Applied Regression Analysis and Experimental Design

by Brook

• ISBN13: 9780824772529
• ISBN10: 0824772520
• Edition: 1st
• Format: Hardcover
• Copyright: 1985-04-25
• Publisher: CRC Press

Summary

For a solid foundation of important statistical methods, this concise, single-source text unites linear regression with analysis of experiments and provides students with the practical understanding needed to apply theory in real data analysis problems. Stressing principles while keeping computational and theoretical details at a manageable level, Applied Regression Analysis and Experimental Design features an emphasis on vector geometry of least squares to unify and provide an intuitive basis for most topics covered ... abundant examples and exercises using real-life data sets clearly illustrating practical problems of data analysis ... essential exposure to Minitab and Genstat computer packages, including computer printouts ... and important background material such as vector and matrix properties and the distributional properties of quadratic forms. Designed to make theory work for students, this clearly written, easy-to-understand work serves as the ideal text for courses in Regression, Experimental Design, and Linear Models in a broad range of disciplines. Moreover, applied statisticians, biometricians, and research workers in applied statistics will find the book a useful reference for the general application of the linear model. Book jacket.

Author Biography

Richard J. Brook is a Reader in Statistics in the Department of Mathematics and Statistics, Massey University, New Zealand Gregory C. Arnold is a Senior Lecturer in the Department of Mathematics and Statistics at Massey University, New Zealand

Table of Contents

Preface	p. iii
Fitting a Model to Data	p. 1
Introduction	p. 1
How to Fit a Line	p. 3
Residuals	p. 10
Transformations to Obtain Linearity	p. 12
Fitting a Model Using Vectors and Matrices	p. 16
Deviations from Means	p. 21
An Example--Value of a Postage Stamp over Time	p. 24
Problems	p. 28
Goodness of Fit of the Model	p. 30
Introduction	p. 30
Coefficient Estimates for Univariate Regression	p. 31
Coefficient Estimates for Multivariate Regression	p. 32
ANOVA Tables	p. 33
The F-Test	p. 35
The Coefficient of Determination	p. 36
Predicted Values of Y and Confidence Intervals	p. 37
Residuals	p. 41
Reduced Models	p. 45
Pure Error and Lack of Fit	p. 48
Example--Lactation Curve	p. 50
Problems	p. 53
Which Variables Should Be Included in the Model	p. 56
Introduction	p. 56
Orthogonal Predictor Variables	p. 57
Linear Transformations of the Predictor Variables	p. 60
Adding Nonorthogonal Variables Sequentially	p. 61
Correlation Form	p. 64
Variable Selection--All Possible Regressions	p. 68
Variable Selection--Sequential Methods	p. 71
Qualitative (Dummy) Variables	p. 74
Aggregation of Data	p. 78
Problems	p. 81
Peculiarities of Observations	p. 84
Introduction	p. 84
Sensitive, or High Leverage, Points	p. 85
Outliers	p. 86
Weighted Least Squares	p. 87
More on Transformations	p. 91
Eigenvalues and Principal Components	p. 93
Ridge Regression	p. 96
Prior Information	p. 100
Cleaning up Data	p. 101
Problems	p. 103
The Experimental Design Model	p. 106
Introduction	p. 106
What Makes an Experiment	p. 107
The Linear Model	p. 112
Tests of Hypothesis	p. 118
Testing the Assumptions	p. 120
Problems	p. 123
Assessing the Treatment Means	p. 126
Introduction	p. 126
Specific Hypothesis	p. 127
Contrasts	p. 133
Factorial Analysis	p. 139
Unpredicted Effects	p. 144
Conclusion	p. 150
Problems	p. 151
Blocking	p. 153
Introduction	p. 153
Structure of Experimental Units	p. 154
Balanced Incomplete Block Designs	p. 159
Confounding	p. 165
Miscellaneous Tricks	p. 173
Problems	p. 176
Extensions to the Model	p. 182
Introduction	p. 182
Hierarchic Designs	p. 182
Repeated Measures	p. 190
Covariance Analysis	p. 192
Unequal Replication	p. 198
Modelling the Data	p. 204
Problems	p. 207
Review of Vectors and Matrices	p. 212
Some Properties of Vectors	p. 212
Some Properties of Vector Spaces	p. 215
Some Properties of Matrices	p. 217
Expectation, Linear and Quadratic Forms	p. 219
Expectation	p. 219
Linear Forms	p. 219
Quadratic Forms	p. 220
The F-Statistic	p. 220
Data Sets	p. 221
Ultra-Sound Measurements of Horses' Hearts	p. 221
Ph Measurement of Leaf Protein	p. 222
Lactation Records of Cows	p. 223
Sports Cars	p. 224
House Price Data	p. 225
Computer Teaching Data
Weedicide Data	p. 227
References	p. 229
Index	p. 231
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