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(___)
mdl— Full, fitted linear regression model
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.
Specify optional comma-separated pairs of
Name is the argument
Value is the corresponding
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
'Color'— Color of line or marker
'LineStyle'— Line style
Chart Line Propertiesspecification
'LineWidth'— Width of line or edges
Width of the line or edges of filled area, in points, specified
as the comma-separated pair consisting of
a positive numeric value. One point is equal to 1/72 inch.
'MarkerEdgeColor'— Color of marker or edge
'MarkerFaceColor'— Color of marker face
'MarkerSize'— Size of marker
Size of the marker in points, specified as the comma-separated
pair consisting of
'MarkerSize' and a positive
numeric value. One point is 1/72 inch.
h— Graphics handles
Graphics handles, returned as a vector of graphics handles corresponding to the lines or patches in the plot.
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.