Chemometrics in Excel

Providing an easy explanation of the fundamentals, methods, and
applications of chemometrics

• Acts as a practical guide to multivariate data
  analysis techniques

• Explains the methods used in Chemometrics and teaches
  the reader to perform all relevant calculations

• Presents the basic chemometric methods as worksheet
  functions in Excel

• Includes Chemometrics Add In for download which uses
  Microsoft Excel® for chemometrics training

• Online downloads includes workbooks with examples

Autorentext

Alexey L Pomerantsev is a Leading Researcher at The Russian
Academy of Science. He is a founding member and Chair of the
Russian Chemometrics Society, being instrumental in organizing the
annual Winter Symposium on Chemometrics. He is a peer reviewer and
member of Editorial Board of the Journal 'Chemometrics and
Intelligent Laboratory Systems.' Dr. Pomerantsev has over 100
publications, many of them dealing with Chemometric Investigations.

Zusammenfassung

Providing an easy explanation of the fundamentals, methods, and applications of chemometrics

• Acts as a practical guide to multivariate data analysis techniques
• Explains the methods used in Chemometrics and teaches the reader to perform all relevant calculations
• Presents the basic chemometric methods as worksheet functions in Excel
• Includes Chemometrics Add In for download which uses Microsoft Excel® for chemometrics training
• Online downloads includes workbooks with examples

Inhalt

Preface xvii

PART I INTRODUCTION 1

1 What is Chemometrics? 3

1.1 Subject of Chemometrics, 3

1.2 Historical Digression, 5

2 What the Book Is About? 8

2.1 Useful Hints, 8

2.2 Book Syllabus, 9

2.3 Notations, 10

3 Installation of Chemometrics Add-In 11

3.1 Installation, 11

3.2 General Information, 14

4 Further Reading on Chemometrics 15

4.1 Books, 15

4.1.1 The Basics, 15

4.1.2 Chemometrics, 16

4.1.3 Supplements, 16

4.2 The Internet, 17

4.2.1 Tutorials, 17

4.3 Journals, 17

4.3.1 Chemometrics, 17

4.3.2 Analytical, 18

4.3.3 Mathematical, 18

4.4 Software, 18

4.4.1 Specialized Packages, 18

4.4.2 General Statistic Packages, 19

4.4.3 Free Ware, 19

PART II THE BASICS 21

5 Matrices and Vectors 23

5.1 The Basics, 23

5.1.1 Matrix, 23

5.1.2 Simple Matrix Operations, 24

5.1.3 Matrices Multiplication, 25

5.1.4 Square Matrix, 26

5.1.5 Trace and Determinant, 27

5.1.6 Vectors, 28

5.1.7 Simple Vector Operations, 29

5.1.8 Vector Products, 29

5.1.9 Vector Norm, 30

5.1.10 Angle Between Vectors, 30

5.1.11 Vector Representation of a Matrix, 30

5.1.12 Linearly Dependent Vectors, 31

5.1.13 Matrix Rank, 31

5.1.14 Inverse Matrix, 31

5.1.15 Pseudoinverse, 32

5.1.16 MatrixVector Product, 33

5.2 Advanced Information, 33

5.2.1 Systems of Linear Equations, 33

5.2.2 Bilinear and Quadratic Forms, 34

5.2.3 Positive Definite Matrix, 34

5.2.4 Cholesky Decomposition, 34

5.2.5 Polar Decomposition, 34

5.2.6 Eigenvalues and Eigenvectors, 35

5.2.7 Eigenvalues, 35

5.2.8 Eigenvectors, 35

5.2.9 Equivalence and Similarity, 36

5.2.10 Diagonalization, 37

5.2.11 Singular Value Decomposition (SVD), 37

5.2.12 Vector Space, 38

5.2.13 Space Basis, 39

5.2.14 Geometric Interpretation, 39

5.2.15 Nonuniqueness of Basis, 39

5.2.16 Subspace, 40

5.2.17 Projection, 40

6 Statistics 42

6.1 The Basics, 42

6.1.1 Probability, 42

6.1.2 Random Value, 43

6.1.3 Distribution Function, 43

6.1.4 Mathematical Expectation, 44

6.1.5 Variance and Standard Deviation, 44

6.1.6 Moments, 44

6.1.7 Quantiles, 45

6.1.8 Multivariate Distributions, 45

6.1.9 Covariance and Correlation, 45

6.1.10 Function, 46

6.1.11 Standardization, 46

6.2 Main Distributions, 46

6.2.1 Binomial Distribution, 46

6.2.2 Uniform Distribution, 47

6.2.3 Normal Distribution, 48

6.2.4 Chi-Squared Distribution, 50

6.2.5 Student's Distribution, 52

6.2.6 F-Distribution, 53

6.2.7 Multivariate Normal Distribution, 54

6.2.8 Pseudorandom Numbers, 55

6.3 Parameter Estimation, 56

6.3.1 Sample, 56

6.3.2 Outliers and Extremes, 56

6.3.3 Statistical Population, 56

6.3.4 Statistics, 57

6.3.5 Sample Mean and Variance, 57

6.3.6 Sample Covariance and Correlation, 58

6.3.7 Order Statistics, 59

6.3.8 Empirical Distribution and Histogram, 60

6.3.9 Method of Moments, 61

6.3.10 The Maximum Likelihood Method, 62

6.4 Properties of the Estimators, 62

6.4.1 Consistency, 62

6.4.2 Bias, 63

6.4.3 Effectiveness, 63

6.4.4 Robustness, 63

6.4.5 Normal Sample, 64 6.5 Confiden...