The Relationship among Sums of Squares, Correlation Coefficients, and Suppression

We examine the relationship between the extra sum of squares SSR(x 2 |x 1 ), the regression sum of squares SSR(x 2 ), and the correlation coefficients r y1 , r y2 , and r 12 . From this we develop a necessary and sufficient condition for suppression in terms of the correlation coefficients. We use t...

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Bibliographic Details
Published in:The American statistician 1997-02, Vol.51 (1), p.46-48
Main Authors: Sharpe, N. Radke, Roberts, R. A.
Format: Article
Language:English
Subjects:
Algebra
Correlation coefficients
Exact sciences and technology
Geometry
Inference from stochastic processes
time series analysis
Linear regression
Mathematical analysis
Mathematical models
Mathematics
Modeling
Multiple regression
Multivariate analysis
Probability and statistics
Ratios
Sciences and techniques of general use
Statistics
Students
Sufficient conditions
Suppression
Teacher's Corner
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Summary:We examine the relationship between the extra sum of squares SSR(x 2 |x 1 ), the regression sum of squares SSR(x 2 ), and the correlation coefficients r y1 , r y2 , and r 12 . From this we develop a necessary and sufficient condition for suppression in terms of the correlation coefficients. We use this to investigate the conditions under which suppression can occur algebraically and graphically. We believe that expressing suppression in terms of correlation coefficients may help students and applied researchers to identify cases of suppression and to understand when suppression can occur.
ISSN:0003-1305
1537-2731
DOI:10.1080/00031305.1997.10473587