h = plotDiagnostics(...)
h = plotDiagnostics(mdl,plottype,Name,Value)
plotDiagnostics(mdl) plots diagnostics from the mdl linear model using scaled delete-1 fitted values.
h = plotDiagnostics(...) returns handles to the lines in the plot.
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.
String specifying the type of plot:
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,Value arguments. Name is 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 Name1,Value1,...,NameN,ValueN.
Width of the line or edges of filled area, in points, a positive scalar. One point is 1/72 inch.
Size of the marker in points, a strictly positive scalar. One point is 1/72 inch.
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 LinearModel object.
Plot the leverage values of observations in a fitted model.
Load the carsmall data and fit a linear model of the mileage as a function of model year, weight, and weight squared.
load carsmall ds = dataset(MPG,Weight); ds.Year = ordinal(Model_Year); mdl = fitlm(ds,'MPG ~ Year + Weight^2');
Plot the leverage values.
Plot the Cook's distance.
The two diagnostic plots give different results.
 Neter, J., M. H. Kutner, C. J. Nachtsheim, and W. Wasserman. Applied Linear Statistical Models, Fourth Edition. Irwin, Chicago, 1996.
The mdl.Diagnostics property contains the information that plotDiagnostics uses to create plots.