Weighted Linear Regression Improves Accuracy of Quantitative Elemental Bioimaging by Means of LA-ICP-MS

The application of ordinary least squares (OLS) linear regression is widely used in order to approximate linear external calibration data. However, the assumption of homoscedasticity is often not considered as a requirement for correct data approximation, which can result in a poor regression fit that is often more prominent in the lower concentration range. Heteroscedasticity in inductively coupled plasma-mass spectrometry (ICP-MS) data has been discussed in literature as an intrinsic problem and was found to be addressed better by the use of weighted least squares (WLS) regression in multiple studies. In this study, the effects of OLS and WLS linear regression models have been investigated for quantitative imaging experiments by means of laser ablation (LA)-ICP-MS using matrix-matched standards. The calibration data produced by this technique was found to be heteroscedastic in all 60 analyzed datasets, which yielded poor regression fits for OLS linear regression. In comparison to conventional ICP-MS analysis, the resulting negative effects were found to become even more visible in imaging LA-ICP-MS due to an inaccurate estimation of the regression line's intercept. Also, the calculation of average concentrations in selected regions of interest (ROIs) yields incorrect quantification results at the lower end of the calibration range. The application of WLS linear regression resulted in an improved goodness of fit (GOF), although the weighting factor should be selected carefully. Besides the reciprocal of the variance of each calibration standard (1/s(i)(2)), more empirical weighting factors that have been discussed in the literature were also evaluated regarding the GOF.