Fitting Straight Lines with Replicated Observations by Linear Regression: The Least Squares Postulates

Abstract

The results obtained by statistical techniques are valid if the assumed conditions are satisfied. Fitting straight lines with replicated observations by linear regression is considered in this article paying special attention to the compliance of the least squares postulates. Normality, robustness, independence, abscissa free from error, and proper weights are contemplated sequentially in this article. A detailed consideration of multiple measurements at one or more points is included, with the importance of genuine replicates as well the number of necessary replications being emphasized. The authors expect the results of this review to be of value to investigators and also in the teaching.

Keywords:

• least squares postulates
• replicated observations
• straight lines