com.numericalmethod.suanshu.stats.regression.linear.ols

Class Diagnostics

java.lang.Object

com.numericalmethod.suanshu.stats.regression.linear.ols.Diagnostics

All Implemented Interfaces:

java.io.Serializable

public class Diagnostics
extends java.lang.Object
implements java.io.Serializable

This class collects some diagnostics measures for the goodness of fit for an Ordinary Least Square linear regression model.

DFFITS is a diagnostic meant to show how influential a point is in a statistical regression. It is defined as the change ("DFFIT"), in the predicted value for a point, obtained when that point is left out of the regression, "Studentized" by dividing by the estimated standard deviation of the fit at that point.

Cook's distance is a commonly used estimate of the influence of a data point. Cook's distance can be used in several ways: to indicate data points that are particularly worth checking for validity; to indicate regions of the design space where it would be good to be able obtain more data points.

Hadi proposed a measure of influence of the i-th observation based on the fact that influential observations are outliers in either the response variable or in the predictors, or both.

See Also:

Wikipedia: Cook's distance
• Wikipedia: DFFITS

, Serialized Form

Field Summary

Fields

Modifier and Type	Field and Description
ImmutableVector	cookDistances Cook distance
ImmutableVector	DFFITS DFFITS, Welsch and Kuh Measure
ImmutableVector	Hadi Hadi's influence measure

Method Summary

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

DFFITS

public final ImmutableVector DFFITS

DFFITS, Welsch and Kuh Measure

See Also:

• "p.105 (4.23). Section 4.9.2. Regression Analysis by Example, 3rd edition, 2000. Chatterjee, Hadi and Price. Wiley Series in Probability and Statistics."
• Belsley, David A.; Edwin Kuh, Roy E. Welsch. Regression diagnostics : identifying influential data and sources of collinearity. Wiley series in probability and mathematical statistics. New York: John Wiley & Sons. ISBN 0471058564. 1980.

cookDistances

public final ImmutableVector cookDistances

Cook distance

See Also:

"p.200. Applied Linear Regression, 3rd edition, 2005. Sanford Weisberg. Wiley-Interscience."

Hadi

public final ImmutableVector Hadi

Hadi's influence measure

See Also:

"p.105 (4.24). Section 4.9.2. Regression Analysis by Example, 3rd edition, 2000. Chatterjee, Hadi and Price. Wiley Series in Probability and Statistics."