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An Application of Pairwise Independence of Random Variables to Regression Analysis

Published online by Cambridge University Press:  20 November 2018

Ronald A. Schaufele*
Affiliation:
York University
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Abstract

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The exact probability of making an error at the first stage of a stepwise regression is found, both when the independent variables are fixed and when they are random. The probabilities differ in the two cases because the random variables involved are pairwise independent but not jointly independent.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Anderson, T. W., An introduction to multivariate statistical analysis, Wiley, 1958.Google Scholar
2. Cramer, Harald, Mathematical methods of statistics, Princeton University Press, 1946.Google Scholar
3. Draper, N. R., Guttman, I., and Kanemasu, A., The distribution of certain regression statistics y Biometrika, 1971, 58 295-298.Google Scholar
4. Draper, Norman and Smith, Harry, Applied regression analysis, Wiley, 1966.Google Scholar
5. Feller, W., An introduction to probability theory and its applications (2nd edition), Wiley, 1957.Google Scholar
6. Geisser, Seymour and Mantel, Nathan, Pairwise independence of jointly dependent variables, Ann. Math. Statist., 1965, 36 1313-17.Google Scholar