Applied Regression Analysis and Experimental Design

ISBN-13: 9780824772529 / Angielski / Twarda / 1985 / 237 str.

Richard J. Brook; Gregory C. Arnold

Opis

Designed to make theory work for students, this clearly written, easy-to-understand work serves as the ideal texts for courses Regression, Experimental Design, and Linear Models in a broad range of disciplines. Moreover, applied statisticians will find the book a useful reference for the general application of the linear model.

Spis treści

Preface
Fitting a Model to Data
Introduction
How to Fit a Line
Residuals
Transformations to Obtain Linearity
Fitting a Model Using Vectors and Matrices
Deviations from Means
An Example- Value of a Postage Stamp Over Time
Problems
Goodness of Fit of the Model
Introduction
Coefficient Estimates for Univariate Regression
Coefficient Estimates for Mulitvariate Regression
ANOVA Tables
The F Test
The Coefficient of Determination
Predicted Values of Y and Confidence Intervals
Residuals
Reduced Models
Pure Error and Lack of Fit
Example- Lactation Curve
Problems
Which Variable Should Be Included in the Model
Introduction
Orthogonal Predictor Variables
Linear Transformations of the Predictor Variables
Adding Nonorthogonal Variables Sequentially
Correlation Form
Variable Selection- All Possible Regressions
Variable Selection- Sequential Methods
Qualitative (Dummy) Variables
Aggregation of Data
Problems
Peculiarities of Observations
Introduction
Sensitive or High Leverage Points
Outliers
Weighted Least Squares
More on Transformations
Eigenvalues and Principal Components
Ridge Regression
Prior Information
Cleaning up Data
Problems
The Experimental Design Model
Introduction
What Makes an Experiment
The Linear Model
Tests of Hypothesis
Testing of Assumptions
Problems
Assessing the Treatment Methods
Introduction
Specific Hypothesis
Contrasts
Factorial Analysis
Unpredicted Effects
Conclusion
Problems
Blocking
Introduction
Structure of Experimental Units
Balanced Incomplete Block Designs
Confounding
Miscellaneous Tricks
Problems
Extensions to the Model
Introduction
Hierarchic Designs
Repeated Measures
Covariance Analysis
Unequal Replication
Modeling the Data
Problems
Appendix A Review of Vectors and Matrices
Some Properties of Vectors
Some Properties of Vector Spaces
Some Properties of Matrices
Appendix B Expectation, Linear and Quadratic Forms
Expectations
Linear Forms
Quadratic Forms
The F-Statistic
Appendix C Data Sets
Ultra-Sound Measurements of Horses Hearts
Ph Measurement of Leaf Protein
Lactation Records of Cows
Sports Cars
House-Price Data
Computer Teaching Data
Weedicide Data
References
Index

O autorze

Brook, Richard J.; Arnold, Gregory C.