar or character vector that starts with a hash symbol (#) followed by three or six hexadecimal digits, which can range from 0 to F. The values are not case sensitive. Therefore, the color codes "#FF8800", "#ff8800", "#F80", and "#f80" are equivalent.

Alternatively, you can specify some common colors by name. This table lists the named color options, the equivalent RGB triplets, and the hexadecimal color codes.

Color NameShort NameRGB TripletHexadecimal Color CodeAppearance
"red""r"[1 0 0]"#FF0000"

Sample of the color red

"green""g"[0 1 0]"#00FF00"

Sample of the color green

"blue""b"[0 0 1]"#0000FF"

Sample of the color blue

"cyan" "c"[0 1 1]"#00FFFF"

Sample of the color cyan

"magenta""m"[1 0 1]"#FF00FF"

Sample of the color magenta

"yellow""y"[1 1 0]"#FFFF00"

Sample of the color yellow

"black""k"[0 0 0]"#000000"

Sample of the color black

"white""w"[1 1 1]"#FFFFFF"

Sample of the color white

"none"Not applicableNot applicableNot applicableNo color

This table lists the default color palettes for plots in the light and dark themes.

PalettePalette Colors

"gem" — Light theme default

Before R2025a: Most plots use these colors by default.

Sample of the "gem" color palette

"glow" — Dark theme default

Sample of the "glow" color palette

You can get the RGB triplets and hexadecimal color codes for these palettes using the orderedcolors and rgb2hex functions. For example, get the RGB triplets for the "gem" palette and convert them to hexadecimal color codes.

RGB = orderedcolors("gem");
H = rgb2hex(RGB);

Before R2023b: Get the RGB triplets using RGB = get(groot,"FactoryAxesColorOrder").

Before R2024a: Get the hexadecimal color codes using H = compose("#%02X%02X%02X",round(RGB*255)).

Example: Color="blue"

Data Types: single | double | string | char

Line width, specified as a positive value in points. If the line has markers, then the line width also affects the marker edges.

Example: LineWidth=0.75

Data Types: single | double

Marker symbol, specified as one of the values in this table.

MarkerDescriptionResulting Marker
"o"Circle

Sample of circle marker

"+"Plus sign

Sample of plus sign marker

"*"Asterisk

Sample of asterisk marker

"."Point

Sample of point marker

"x"Cross

Sample of cross marker

"_"Horizontal line

Sample of horizontal line marker

"|"Vertical line

Sample of vertical line marker

"square"Square

Sample of square marker

"diamond"Diamond

Sample of diamond marker

"^"Upward-pointing triangle

Sample of upward-pointing triangle marker

"v"Downward-pointing triangle

Sample of downward-pointing triangle marker

">"Right-pointing triangle

Sample of right-pointing triangle marker

"<"Left-pointing triangle

Sample of left-pointing triangle marker

"pentagram"Pentagram

Sample of pentagram marker

"hexagram"Hexagram

Sample of hexagram marker

"none"No markersNot applicable

Example: Marker="+"

Data Types: string | char

Marker outline color, specified an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the Color name-value argument.

The default value "auto" uses the same color specified by using the Color name-value argument. You can also specify "none" for no color.

Example: MarkerEdgeColor="blue"

Data Types: single | double | string | char

Marker fill color, specified as an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the Color name-value argument. The default value "none" specifies no color.

The "auto" value uses the same color specified by using the Color name-value argument.

Example: MarkerFaceColor="blue"

Data Types: single | double | string | char

Marker size, specified as a positive value in points.

Example: MarkerSize=2

Data Types: single | double

Output Arguments

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Graphics objects corresponding to the lines or contour in the plot, returned as a graphics array. Use dot notation to query and set properties of the graphics objects. For details, see Line Properties and Contour Properties.

You can use name-value pair arguments to specify the appearance of diagnostic data points corresponding to the first graphics object h(1). If plottype is 'dfbetas', the plot includes a line object for each coefficient. Name-value pair arguments specify the line object properties of all coefficients. You can modify the properties of each coefficient separately by using the corresponding graphics object.

More About

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Tips

  • The data cursor displays the values of the selected plot point in a data tip (small text box located next to the data point). The data tip includes the x-axis and y-axis values for the selected point, along with the observation name or number.

  • Use legend('show') to show the pre-populated legend.

Alternative Functionality

  • A LinearModel object provides multiple plotting functions.

    • When creating a model, use plotAdded to understand the effect of adding or removing a predictor variable.

    • When verifying a model, use plotDiagnostics to find questionable data and to understand the effect of each observation. Also, use plotResiduals to analyze the residuals of the model.

    • After fitting a model, use plotAdjustedResponse, plotPartialDependence, and plotEffects to understand the effect of a particular predictor. Use plotInteraction to understand the interaction effect between two predictors. Also, use plotSlice to plot slices through the prediction surface.

References

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

Extended Capabilities

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Version History

Introduced in R2012a

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