A Criterion for Stepwise Regression |
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Authors: | R B Bendel A A Afifi |
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Institution: | 1. Statistical Service, College of Agriculture , Washington State Univ. , Pullman , WA , 99163 , USA;2. School of Public Health , Univ. of California , Los Angeles , CA , 90024 , USA |
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Abstract: | In “stepwise” regression analysis, the usual procedure enters or removes variables at each “step” on the basis of testing whether certain partial correlation coefficients are zero. An alternative method suggested in this paper involves testing the hypothesis that the mean square error of prediction does not decrease from one step to the next. This is equivalent to testing that the partial correlation coefficient is equal to a certain nonzero constant. For sample sizes sufficiently large, Fisher's z transformation can be used to obtain an asymptotically UMP unbiased test. The two methods are contrasted with an example involving actual data. |
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Keywords: | Central limit theorem Economic statistics Economic variables Normal distribution Pareto's law Regression disturbances Stable distributions |
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