Applied Regression Analysis and Experimental Design

Content: Cover
 Half Title
 Title Page
 Copyright Page
 Preface
 Table of Contents
 1: Fitting a Model to Data
 1.1 Introduction
 1.2 How to Fit a Line
 1.3 Residuals
 1.4 Transformations to Obtain Linearity
 1.5 Fitting a Model Using Vectors and Matrices
 1.6 Deviations from Means
 1.7 An Example --
Value of a Postage Stamp over Time
 Problems
 2: Goodness of Fit of the Model
 2.1 Introduction
 2.2 Coefficient Estimates for Univariate Regression
 2.3 Coefficient Estimates for Multivariate Regression
 2.4 ANOVA Tables
 2.5 The F-Test
 2.6 The Coefficient of Determination 2.7 Predicted Values of Y and Confidence Intervals2.8 Residuals
 2.9 Reduced Models
 2.10 Pure Error and Lack of Fit
 2.11 Example --
Lactation Curve
 Problems
 3: Which Variables Should Be Included in the Model
 3.1 Introduction
 3.2 Orthogonal Predictor Variables
 3.3 Linear Transformations of the Predictor Variables
 3.4 Adding Nonorthogonal Variables Sequentially
 3.5 Correlation Form
 3.6 Variable Selection --
All Possible Regressions
 3.7 Variable Selection --
Sequential Methods
 3.8 Qualitative (Dummy) Variables
 3.9 Aggregation of Data
 Problems
 4: Peculiarities of Observations 4.1 Introduction4.2 Sensitive, or High Leverage, Points
 4.3 Outliers
 4.4 Weighted Least Squares
 4.5 More on Transformations
 4.6 Eigenvalues and Principal Components
 4.7 Ridge Regression
 4.8 Prior Information
 4.9 Cleaning up Data
 Problems
 5: The Experimental Design Model
 5.1 Introduction
 5.2 What Makes an Experiment
 5.3 The Linear Model
 5.4 Tests of Hypothesis
 5.5 Testing the Assumptions
 Problems
 6: Assessing the Treatment Means
 6.1 Introduction
 6.2 Specific Hypothesis
 6.3 Contrasts
 6.4 Factorial Analysis
 6.5 Unpredicted Effects
 6.6 Conclusion
 Problems
 7: Blocking 7.1 Introduction7.2 Structure of Experimental Units
 7.3 Balanced Incomplete Block Designs
 7.4 Confounding
 7.5 Miscellaneous Tricks
 Problems
 8: Extensions to the Model
 8.1 Introduction
 8.2 Hierarchic Designs
 8.3 Repeated Measures
 8.4 Covariance Analysis
 8.5 Unequal Replication
 8.6 Modelling the Data
 Problems
 Appendix A: Review of Vectors and Matrices
 A.1 Some Properties of Vectors
 A.2 Some Properties of Vector Spaces
 A.3 Some Properties of Matrices
 Appendix B: Expectation, Linear and Quadratic Forms
 B.1 Expectation
 B.2 Linear Forms
 B.3 Quadratic Forms
 B.4 The F-Statistic Appendix C: Data SetsC. 1 Ultra-Sound Measurements of Horses' Hearts
 C.2 Ph Measurement of Leaf Protein
 C.3 Lactation Records of Cows
 C.4 Sports Cars
 C.5 House Price Data
 C.6 Computer Teaching Data
 C.7 Weedicide Data
 References
 Index