MULTICOLLINEARITY AND THE ASTATISTICAL POWER OF REGRESSION ANALYSIS,
Abstract
The note has attempted to show two things: (1) In general, collinearity lowers the power of the statistical tests of significance in regression analysis. However, if one of two collinear variables is incorrectly dropped from the equation, we frequently will be less likely to accept the null hypothesis of no relationship than if the variables had been orthogonal. (2) If only one of two potential explanatory variables actually belongs in the model, the one which actually belongs 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 variable has the higher t-statistic. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1969
- Accession Number
- AD0695447
Entities
People
- Joseph P. Newhouse
Organizations
- RAND Corporation