Preface ........................................................ xi
Note to Readers .............................................. xiii
1 A New Beginning .............................................. 1
2 Elementary Matrix Algebra: Part 1 ............................ 9
3 Elementary Matrix Algebra: Part 2 ........................... 17
4 Matrix Algebra and Multiple Linear Regression: Part 1 ....... 23
5 Matrix Algebra and Multiple Linear Regression: Part 2 ....... 33
6 Matrix Algebra and Multiple Linear Regression: Part 3 - The
Concept of Determinants ..................................... 43
7 Matrix Algebra and Multiple Linear Regression: Part 4 -
Concluding Remarks .......................................... 47
8 Experimental Designs: Part 1 ................................ 51
9 Experimental Designs: Part 2 ................................ 57
10 Experimental Designs: Part 3 ................................ 63
11 Analytic Geometry: Part 1 - The Basics in Two and Three
Dimensions .................................................. 71
12 Analytic Geometry: Part 2 - Geometric Representation of
Vectors and Algebraic Operations ............................ 77
13 Analytic Geometry: Part 3 - Reducing Dimensionality ......... 81
14 Analytic Geometry: Part 4 - The Geometry of Vectors and
Matrices .................................................... 85
15 Experimental Designs: Part 4 - Varying Parameters to
Expand the Design ........................................... 89
16 Experimental Designs: Part 5 - One-at-a-time Designs ........ 91
17 Experimental Designs: Part 6 - Sequential Designs ........... 93
18 Experimental Designs: Part 7 - Я, the Power of a Test ....... 97
19 Experimental Designs: Part 8 - Я, the Power of a Test
(Continued) ................................................ 101
20 Experimental Designs: Part 9 - Sequential Designs
Concluded .................................................. 103
21 Calculating the Solution for Regression Techniques:
Part 1 - Multivariate Regression Made Simple ............... 107
22 Calculating the Solution for Regression Techniques:
Part 2 - Principal Component(s) Regression Made Simple ..... 109
23 Calculating the Solution for Regression Techniques:
Part 3 - Partial Least Squares Regression Made Simple ...... 113
24 Looking Behind and Ahead: Interlude ........................ 117
25 A Simple Question: The Meaning of Chemometrics Pondered .... 119
26 Calculating the Solution for Regression Techniques:
Part 4 - Singular Value Decomposition ...................... 127
27 Linearity in Calibration ................................... 131
28 Challenges: Unsolved Problems in Chemometrics .............. 135
29 Linearity in Calibration: Act II Scene I ................... 141
30 Linearity in Calibration: Act II Scene II - Reader's
Comments ................................................... 145
31 Linearity in Calibration: Act II Scene III ................. 149
32 Linearity in Calibration: Act II Scene IV .................. 159
33 Linearity in Calibration: Act II Scene V ................... 163
34 Collaborative Laboratory Studies: Part 1 - A Blueprint ..... 167
35 Collaborative Laboratory Studies: Part 2 - using ANOVA ..... 179
36 Collaborative Laboratory Studies: Part 3 - Testing for
Systematic Error ........................................... 183
37 Collaborative Laboratory Studies: Part 4 - Ranking Test .... 185
38 Collaborative Laboratory Studies: Part 5 - Efficient
Comparison of Two Methods .................................. 187
39 Collaborative Laboratory Studies: Part 6 - MathCad
Worksheet Text ............................................. 193
40 Is Noise Brought by the Stork? Analysis of Noise: Part 1 ... 223
41 Analysis of Noise: Part 2 .................................. 227
42 Analysis of Noise: Part 3 .................................. 235
43 Analysis of Noise: Part 4 .................................. 243
44 Analysis of Noise: Part 5 .................................. 253
45 Analysis of Noise: Part 6 .................................. 271
46 Analysis of Noise: Part 7 .................................. 277
47 Analysis of Noise: Part 8 .................................. 285
48 Analysis of Noise: Part 9 .................................. 293
49 Analysis of Noise: Part 10 ................................. 299
50 Analysis of Noise: Part 11 ................................. 313
51 Analysis of Noise: Part 12 ................................. 317
52 Analysis of Noise: Part 13 ................................. 323
53 Analysis of Noise: Part 14 ................................. 329
54 Derivatives in Spectroscopy: Part 1 - The Behavior of the
Derivative ................................................. 339
55 Derivatives in Spectroscopy: Part 2 - The "True"
Derivative ................................................. 351
56 Derivatives in Spectroscopy: Part 3 - Computing the
Derivative ................................................. 359
57 Derivatives in Spectroscopy: Part 4 - Calibrating with
Derivatives ................................................ 371
58 Comparison of Goodness of Fit Statistics for Linear
Regression: Part 1 - Introduction .......................... 379
59 Comparison of Goodness of Fit Statistics for Linear
Regression: Part 2 - The Correlation Coefficient ........... 385
60 Comparison of Goodness of Fit Statistics for Linear
Regression: Part 3 - Computing Confidence Limits for the
Correlation Coefficient .................................... 393
61 Comparison of Goodness of Fit Statistics for Linear
Regression: Part 4 - Confidence Limits for Slope and
Intercept .................................................. 399
62 Correction and Discussion Regarding Derivatives ............ 413
63 Linearity in Calibration: Act III Scene I - Importance of
Nonlinearity ............................................... 421
64 Linearity in Calibration: Act III Scene II - A Discussion
of the Durbin-Watson Statistic, a Step in the Right
Direction .................................................. 427
65 Linearity in Calibration: Act III Scene III - Other Tests
for Nonlinearity ........................................... 435
66 Linearity in Calibration: Act III Scene IV - How to Test
for Nonlinearity ........................................... 439
67 Linearity in Calibration: Act III Scene V - Quantifying
Nonlinearity ............................................... 451
68 Linearity in Calibration: Act III Scene VI - Quantifying
Nonlinearity, Part II, and a News Flash .................... 459
69 Connecting Chemometrics to Statistics: Part 1 - The
Chemometrics Side .......................................... 471
70 Connecting Chemometrics to Statistics: Part 2 - The
Statistics Side ............................................ 477
71 Limitations in Analytical Accuracy: Part 1 - Horwitz's
Trumpet .................................................... 481
72 Limitations in Analytical Accuracy: Part 2 - Theories to
Describe the Limits in Analytical Accuracy ................. 487
73 Limitations in Analytical Accuracy: Part 3 - Comparing
Test Results for Analytical Uncertainty .................... 491
74 The Statistics of Spectral Searches ........................ 497
75 The Chemometrics of Imaging Spectroscopy ................... 503
Glossary of Terms ............................................. 509
Index ......................................................... 513
Colour Plate Section
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