Added variable plot
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.
Note: 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.
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 fitted line has intercept zero because, under typical linear model assumptions, both of the plotted variables have mean zero. 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.
Added variable plots are sometimes known as partial regression leverage plots.
Load the data in hald.mat, which contains observations of the heat of reaction of various cement mixtures:
load hald whos 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 addition of the third column of ingredients to a model consisting of the first two columns:
inmodel = [true true false false]; addedvarplot(ingredients,heat,3,inmodel)
The wide scatter and the low slope of the fitted line are evidence against the statistical significance of adding the third column to the model.