Fitting Equations to Data: Computer Analysis of Multifactor Data / Edition 2by Cuthbert Daniel, Fred S. Wood
Pub. Date: 04/25/1980
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… See more details below
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.
Table of ContentsAssumptions 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.
Selection of Variables in Nested Data.
Nonlinear Least Squares, a Complex Example.
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