Plot residuals of linear regression model (2024)

Plot residuals of linear regression model

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Syntax

plotResiduals(mdl)

plotResiduals(mdl,plottype)

plotResiduals(mdl,plottype,Name,Value)

plotResiduals(ax,___)

h = plotResiduals(___)

Description

example

plotResiduals(mdl) creates a histogram plot of the linear regression model (mdl) residuals.

example

plotResiduals(mdl,plottype) specifies the residual plot type plottype.

plotResiduals(mdl,plottype,Name,Value) specifies additional options using one or more name-value pair arguments. For example, you can specify the residual type and the graphical properties of residual data points.

plotResiduals(ax,___) creates the plot in the axes specified by ax instead of the current axes, using any of the input argument combinations in the previous syntaxes.

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

Examples

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Histogram of Residuals

Open Live Script

Plot a histogram of the residuals of a fitted linear regression model.

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 carsmalltbl = table(MPG,Weight);tbl.Year = categorical(Model_Year);mdl = fitlm(tbl,'MPG ~ Year + Weight^2');

Create a histogram of the raw residuals using probability density function scaling.

plotResiduals(mdl)

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The area of each bar is the relative number of observations. The sum of the bar areas is equal to 1.

Normal Probability Plot of Residuals

Open Live Script

Create a normal probability plot of the residuals of a fitted linear regression model.

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 carsmallX = [Weight,Model_Year];mdl = fitlm(X,MPG,... 'y ~ x2 + x1^2','Categorical',2);

Create a normal probability plot of the residuals of the fitted model.

plotResiduals(mdl,'probability')

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Input Arguments

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Name-Value Arguments

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 for lines and Patch Properties for histogram. The specified properties apply to the appearance of residual data points or the appearance of the histogram.

ColorLine color
RGB triplet | hexadecimal color code | color name | short name

Line color, specified as the comma-separated pair consisting of 'Color' and 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 pair 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 hexadecimal color codes.

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

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

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

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

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

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

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

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

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"none"Not applicableNot applicableNot applicableNo color

Here are the RGB triplets and hexadecimal color codes for the default colors MATLAB® uses in many types of plots.

RGB TripletHexadecimal Color CodeAppearance
[0 0.4470 0.7410]"#0072BD"

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[0.8500 0.3250 0.0980]"#D95319"

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[0.9290 0.6940 0.1250]"#EDB120"

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[0.4940 0.1840 0.5560]"#7E2F8E"

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[0.4660 0.6740 0.1880]"#77AC30"

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[0.3010 0.7450 0.9330]"#4DBEEE"

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[0.6350 0.0780 0.1840]"#A2142F"

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Example: 'Color','blue'

LineWidthLine width
positive value

Line width, specified as the comma-separated pair consisting of 'LineWidth' and a positive value in points. If the line has markers, then the line width also affects the marker edges.

Example: 'LineWidth',0.75

MarkerMarker symbol
'o' | '+' | '*' | '.' | 'x' | ...

Marker symbol, specified as the comma-separated pair consisting of 'Marker' and one of the values in this table.

MarkerDescriptionResulting Marker
"o"Circle

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"+"Plus sign

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"*"Asterisk

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"."Point

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"x"Cross

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"_"Horizontal line

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"|"Vertical line

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"square"Square

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"diamond"Diamond

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"^"Upward-pointing triangle

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"v"Downward-pointing triangle

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">"Right-pointing triangle

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"<"Left-pointing triangle

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"pentagram"Pentagram

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"hexagram"Hexagram

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"none"No markersNot applicable

Example: 'Marker','+'

MarkerEdgeColorMarker outline color
'auto' (default) | 'none' | RGB triplet | hexadecimal color code | color name | short name

Marker outline color, specified as the comma-separated pair consisting of 'MarkerEdgeColor' and an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the Color name-value pair argument.

The default value of 'auto' uses the same color specified by using 'Color'.

Example: 'MarkerEdgeColor','blue'

MarkerFaceColorMarker fill color
'none' (default) | 'auto' | RGB triplet | hexadecimal color code | color name | short name

Marker fill color, specified as the comma-separated pair consisting of 'MarkerFaceColor' and an RGB triplet, hexadecimal color code, color name, or short name for one of the color options listed in the Color name-value pair argument.

The 'auto' value uses the same color specified by using 'Color'.

Example: 'MarkerFaceColor','blue'

MarkerSizeMarker size
6 (default) | positive value

Marker size, specified as the comma-separated pair consisting of 'MarkerSize' and a positive value in points.

Example: 'MarkerSize',2

Output Arguments

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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.

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.

Extended Capabilities

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced in R2012a

See Also

LinearModel | plotDiagnostics

Topics

  • Residuals
  • Compare Large and Small Stepwise Models
  • Compare Results of Standard and Robust Least-Squares Fit
  • Interpret Linear Regression Results
  • Linear Regression Workflow
  • Linear Regression

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Plot residuals of linear regression model (2024)
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