Data analysis using the method of least squares : extracting the most information from experiments / J. Wolberg.

Format:

Book

Author/Creator:

Wolberg, John R.

Language:

English

Subjects (All):

Least squares.

Engineering mathematics.

Engineering--Experiments.

Engineering.

Physical Description:

xiii, 250 pages : illustrations ; 24 cm

Place of Publication:

Berlin ; New York : Springer, [2006]

Summary:

The preferred method of data analysis of quantitative experiments is the method of least squares. Often, however, the full power of the method is overlooked and very few books deal with this subject at the level that it deserves. The purpose of Data Analysis Using the Method of Least Squares is to fill this gap and include the type of information required to help scientists and engineers apply the method to problems in their special fields of interest. In addition, graduate students in science and engineering doing work of experimental nature can benefit from this book. Particularly, both linear and non-linear least squares, the use of experimental error estimates for data weighting, procedures to include prior estimates, methodology for selecting and testing models, prediction analysis, and some non-parametric methods are discussed.

Contents:

1.1 Quantitative Experiments 1

1.2 Dealing with Uncertainty 5

1.3 Statistical Distributions 6

The normal distribution 8

The binomial distribution 10

The Poisson distribution 11

The x[superscript 2] distribution 13

The t distribution 15

The F distribution 16

1.4 Parametric Models 17

1.6 Systematic Errors 22

1.7 Nonparametric Models 24

1.8 Statistical Learning 27

Chapter 2 The Method of Least Squares 31

2.2 The Objective Function 34

2.3 Data Weighting 38

2.4 Obtaining the Least Squares Solution 44

2.5 Uncertainty in the Model Parameters 50

2.6 Uncertainty in the Model Predictions 54

2.7 Treatment of Prior Estimates 60

2.8 Applying Least Squares to Classification Problems 64

Chapter 3 Model Evaluation 73

3.2 Goodness-of-Fit 74

3.3 Selecting the Best Model 79

3.4 Variance Reduction 85

3.5 Linear Correlation 88

3.6 Outliers 93

3.7 Using the Model for Extrapolation 96

3.8 Out-of-Sample Testing 99

3.9 Analyzing the Residuals 105

Chapter 4 Candidate Predictors 115

4.2 Using the F Distribution 116

4.3 Nonlinear Correlation 122

4.4 Rank Correlation 131

Chapter 5 Designing Quantitative Experiments 137

5.2 The Expected Value of the Sum-of-Squares 139

5.3 The Method of Prediction Analysis 140

5.4 A Simple Example: A Straight Line Experiment 143

5.5 Designing for Interpolation 147

5.6 Design Using Computer Simulations 150

5.7 Designs for Some Classical Experiments 155

5.8 Choosing the Values of the Independent Variables 162

5.9 Some Comments about Accuracy 167

Chapter 6 Software 169

6.2 General Purpose Nonlinear Regression Programs 170

6.3 The NIST Statistical Reference Datasets 173

6.4 Nonlinear Regression Convergence Problems 178

6.5 Linear Regression: a Lurking Pitfall 184

6.6 Multi-Dimensional Models 191

6.7 Software Performance 196

6.8 The Regress Program 198

Chapter 7 Kernel Regression 203

7.2 Kernel Regression Order Zero 205

7.3 Kernel Regression Order One 208

7.4 Kernel Regression Order Two 212

7.5 Nearest Neighbor Searching 215

7.6 Kernel Regression Performance Studies 223

7.7 A Scientific Application 225

7.8 Applying Kernel Regression to Classification 232

7.9 Group Separation: An Alternative to Classification 236

Appendix A Generating Random Noise 239

Appendix B Approximating the Standard Normal Distribution 243.

Notes:

Includes bibliographical references (pages [245]-248) and index.

ISBN:

3540256741

OCLC:

63698840

Publisher Number:

9783540256748