plotAdjustedResponse

Adjusted response plot of linear regression model

Syntax

plotAdjustedResponse(mdl,var)

plotAdjustedResponse(mdl,var,Name,Value)

plotAdjustedResponse(ax,___)

h = plotAdjustedResponse(___)

Description

plotAdjustedResponse(mdl,var) creates an adjusted response plot for the variable var in the linear regression model mdl.

plotAdjustedResponse(mdl,var,Name,Value) specifies additional options using one or more name-value arguments. For example, you can specify the marker symbol and size for the data points.

plotAdjustedResponse(ax,___) plots into the axes specified by ax instead of the current axes (gca) using any of the input argument combinations in the previous syntaxes. (since R2024a)

h = plotAdjustedResponse(___) returns line objects. Use h to modify the properties of a specific line after you create the plot. For a list of properties, see Line Properties.

Examples

Plot Adjusted Responses

Load the carsmall data set 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 effect of Weight averaged over Year.

plotAdjustedResponse(mdl,'Weight')

Plot the effect of Year averaged over Weight.

plotAdjustedResponse(mdl,'Year');

Input Arguments

mdl — Linear regression model

LinearModel object

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

var — Variable for adjusted response plot

character vector | string array | positive integer

Variable for the adjusted response plot, specified as a character vector or string array of a name in mdl.PredictorNames, or a positive integer representing the index of a predictor from the names in mdl.VariableNames.

Data Types: char | string | single | double

ax — Target axes

Axes object

Since R2024a

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

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','*'

Note

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

Color — Line 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 Name	Short Name	RGB Triplet	Hexadecimal Color Code	Appearance
"red"	"r"	[1 0 0]	"#FF0000"
"green"	"g"	[0 1 0]	"#00FF00"
"blue"	"b"	[0 0 1]	"#0000FF"
"cyan"	"c"	[0 1 1]	"#00FFFF"
"magenta"	"m"	[1 0 1]	"#FF00FF"
"yellow"	"y"	[1 1 0]	"#FFFF00"
"black"	"k"	[0 0 0]	"#000000"
"white"	"w"	[1 1 1]	"#FFFFFF"
"none"	Not applicable	Not applicable	Not applicable	No color

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

RGB Triplet	Hexadecimal Color Code	Appearance
[0 0.4470 0.7410]	"#0072BD"
[0.8500 0.3250 0.0980]	"#D95319"
[0.9290 0.6940 0.1250]	"#EDB120"
[0.4940 0.1840 0.5560]	"#7E2F8E"
[0.4660 0.6740 0.1880]	"#77AC30"
[0.3010 0.7450 0.9330]	"#4DBEEE"
[0.6350 0.0780 0.1840]	"#A2142F"

Example: 'Color','blue'

LineWidth — Line 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

Marker — Marker symbol

'o' | '+' | '*' | '.' | 'x' | ...

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

Marker	Description	Resulting Marker
"o"	Circle
"+"	Plus sign
"*"	Asterisk
"."	Point
"x"	Cross
"_"	Horizontal line
"|"	Vertical line
"square"	Square
"diamond"	Diamond
"^"	Upward-pointing triangle
"v"	Downward-pointing triangle
">"	Right-pointing triangle
"<"	Left-pointing triangle
"pentagram"	Pentagram
"hexagram"	Hexagram
"none"	No markers	Not applicable

Example: 'Marker','+'

MarkerEdgeColor — Marker 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'

MarkerFaceColor — Marker 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'

MarkerSize — Marker 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

h — Line objects

vector

Line objects, returned as a 2-by-1 vector. h(1) corresponds to the adjusted response data points, and h(2) corresponds to the adjusted response function. Use dot notation to query and set properties of the line objects. For details, see Line Properties.

You can use name-value pair arguments to specify the appearance of adjusted response data points corresponding to the first graphics object h(1).

More About

Adjusted Response

An adjusted response function describes the relationship between the fitted response and a single predictor, with the other predictors averaged out by averaging the fitted values over the data used in the fit.

A regression model for the predictor variables (x₁, x₂, …, x_p) and the response variable y has the form

y_i = f(x_1i, x_2i, …, x_pi) + r_i,

where f is a fitted regression function and r is a residual. The subscript i represents the observation number.

The adjusted response function for the first predictor variable x₁, for example, is defined as

$$g\left(x_1\right)=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}f\left(x_1,x_{2i},x_{3i},\mathrm{...},x_{pi}\right)},$$

where n is the number of observations. The adjusted response data value is the sum of the adjusted fitted value and the residual for each observation.

$${\tilde{y}}_i=g\left(x_{1i}\right)+r_i.$$

plotAdjustedResponse plots the adjusted response function and the adjusted response data values for a selected predictor variable.

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.

• plotPartialDependence creates either a line plot or a surface plot of predicted responses against a single feature or a pair of features, respectively, by marginalizing over the other variables. A line plot for a single feature from plotPartialDependence and an adjusted response function plot from plotAdjustedResponse are the same within numerical precision.

• plotEffects creates a summary plot that shows separate effects for all predictors.

• plotAdded shows the incremental effect on the response of specified terms by removing the effects of the other terms, whereas plotAdjustedResponse shows the effect of a selected predictor in the model fit with the other predictors averaged out by averaging the fitted values. Note that the definitions of adjusted values in plotAdded and plotAdjustedResponse are not the same.

Extended Capabilities

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

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

Version History

Introduced in R2012a

R2024a: Specify target axes

Specify the target axes for the plot by using the ax input argument.