Avoiding some common mistakes in straight line regression. Part 1

Analytical scientists generate and use bivariate experimental data mostly in two distinct application areas. In a quantitative calibration experiment standard materials are used to establish a calibration line that can be applied to estimate the concentrations of test samples. A second source of bivariate data is in the comparison of two analytical methods, often for validation purposes: results from the two methods as applied to the same set of test materials are plotted against each other in the hope of obtaining an excellent straight line fit to demonstrate agreement between them. There are several ways of deriving a straight line from bivariate data: the best will depend on which of these applications is involved and on the methods used in assembling the data. In practice a straight line may not be an adequate model for the data, but even if it is, regression methods are often misused and misinterpreted.