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Create added variable plot using input data




addedvarplot(X,y,num,inmodel) displays an added variable plot using the predictive terms in X, the response values in y, the added term in column num of X, and the model with current terms specified by inmodel. X is an n-by-p matrix of n observations of p predictive terms. y is vector of n response values. num is a scalar index specifying the column of X with the term to be added. inmodel is a logical vector of p elements specifying the columns of X in the current model. By default, all elements of inmodel are false.


addedvarplot automatically includes a constant term in all models. Do not enter a column of 1s directly into X.

addedvarplot(X,y,num,inmodel,stats) uses the stats output from the stepwisefit function to improve the efficiency of repeated calls to addedvarplot. Otherwise, this syntax is equivalent to the previous syntax.

addedvarplot(ax,___) creates the plot in the axes specified by ax instead of the current axes (gca). The option ax can precede any of the input argument combinations in the previous syntaxes. For more information on creating an Axes object, see axes and gca.

Added variable plots are used to determine the unique effect of adding a new term to a multilinear model. The plot shows the relationship between the part of the response unexplained by terms already in the model and the part of the new term unexplained by terms already in the model. The “unexplained” parts are measured by the residuals of the respective regressions. A scatter of the residuals from the two regressions forms the added variable plot. In addition to the scatter of residuals, the plot produced by addedvarplot shows 95% confidence intervals on predictions from the fitted line. The slope of the fitted line is the coefficient that the new term would have if it were added to the model with terms inmodel. For more details, see Added Variable Plot.

Added variable plots are sometimes known as partial regression leverage plots.


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Load the data in hald.mat, which contains observations of the reaction to heat for various cement mixtures.

load hald
  Name              Size            Bytes  Class     Attributes

  Description      22x58             2552  char                
  hald             13x5               520  double              
  heat             13x1               104  double              
  ingredients      13x4               416  double              

Create an added variable plot to investigate the effect of adding the third column of ingredients to a model that contains the first two columns.

inmodel = [true true false false];

The wide scatter plot and the low slope of the fitted line are evidence against the statistical significance of adding the third column to the model.

Alternative Functionality

You can create a linear regression model object LinearModel by using fitlm or stepwiselm and use the object function plotAdded to create an added variable plot.

A LinearModel object provides the object properties and the object functions to investigate a fitted linear regression model. The object properties include information about coefficient estimates, summary statistics, fitting method, and input data. Use the object functions to predict responses and to modify, evaluate, and visualize the linear regression model.

Version History

Introduced before R2006a