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Methods and Applications of Linear Models Regression and the Analysis of Variance

ISBN-10: 047159282X

ISBN-13: 9780471592822

Edition: 1st 1996

Authors: Ronald R. Hocking

List price: $105.00
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Description:

Written by R. R. Hocking, this book aims to present methods in a conceptually simple way so the reader may more easily understand the applications of the methods. It contains a good balance of theory and applications; a solutions manual and data sets disk.
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Book details

List price: $105.00
Edition: 1st
Copyright year: 1996
Publisher: John Wiley & Sons, Incorporated
Publication date: 6/27/1996
Binding: Hardcover
Pages: 768
Size: 6.50" wide x 9.75" long x 1.50" tall
Weight: 2.750
Language: English

Michael G. Shields is the librarian at the Lonergan Research Institute, Regis College, University of Toronto, and translator of several volumes in the Collected Works of Bernard Lonergan.

Preface to the Second Edition
Preface to the First Edition
Regression Models
Introduction to Linear Models
Background Information
Mathematical and Statistical Models
Definition of the Linear Model
Examples of Regression Models
Concluding Comments
Exercises
Regression on Functions of One Variable
Simple Linear Regression Model
Parameter Estimation
Properties of the Estimators
Analysis of the Simple Linear Regression Model
Examining the Data and the Model
Test for Lack of Fit
Polynomial Regression Models
Exercises
Transforming the Data
Need for Transformations
Weighted Least Squares
Variance Stabilizing Transformations
Transformations to Achieve a Linear Model
Analysis of the Transformed Model
Transformations with Forbes Data
Exercises
Regression on Functions of Several Variables
Multiple Linear Regression Model
Preliminary Data Analysis
Analysis of the Multiple Linear Regression Model
Partial Correlation and Added-Variable Plots
Variable Selection
Model Specification
Exercises
Collinearity in Multiple Linear Regression
Collinearity Problem
Example With Collinearity
Collinearity Diagnostics
Remedial Solutions: Biased Estimators
Exercises
Influential Observations in Multiple Linear Regression
Influential Data Problem
Hat Matrix
Effects of Deleting Observations
Numerical Measures of Influence
Dilemma Data
Plots for Identifying Unusual Cases
Robust/Resistant Methods in Regression Analysis
Exercises
Polynomial Models and Qualitative Predictors
Polynomial Models
Analysis of Response Surfaces
Models with Qualitative Predictors
Exercises
Additional Topics
Non-Linear Regression Models
Non-Parametric Model-Fitting Methods
Logistic Regression
Random Input Variables
Errors in the Inputs
Calibration
Exercises
Analysis of Variance Models
Introduction to Analysis of Variance Models
Background Information
Cell Means Model
Fixed Effects Models
Mixed Effects Models
Concluding Comments
Exercises
Fixed Effects Models I: One-Way Classification of Means
Introduction
One-Way Classification: Balanced Data
One-Way Classification: Unbalanced Data
Analysis of Covariance
Exercises
Fixed Effects Models II: Two-Way Classification of Means
Unconstrained Model: Balanced Data
Unconstrained Model: Unbalanced Data
No-Interaction Model: Balanced Data
No-Interaction Model: Unbalanced Data
Non-Homogeneous Experimental Units: The Concept of Blocking
Exercises
Fixed Effects Models III: Multiple Crossed and Nested Factors
Three-Factor Cross-Classified Model
General Structure for Balanced, Factorial Models
Two-Fold Nested Model
General Structure for Balanced, Nested Models
Three-Factor, Nested-Factorial Model
General Structure for Balanced, Nested-Factorial Models
Exercises
Mixed Models I: The AOV Method with Balanced Data
Introduction
One-Way Classification, Random Model
Two-Way Classification, Mixed Model
Three-Factor, Nested-Factorial Model
General Analysis for Balanced, Mixed Models
Additional Examples
Alternative Development of Mixed Models
Exercises
Mixed Models II: The AVE Method with Balanced Data
Introduction
Two-Way Cross-Classification Model
Two-Fold Nested Model
Three Factor, Nested-Factorial Model
General Description of the AVE Table
Additional Examples
Computational Procedure for the AVE Method
Properties of the AVE Estimates
Exercises
Mixed Models III: Unbalanced Data
Introduction
Parameter Estimation: Likelihood Methods
ML and REML Estimates with Balanced Data
EM Algorithm for REML Estimation
EM Algorithm Applied to the AVE Method
Models with Covariates
Summary
Exercises
Mathematical Theory of Linear Models
Distribution of Linear and Quadratic Forms
Linear and Quadratic Forms
Multivariate Normal Distribution
Distribution of Quadratic Forms
Other Non-Central Distributions
Exercises
Estimation and Inference for Linear Models
Estimation of Parameters
Tests of Linear Hypotheses on [beta]
Confidence Regions and Intervals
Exercises
Simultaneous Inference: Tests and Confidence Intervals
Simultaneous Tests
Simultaneous Confidence Intervals
Exercises
Mathematics
Matrix Algebra
Optimization
Statistics
Estimation
Tests of Hypotheses and Confidence Regions
Statistical Tables
Data Tables
References
Index