## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 31, Number 4 (1960), 929-938.

### 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.

#### Article information

**Source**

Ann. Math. Statist., Volume 31, Number 4 (1960), 929-938.

**Dates**

First available in Project Euclid: 27 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177705667

**Digital Object Identifier**

doi:10.1214/aoms/1177705667

**Mathematical Reviews number (MathSciNet)**

MR119376

**Zentralblatt MATH identifier**

0100.14802

**JSTOR**

links.jstor.org

#### Citation

Siddiqui, M. M. Tests for Regression Coefficients When Errors are Correlated. Ann. Math. Statist. 31 (1960), no. 4, 929--938. doi:10.1214/aoms/1177705667. https://projecteuclid.org/euclid.aoms/1177705667