Data Analysis Using the Method of Least Squares Extracting the Most Information from Experiments

Name: Data Analysis Using the Method of Least Squares Extracting the Most Information from Experiments
Price: 49.37 USD
Availability: InStock
ISBN: 9783540256748

ISBN-10: 3540256741

ISBN-13: 9783540256748

Edition: 2006

Authors: John Wolberg

List price: $54.99

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Description:

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 these techniques at the level of detail that the subject deserves. The purpose of Data Analysis Using the Least-Square Methods is to fill this gap and include the type of information required to help scientists and engineers apply the method to the problems of interest in their special field. 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…

Book details

List price: $54.99
Copyright year: 2006
Publisher: Springer Berlin / Heidelberg
Publication date: 12/16/2005
Binding: Paperback
Pages: 250
Size: 5.98" wide x 9.02" long x 0.25" tall
Weight: 0.990
Language: English




Introduction



Quantitative Experiments



Dealing with Uncertainty



Statistical Distributions


The normal distribution


The binomial distribution


The Poisson distribution


The x[superscript 2] distribution


The t distribution


The F distribution



Parametric Models



Basic Assumptions



Systematic Errors



Nonparametric Models



Statistical Learning



The Method of Least Squares



Introduction



The Objective Function



Data Weighting



Obtaining the Least Squares Solution



Uncertainty in the Model Parameters



Uncertainty in the Model Predictions



Treatment of Prior Estimates



Applying Least Squares to Classification Problems



Model Evaluation



Introduction



Goodness-of-Fit



Selecting the Best Model



Variance Reduction



Linear Correlation



Outliers



Using the Model for Extrapolation



Out-of-Sample Testing



Analyzing the Residuals



Candidate Predictors



Introduction



Using the F Distribution



Nonlinear Correlation



Rank Correlation



Designing Quantitative Experiments



Introduction



The Expected Value of the Sum-of-Squares



The Method of Prediction Analysis



A Simple Example: A Straight Line Experiment



Designing for Interpolation



Design Using Computer Simulations



Designs for Some Classical Experiments



Choosing the Values of the Independent Variables



Some Comments about Accuracy



Software



Introduction



General Purpose Nonlinear Regression Programs



The NIST Statistical Reference Datasets



Nonlinear Regression Convergence Problems



Linear Regression: a Lurking Pitfall



Multi-Dimensional Models



Software Performance



The Regress Program



Kernel Regression



Introduction



Kernel Regression Order Zero



Kernel Regression Order One



Kernel Regression Order Two



Nearest Neighbor Searching



Kernel Regression Performance Studies



A Scientific Application



Applying Kernel Regression to Classification



Group Separation: An Alternative to Classification



Generating Random Noise



Approximating the Standard Normal Distribution


References


Index