Fitting Straight Lines with Replicated Observations by Linear Regression: Part II. Testing for Homogeneity of Variances

Abstract

The purpose of the previous, this, and subsequent articles in the series is to deal with the fitting of a straight line to experimental data in those cases in which replicate observations are realized. Special attention has been paid in this occasion to the straight line model, to the determination of the variance from a number of small samples, and to the problem of testing for homogeneity of variances. Ideally, weights should be determined by replicate measurements. However, little attention has been paid to the effect of replicating the response measurements in the context of regression analysis. Several methods that compare variances at different factor levels, such as the F, Bartlett, Cochran, Burr and Foster, Hartley, and Levene tests have been envisaged. Weighting and data transformation and variance analysis will be the subject of a future report. The authors expect the results of this critical review to be of value to investigators making use of these methods and also in the teaching.

Keywords:

• least squares method
• replicated observations
• straight line model
• straight lines
• testing for homogeneity of variances