Metrohm Vision – Theory - Manual (Page 5)

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Table of contents
1 Calibration Development ................................................................................................ 5
1.1 Simple Linear Regression .............................................................................. 5
1.1.1 Overview ................................................................................................................ 5
1.1.2 Correlation ............................................................................................................. 5
1.1.3 Sensitivity ............................................................................................................... 5
1.2 Multilinear Regression .................................................................................. 6
1.2.1 Overview ................................................................................................................ 6
1.2.2 Colinearity .............................................................................................................. 6
1.2.3 Multiple Correlation Coefficient .............................................................................. 6
1.3 Partial Least Squares (PLS) ............................................................................ 6
1.3.1 Overview ................................................................................................................ 6
1.3.2 Preprocessing Calibration Data................................................................................ 7
1.3.3 Selecting the Number of Factors ............................................................................. 7
1.3.4 Cross Validation ...................................................................................................... 7
1.4 Statistical Evaluation of Calibration Equations .............................................. 7
1.4.1 Multiple Correlation Coefficient .............................................................................. 7
1.4.2 Standard Error of Calibration................................................................................... 8
1.4.3 Standard Error of Prediction .................................................................................... 8
1.4.4 The F-Statistic ......................................................................................................... 8
1.4.5 Bias ........................................................................................................................ 8
2 Math Pretreatment Methods .......................................................................................... 9
2.1 N-Point Smooth ............................................................................................ 9
2.2 First Derivative .............................................................................................. 9
2.2.1 Calculation of the First Derivative ............................................................................ 9
2.2.2 Segment and Gap Size .......................................................................................... 10
2.3 Second Derivative ....................................................................................... 10
2.3.1 Calculation of the Second Derivative ..................................................................... 11
2.3.2 Segment and Gap Size .......................................................................................... 11
2.4 Third and Fourth Derivative ........................................................................ 12
2.5 Standard Normal Variate ............................................................................ 12
2.6 Baseline Correction ..................................................................................... 12
2.7 Detrend....................................................................................................... 12
2.8 Savitzky-Golay ............................................................................................ 13
2.9 Multiplicative Scatter Correction ................................................................. 13
3 Qualitative Library Development .................................................................................. 15
3.1 Principal Component Analysis ..................................................................... 15
3.2 Distance Metrics ......................................................................................... 16
3.2.1 Euclidean Distance ................................................................................................ 16
3.2.2 Mahalanobis Distance ........................................................................................... 16
3.2.3 Maximum Distance ............................................................................................... 17
3.2.4 Correlation ........................................................................................................... 17