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The aim of this paper is the application of multivariate linear calibration for quantitative determination of elements (K, Cd, Co, Hg, As, Pb, Ni, and Al) in water by using Total Reflection X‐ray Fluorescence Analysis with partial least squares (PLS) as a regression method to improve a result of common univariate method. In purpose of elimination of matrix effects in X‐ray fluorescence analysis, experimental design was applied. As a set of standard samples for multivariate calibration, a five‐level eight‐factor calibration design of 25 samples was chosen, ensuring mutual orthogonality of factors. For model's validation, the independent test set of 15 samples was examined. The collection of spectra and quantitative measurements was carried out on S2 PICOFOX. The PLS regression was performed by using software package STATISTICA. Quality indicators of multivariate calibration as slope (b) and intercept (a) of calibration, correlation coefficient (r), determination coefficient (R2), root mean square errors of calibration and of prediction, standard errors of calibration and of prediction, biases of calibration, and biases of prediction were calculated. These results were compared with the univariate model, and as a result, the multivariate calibration method exceeds the univariate one. The obtained results could be applied in a laboratory for an analysis of water solutions in the concentration range 0.05–2.00 mg/L. In many real situations, when analytical chemist deals with multi‐element mixtures, multivariate calibration approach combined with orthogonal design for multivariate calibration set could be successfully used to improve a conventional univariate calibration.

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The provenance study of archaeological materials is an important step in understanding the cultural and economic life of ancient human communities. One of the most popular approaches in provenance studies is to obtain the chemical composition of material and process it with chemometric methods. In this paper, we describe a combination of the total-reflection X-ray fluorescence (TXRF) method and chemometric techniques (PCA, k-means cluster analysis, and SVM) to study Neolithic ceramic samples from eastern Siberia (Baikal region). A database of ceramic samples was created and included 10 elements/indicators for classification by geographical origin and ornamentation type. This study shows that PCA cannot be used as the primary method for provenance purposes, but can show some patterns in the data. SVM and k-means cluster analysis classified most of the ceramic samples by archaeological site and type with high accuracy. The application of chemometric techniques also showed the similarity of some samples found at sites located close to each other. A database created and processed by SVM or k-means cluster analysis methods can be supplemented with new samples and automatically classified.