A note on the effect of multicollinearity on the power of regression analysis. (1) In general, collinearity lowers the power of statistical tests of significance in regression analysis. However, if one of two collinear variables is incorrectly dropped, frequently the null hypotheses of no relationship is less likely to be accepted than if the variables had been orthogonal. (2) If only one of two potential explanatory variables actually belongs in the model, the correct one will have: (a) the higher expected t-statistic if two simple regressions are run, each with one of the two variables as an explanatory variable; (b) the higher expected t-statistic if both variables are included. Increasing the degree of collinearity can, however, make the expected values of the t-statistics arbitrarily close. In such a case, sampling error can be a major determinant of which has the higher t-statistic. 7 pp. (AR)
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