Principal Component Regression and Partial Least Squares Modeling

<jats:title>Abstract</jats:title><jats:p>The sections in this article are</jats:p><jats:sec><jats:title>Introduction</jats:title><jats:sec><jats:title>Data Modeling by Latent Variables</jats:title><jats:sec><jats:title>Decomposition of Spectral Data Using Latent Variables</jats:title></jats:sec><jats:sec><jats:title>Least Squares Regression by Matrix Algebra</jats:title></jats:sec><jats:sec><jats:title>“Partial”<jats:styled-content style="fixed-case">CLS</jats:styled-content>to Yield a Principal Component</jats:title></jats:sec></jats:sec></jats:sec><jats:sec><jats:title>Principal Component Regressions</jats:title><jats:sec><jats:title>Comparison of<jats:named-content content-type="abbreviation"><jats:styled-content style="fixed-case">CLS</jats:styled-content></jats:named-content>and<jats:named-content content-type="abbreviation"><jats:styled-content style="fixed-case">ILS</jats:styled-content></jats:named-content></jats:title></jats:sec><jats:sec><jats:title>Generate Factors by<jats:styled-content style="fixed-case">PCA</jats:styled-content>for<jats:styled-content style="fixed-case">ILS</jats:styled-content></jats:title></jats:sec><jats:sec><jats:title>Protocols of<jats:named-content content-type="abbreviation"><jats:styled-content style="fixed-case">PCR</jats:styled-content></jats:named-content></jats:title><jats:sec><jats:title>Calculation Steps of<jats:named-content content-type="abbreviation"><jats:styled-content style="fixed-case">PCR</jats:styled-content></jats:named-content>Calibration</jats:title></jats:sec><jats:sec><jats:title>Calculation Steps for Concentration Prediction by<jats:named-content content-type="abbreviation"><jats:styled-content style="fixed-case">PCR</jats:styled-content></jats:named-content></jats:title></jats:sec></jats:sec><jats:sec><jats:title>Selection of Significant Factors</jats:title><jats:sec><jats:title>Analysis of Error</jats:title></jats:sec><jats:sec><jats:title>Empirically Defined Method of Error Estimation</jats:title></jats:sec><jats:sec><jats:title>Statistical Method for Error Estimation</jats:title></jats:sec><jats:sec><jats:title>Selection by Validation</jats:title></jats:sec></jats:sec><jats:sec><jats:title>Abstract Spectra and Residuals</jats:title></jats:sec><jats:sec><jats:title>Optional Pretreatment</jats:title><jats:sec><jats:title>Mean Centering</jats:title></jats:sec><jats:sec><jats:title>Scaling</jats:title></jats:sec><jats:sec><jats:title>Normalization</jats:title></jats:sec></jats:sec></jats:sec><jats:sec><jats:title>Partial Least Squares Regression</jats:title><jats:sec><jats:title><jats:styled-content style="fixed-case">PLS</jats:styled-content>2 (Global<jats:styled-content style="fixed-case">PLS</jats:styled-content>)</jats:title><jats:sec><jats:title><jats:styled-content style="fixed-case">PLS</jats:styled-content>2 Calibration</jats:title></jats:sec><jats:sec><jats:title>Discussion of the<jats:styled-content style="fixed-case">PLS</jats:styled-content>2 Algorithm</jats:title></jats:sec><jats:sec><jats:title>Selection of Basis Factors for<jats:styled-content style="fixed-case">PLS</jats:styled-content>Modeling</jats:title></jats:sec><jats:sec><jats:title><jats:styled-content style="fixed-case">PLS</jats:styled-content>Prediction</jats:title></jats:sec><jats:sec><jats:title><jats:styled-content style="fixed-case">PLS</jats:styled-content>Modeling by Eigenvector Calculation</jats:title></jats:sec><jats:sec><jats:title><jats:styled-content style="fixed-case">PLS</jats:styled-content>1 (Standard<jats:styled-content style="fixed-case">PLS</jats:styled-content>)</jats:title></jats:sec><jats:sec><jats:title>Comparison of<jats:styled-content style="fixed-case">PLS</jats:styled-content>2 with<jats:styled-content style="fixed-case">PLS</jats:styled-content>1</jats:title></jats:sec></jats:sec><jats:sec><jats:title>Comparison of<jats:styled-content style="fixed-case">PLS</jats:styled-content>with<jats:named-content content-type="abbreviation"><jats:styled-content style="fixed-case">PCR</jats:styled-content></jats:named-content></jats:title></jats:sec></jats:sec>