Fitting Equations to Data: Computer Analysis of Multifactor Data

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9780471376842: Fitting Equations to Data: Computer Analysis of Multifactor Data
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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.

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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.

About the Author:

Cuthbert Daniel, Consultant in Engineering Statistics, earned his B.S. and M.S. degrees in Chemical Engineering at the Massachusetts Institute of Technology, studying further at the University of Berlin in 1928 and at Harvard University, 1930-31. He has taught courses in design of experiments and industrial statistics at Columbia University and at the University of California, Berkeley. In the mid-40's he worked as a Statistician at the Gaseous Diffusion Plant, Manhattan Project, Oak Ridge, Tennessee. Mr. Daniel has served as a consultant in statistics to the Research and Development Departments of several large corporations, including Procter and Gamble, United States Steel, General Foods, Interchemical, Standard Oil, and Okonite. Mr. Daniel has been a consultant on design of experiments and analysis of engineering data to the Office of Air Polution, and to the Consumers Union. He was a member of Cancer Clinical Investigations Review Committee of NCI, and of NAS/NRC Committee on National Statistics. He is author of Fitting Equations to Data: Computer Analysis of Multifactor Data for Scientists And Engineers, published by Wiley-Interscience in 1971.

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9780471053705: Fitting Equations to Data: Computer Analysis of Multifactor Data (Wiley Series in Probability and Statistics)

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Book Description John Wiley and Sons Ltd, United States, 1999. Paperback. Condition: New. 2nd Edition. Language: English. Brand new Book. 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. Seller Inventory # AAH9780471376842

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Book Description John Wiley and Sons Ltd, United States, 1999. Paperback. Condition: New. 2nd Edition. Language: English. Brand new Book. 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. Seller Inventory # AAH9780471376842

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Book Description John Wiley and Sons Ltd, United States, 1999. Paperback. Condition: New. 2nd Edition. Language: English. Brand new Book. 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. Seller Inventory # LIE9780471376842

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