Create added variable plot using input data
an added variable plot using the predictive terms in
the response values in
y, the added term in column
and the model with current terms specified by
an n-by-p matrix of n observations
of p predictive terms.
vector of n response values.
a scalar index specifying the column of
the term to be added.
inmodel is a logical vector
of p elements specifying the columns of
the current model. By default, all elements of
addedvarplot automatically includes a constant
term in all models. Do not enter a column of 1s directly into
stats output from the
to improve the efficiency of repeated calls to
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 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.
Load the data in
hald.mat, which contains observations of the reaction to heat for 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 that contains of the first two columns.
inmodel = [true true false false]; addedvarplot(ingredients,heat,3,inmodel)
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.
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.