Ex-Post Determination of Significance in Multivariate Regression when the Independent Variables are Orthogonal

In multivariate regression, when the regressors are orthogonal, the estimates of the coefficients may be regarded, in the normal case, as an independent normal random sample with estimable variance. Significance is determined by the absolute magnitude of the highest member of the sample, after consideration of order statistics more generally in this context.

The method is applied to time series data analysed by Fisher and Yates (1957): while these authors identified, by their essentially ex ante approach, the first and second orthopolynomials as significant, ex post only the second is identifiable.