774 (2002) 215–222 Journal of Chromatography B, www.elsevier.com / locate / chromb Linear regression for calibration lines revisited: weighting schemes for bioanalytical methods * ˜ A.M. Almeida, M.M. Castel-Branco, A.C. Falcao Laboratory of Pharmacology, Faculty of Pharmacy, Coimbra University, 3000-295 Coimbra, Portugal Received 26 January 2002; received in revised form 11 April 2002; accepted 11 April 2002 Abstract When the assumption of homoscedasticity is not met for analytical data, a simple and effective way to counteract the greater influence of the greater concentrations on the fitted regression line is to use weighted least squares linear regression (WLSLR). The purpose of the present paper is to stress the relevance of weighting schemes for linear regression analysis and to show how this approach can be useful in the bioanalytical field. The steps to be taken in the study of the linear calibration approach are described. The application of weighting schemes was shown by using a high-performance liquid chromatog- raphy method for the determination of lamotrigine in biological fluids as a practical example. By using the WLSLR, the accuracy of the analytical method was improved at the lower end of the calibration curve. Bioanalytical methods data analysis was improved by using the WLSLR procedure.  2002 Published by Elsevier Science B.V. Keywords: Linear regression; Heteroscedasticity; Weighting schemes; Bioanalytical methods 1. Introduction data. Obviously, when the range in x-values is somewhat larger—usually a concentration range of A well-designed and interpreted calibration curve more than one order of magnitude—it might be is essential in any analytical methodology. In fact, expected that the variance of each data point might the quality of bioanalytical data is highly dependent be quite different [1]. Larger deviations present at on the quality of the standard curve used to generate larger concentrations tend to influence (weight) the it. Analyte concentrations in unknown samples are regression line more than smaller deviations associ- typically evaluated by using the regression results ated with smaller concentrations, and thus the ac- obtained from calibration curves and although some curacy in the lower end of the range is impaired analytical procedures may require a non-linear cali- [1–3]. A simple and effective way to counteract this bration approach, linear regression is the most com- situation is to use weighted least squares linear monly adopted model. regression (WLSLR) [1,2,4–7]. The aim of the However, the condition of equal variances, termed present paper is to stress the relevance of weighting homoscedasticity, is frequently not met for analytical schemes for linear regression analysis and to show how this approach can be used and be useful in the bioanalytical field. Although statistical considera- *Corresponding author. Tel.: 1351-239-820-510; fax: 1351- tions are not new for mathematical experts, we 239-837-731. ˜ E-mail address: acfalcao@ff.uc.pt (A.C. Falcao). believe the present paper may be of great utility for 1570-0232 / 02 / $ – see front matter  2002 Published by Elsevier Science B.V. PII: S1570-0232(02)00244-1