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Fitting Equations To Data 2ND Editionby Cuthbert Daniel
Synopses & Reviews
The purpose of this book is to help the serious data analyst with a computer to— 1. recognize the strengths and limitations of his data; 2. test the assumptions implicit in the least squares methods used to fit the data; 3. select appropriate forms of the variables; 4. judge which combinations of variables are most influential; and 5. state the conditions under which the fitted equations are applicable. In the course of several years of work with research engineers and scientists, the authors have developed a number of devices to meet these requirements. These include ways to detect and handle nested data, to spot bad or critical values, to examine and select from large equations those terms that should be retained, to estimate error of measurement and hence lack-of-fit from neighbors, and to estimate the component effect of each variable on each observation. Two computer programs (one for linear and one for nonlinear equations) implement all of the new methods proposed in addition to using standard least squares. Using interior analysis as well as global statistics, examples are given that arrive at conclusions far different from those of other texts that employ solely "classical" regression techniques. Throughout the book, mathematics is kept at the level of college algebra, and all Greek and matrix nomenclature is relegated to appendices. Statistical derivations are usually omitted but references are made to standard texts. A large part of the text deals with "linear least squares," i.e. with equations that are linear in their unknown constants. However, a detailed example of nonlinear least-squares estimation is given which requires 8 variables and 19 fitted constants. The methods described have been applied in agricultural, biological, environmental, management, marketing, medical, physical and social sciences. The second edition includes a number of extensions and new devices. The search for better subset equations is enlarged to cover 262,144 alternatives. Component and component-plus-residual plots are included to aid in improving the form of the fitted equation. Cross verification with a second sample tests the validity of the equation obtained with the first sample. An Index of Required X-Precision helps to guard against overoptimism in fitting. Programs are now available for Burroughs, Control Data, DECsystem, Honeywell, IBM, and UNIVAC computers.
Other volumes in the Wiley Series in Probability and Mathematical Statistics Applications of Statistics to Industrial Experimentation Cuthbert Daniel Here is a lucid examination of statistical aids and the planning, analysis, and interpretation of industrial experiments. The author scrutinizes the design of multifactor experiments and the methodology, employed in data analysis, with particular focus on time and budget restrictions, and nearness to final decision on marketability. Valuable to experimenters who have some knowledge of elementary statistics, and to statisticians who seek simple explanations, detailed examples, and documentation of the many results that can be expected. 1976 294 pp. Methods for Statistical Data Analysis of Multivariate Observations R. Gnanadesikan Brings together a variety of statistical techniques used and needed in the problems of multivariate data analysis. Concentrates on methods of analysis and the conceptual underpinnings, rather than on statistical theory. The book provides five general objectives for analyzing multivariate data: (1) reduction of dimensionality, (2) development and study of multivariate dependencies, (3) classification and clustering, (4) assessment of specific aspects of models, and (5) summarization and exposure. The author uses several examples of both computer-simulated and real data throughout the book to illustrate the techniques, 1977 311 pp. Introduction to Statistical Time Series Wayne A. Fuller Provides an introduction to representations for statistical time series and the estimation of time series models. Developing both the time and frequency domain approaches, the book concentrates on univariate time series and also discusses vector time series. " well organized, well written, and fairly easy to follow [with] many illustrative worked numerical examples throughout the text as well as a selected bibliography and a useful index. A valuable addition to the market. Recommended for all universities with graduate programs in statistics and economics." —Choice 1976 470 pp.
Helps any serious data analyst with a computer to recognize the strengths and limitations of data, to test the assumptions implicit in the least squares methods used to fit the data, to select appropriate forms of the variables, to judge which combinations of variables are most influential, and to state the conditions under which the fitted equations are applicable. This edition includes numerous extensions and new devices such as component and component-plus-residual plots, cross verification with a second sample, and an index of required x-precision; also, the search for better subset equations is enlarged to cover 262,144 alternatives. The methods described have been applied in agricultural, environmental, management, marketing, medical, physical, and social sciences. Mathematics is kept to the level of college algebra.
About the Author
About the authors CUTHBERT DANIEL is a Consulting Engineering Statistician. He has specialized in applications of statistics to industrial experimentation since 1947. He has worked extensively in design of experiments and regression analysis. His numerous papers have appeared in Technometrics, the Journal of the American Statistical Association, Chemical Engineering Progress, and other journals. He read the R.A. Fisher Memorial Lecture in 1971 and the W.J. Youden Memorial Address in 1974. He was awarded the S.S. Wilks Memorial Medal in 1974. FRED S. WOOD is Senior Operations Research Analyst with the Standard Oil Company with clients in research and development, marketing, manufacturing, production, transportation, finance, and management. His articles have appeared in Technometrics, the Journal of the Society of Automotive Engineers, S.A.E. Transactions, the Oil and Gas Journal, and the Industrial and Chemical Engineering Journal. He holds a number of patents in the fields of both process and product development.
Table of Contents
Assumptions and Methods of Fitting Equations.
One Independent Variable.
Two or More Independent Variables.
Fitting an Equation in Three Independent Variables.
Selection of Independent Variables.
Some Consequences of the Disposition of the Data Points.
LINWOOD User's Manual.
NONLINWOOD User's Manual
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