Fitting Equations to Data: Computer Analysis of Multifactor Data 2nd Revised edition [Kõva köide]

Introduction		1	(4)
Flow diagram of procedure used		1	(1)
Role of computer		1	(2)
Sequence of subjects discussed		3	(2)
Assumptions and Methods of Fitting Equations		5	(14)
Assumptions		5	(1)
Methods of fitting equations		6	(1)
Least squares		6	(3)
Linear least-squares estimation		9	(1)
Nonlinear least-squares estimation		9	(10)
Linear least-squares estimates--one independent variable		10	(1)
Assumptions		10	(1)
Basic idea and derivation		10	(2)
Confidence regions		12	(1)
Linear least-squares estimates--general case		13	(1)
Estimates of coefficients		13	(2)
Variance and standard errors of coefficients		15	(1)
Computer computations		16	(1)
Partitioning sums of squares		16	(1)
Multiple correlation coefficient squared, Ry2		17	(1)
F-value		17	(1)
Bias and random error		17	(1)
Residual mean square		17	(1)
Residual root mean square		18	(1)
One Independent Variable		19	(31)
Plotting data and selecting form of equation		19	(1)
Plots of linearizable equations		19	(3)
Plots of nonlinearizable equations		22	(2)
Statistical independence and clusters of dependent variable		24	(1)
Allocation of data points		25	(1)
Outliers		25	(1)
Use of computer program		26	(1)
Study of residuals		27	(5)
Dealing with error in the independent variable		32	(1)
Example of fitting a straight line to data-one independent variable		32	(18)
Cumulative distribution plots of random normal deviates		33	(1)
Example of fitting a straight line to data--one independent variable		33	(17)
Two or More Independent Variables		50	(10)
Inadequacies of x-y plots with two or more independent variables		50	(3)
Equation forms and transformations		53	(2)
Variances of estimated coefficients, bt, and fitted values, Yj		55	(1)
Use of indicator variables for discontinuous or qualitative classifications		56	(1)
One qualitative factor at two levels
One qualitative two-level factor and one quantitative (continuous) factor
Discrete factors at more than two levels
Discrete factors interacting with continuous factors
Allocation of data in factor space		57	(3)
Linear dependences among the xi
The outermost points in data space
Nested data
Fitting an Equation in Three Independent Variables		60	(23)
Introduction		60	(1)
First trials		60	(1)
Possible causes of disturbance		61	(4)
Outlier or logged response or squared independent variable		65	(7)
Random error estimated from near neighbors		72	(1)
Independence of observations		73	(2)
Systematic examination of alternatives discovered sequentially		75	(2)
Remote points in factor space		77	(1)
Equation using ``lined-out'' data		77	(4)
Conclusions on stack loss problem		81	(1)
General conclusions		82	(1)
Selection of Independent Variables		83	(38)
Introduction		83	(3)
Assumptions
Obvious imperfections
2K possible equations from K candidate variables
On stepwise regression
F-test
All 2K equations and fractions
Total squared error as a criterion for goodness of fit-CP		86	(3)
Definition
Derivation of the CP statistic
Mallows' graphical method of comparing fitted equations
A four-variable example		89	(2)
Disposition of data in factor space		91	(4)
A six-variable example		95	(26)
Search for all 2K equations
TK, t- directed search
Fractional replicates
Computer printouts of four-variable example		104	(1)
Computer printouts of six-variable example		104	(1)
Fractional replication for 2K equations		104	(17)
Some Consequences of the Disposition of the Data Points		121	(113)
Introduction		121	(1)
Description of example with ten independent variables		122	(1)
First steps
Interior analysis I. ``Component effects'' table		123	(1)
Interior analysis II. Component and component-plus-residual plots		124	(2)
Search of all 2K possible subset equations		126	(1)
tK, t-directed search		126	(1)
Test for an outlier		127	(2)
Interior analysis III. Weighted-squared-standardized-distance to look for far-out points of influential variables		129	(2)
Interior analysis IV Variance ratio to look for far-out points of uninfluential variables		131	(2)
Interior analysis V Error estimation from near neighbors		133	(3)
Cross verification		136	(1)
Other examples of error estimation from near neighbors		137	(2)
Six-variable example of Chapter 6
Stack loss example of Chapter 5
Additional examples of using component and component-plus-residual plots		139	(6)
Example of the use of plots in choosing the form of equation
Distribution of observations over each independent variable
Four-variable example-Distribution of independent variables
Eleven-variable example-Inner and outer observations
Other conditions identified by component and component-plus-residual plots		145	(1)
Summary		146	(88)
Computer printouts of ten-variable example		150	(49)
Computer printout of six-variable example		199	(1)
Computer printouts of stack loss example		200	(7)
Computer printouts of four-variable octane example		207	(11)
Computer printouts of eleven-variable example		218	(14)
Critical values for studentized residual to test for single outlier		232	(2)
Selection of Variables in Nested Data		234	(33)
Background of example		234	(2)
Fitting equation		236	(1)
Recognition of nested data		236	(1)
Data identification and entry		236	(1)
Fitting equation to nested data		236	(4)
Use of indicator (dummy) variables
Test for significance of added variables; ``individual'' versus ``common'' slopes
Fitting equation among sets of nested data		240	(3)
Selecting variables based on total error, recognizing bias and random error		243	(1)
Properties of final equation		244	(3)
Comparison of equations		247	(20)
Data preparation and computer printouts of example		248	(19)
Nonlinear Least Squares, a Complex Example		267	(71)
Introduction		267	(1)
Background of example		268	(3)
Replicates		271	(2)
Potential equations		273	(3)
Nonlinear fit-observations of individual cements versus time		276	(1)
Fit with indicator variables		277	(3)
Fit with composition		280	(13)
Possible nesting within cements		293	(2)
Comparison with previous linear least-square fits		295	(1)
Fit using composition in mol percents		296	(3)
Conclusions		299	(39)
Computer printout of nonlinear example		300	(38)
Glossary		338	(16)
Conventions		338	(1)
Symbols		338	(5)
Computer terms		343	(11)
LINWOOD User's Manual		354	(66)
LINWOOD, a computer linear least-squares curve-fitting program
Abstract		354	(1)
General information		355	(1)
Input		356	(20)
Control card entry		356	(10)
Standard data card entry		366	(1)
Problems using transformation option		367	(7)
Order of cards		374	(2)
Sample problem		376	(5)
Example of weighted observations		381	(15)
Example to measure the precision of calculations		396	(10)
Example of using plots in choosing the form of equation		406	(9)
Execution time		415	(3)
Summary of control cards		418	(1)
Summary of order of cards		419	(1)
NONLINWOOD User's Manual		420	(29)
NONLINWOOD, a computer nonlinear least-squares curve-fitting program
Abstract		420	(1)
General information		421	(1)
Input		422	(6)
Control card		422	(2)
Format card		424	(1)
Starting values of coefficients		424	(1)
Data cards		424	(1)
Order of cards		425	(1)
Control and data card entry forms		425	(1)
Equation subroutine		425	(2)
Example of transformations		427	(1)
Example 1 2 coefficients 2 variables		428	(14)
Example 2 43 coefficients 16 variables		442	(2)
Example 3 19 coefficients 7 variables		444	(2)
Summary of control cards		446	(1)
Example of subroutine model		447	(1)
Summary of order of cards		447	(2)
Bibliography		449	(4)
Index		453

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.