Tests for Regression Coefficients When Errors are Correlated

Abstract

In a previous paper [6] the covariances of least-squares estimates of regression coefficients and the expected value of the estimate of residual variance were investigated when the errors are assumed to be correlated. In this paper we will investigate the distribution of the usual test statistics for regression coefficients under the same assumptions. Applications of the theory to the cases of testing a single sample mean, the difference between the means of two samples, the coefficients in a linear trend and in regression on trigonometric functions will be discussed in some detail under an assumed covariance matrix for errors.