Plot diagnostics of linear regression model
h = plotDiagnostics(___)
h = plotDiagnostics(mdl,plottype,Name,Value)
diagnostics from the
mdl linear model using the
handles to the lines in the plot, using any of the previous syntaxes.
h = plotDiagnostics(___)
plottype— Type of plot
Type of plot, specified as one of the following:
|Residual vs. leverage with overlayed Cook's contours|
|Delete-1 ratio of determinant of covariance|
|Scaled delete-1 coefficient estimates|
|Scaled delete-1 fitted values|
|Delete-1 variance estimate|
Delete-1 means compute a new model without the current observation. If the delete-1 calculation differs significantly from the model using all observations, then the observation is influential.
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside single quotes (
' '). You can
specify several name and value pair arguments in any order as
The plot property name-value pairs apply to the first returned
Plot the leverage values of observations in a fitted model.
carsmall data 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 leverage values.
Plot the Cook's distance.
The two diagnostic plots give different results.
The hat matrix H is defined in terms of the data matrix X:
H = X(XTX)–1XT.
The diagonal elements hii satisfy
where n is the number of observations (rows of X), and p is the number of coefficients in the regression model.
The leverage of observation i is the value of the ith diagonal term, hii, of the hat matrix H. Because the sum of the leverage values is p (the number of coefficients in the regression model), an observation i can be considered to be an outlier if its leverage substantially exceeds p/n, where n is the number of observations.
Cook’s distance is the scaled change in fitted values.
Each element in
CooksDistance is the normalized
change in the vector of coefficients due to the deletion of an observation.
The Cook’s distance, Di,
of observation i is
is the jth fitted response value.
is the jth fitted response value, where the fit does not include observation i.
MSE is the mean squared error.
p is the number of coefficients in the regression model.
Cook’s distance is algebraically equivalent to the following expression:
where ri is the ith residual, and hii is the ith leverage value.
CooksDistance is an n-by-1
column vector in the
Diagnostics table of the
For many plots, the Data Cursor tool in the figure window displays the x and y values for any data point, along with the observation name or number.
mdl.Diagnostics property contains the
plotDiagnostics uses to create
 Neter, J., M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. Applied Linear Statistical Models, Fourth Edition. Irwin, Chicago, 1996.