Linear Regression Analysis

ISBN-10: 0471415405
ISBN-13: 9780471415404
Edition: 2nd 2003 (Revised)
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Description: Regression analysis is an often used tool in the statistician's toolbox. This new edition takes into serious consideration the furthering development of regression computer programs that are efficient, accurate and considered an important part of  More...

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Book details

List price: $183.00
Edition: 2nd
Copyright year: 2003
Publisher: John Wiley & Sons, Incorporated
Publication date: 2/5/2003
Binding: Hardcover
Pages: 582
Size: 6.50" wide x 9.75" long x 1.50" tall
Weight: 2.046
Language: English

Regression analysis is an often used tool in the statistician's toolbox. This new edition takes into serious consideration the furthering development of regression computer programs that are efficient, accurate and considered an important part of statistical research.

Preface
Vectors of Random Variables
Notation
Statistical Models
Linear Regression Models
Expectation and Covariance Operators
Exercises 1a
Mean and Variance of Quadratic Forms
Exercises 1b
Moment Generating Functions and Independence
Exercises 1c
Miscellaneous Exercises 1
Multivariate Normal Distribution
Density Function
Exercises 2a
Moment Generating Functions
Exercises 2b
Statistical Independence
Exercises 2c
Distribution of Quadratic Forms
Exercises 2d
Miscellaneous Exercises 2
Linear Regression: Estimation and Distribution Theory
Least Squares Estimation
Exercises 3a
Properties of Least Squares Estimates
Exercises 3b
Unbiased Estimation of [sigma superscript 2]
Exercises 3c
Distribution Theory
Exercises 3d
Maximum Likelihood Estimation
Orthogonal Columns in the Regression Matrix
Exercises 3e
Introducing Further Explanatory Variables
General Theory
One Extra Variable
Exercises 3f
Estimation with Linear Restrictions
Method of Lagrange Multipliers
Method of Orthogonal Projections
Exercises 3g
Design Matrix of Less Than Full Rank
Least Squares Estimation
Exercises 3h
Estimable Functions
Exercises 3i
Introducing Further Explanatory Variables
Introducing Linear Restrictions
Exercises 3j
Generalized Least Squares
Exercises 3k
Centering and Scaling the Explanatory Variables
Centering
Scaling
Exercises 3l
Bayesian Estimation
Exercises 3m
Robust Regression
M-Estimates
Estimates Based on Robust Location and Scale Measures
Measuring Robustness
Other Robust Estimates
Exercises 3n
Miscellaneous Exercises 3
Hypothesis Testing
Introduction
Likelihood Ratio Test
F-Test
Motivation
Derivation
Exercises 4a
Some Examples
The Straight Line
Exercises 4b
Multiple Correlation Coefficient
Exercises 4c
Canonical Form for H
Exercises 4d
Goodness-of-Fit Test
F-Test and Projection Matrices
Miscellaneous Exercises 4
Confidence Intervals and Regions
Simultaneous Interval Estimation
Simultaneous Inferences
Comparison of Methods
Confidence Regions
Hypothesis Testing and Confidence Intervals
Confidence Bands for the Regression Surface
Confidence Intervals
Confidence Bands
Prediction Intervals and Bands for the Response
Prediction Intervals
Simultaneous Prediction Bands
Enlarging the Regression Matrix
Miscellaneous Exercises 5
Straight-Line Regression
The Straight Line
Confidence Intervals for the Slope and Intercept
Confidence Interval for the x-Intercept
Prediction Intervals and Bands
Prediction Intervals for the Response
Inverse Prediction (Calibration)
Exercises 6a
Straight Line through the Origin
Weighted Least Squares for the Straight Line
Known Weights
Unknown Weights
Exercises 6b
Comparing Straight Lines
General Model
Use of Dummy Explanatory Variables
Exercises 6c
Two-Phase Linear Regression
Local Linear Regression
Miscellaneous Exercises 6
Polynomial Regression
Polynomials in One Variable
Problem of Ill-Conditioning
Using Orthogonal Polynomials
Controlled Calibration
Piecewise Polynomial Fitting
Unsatisfactory Fit
Spline Functions
Smoothing Splines
Polynomial Regression in Several Variables
Response Surfaces
Multidimensional Smoothing
Miscellaneous Exercises 7
Analysis of Variance
Introduction
One-Way Classification
General Theory
Confidence Intervals
Underlying Assumptions
Exercises 8a
Two-Way Classification (Unbalanced)
Representation as a Regression Model
Hypothesis Testing
Procedures for Testing the Hypotheses
Confidence Intervals
Exercises 8b
Two-Way Classification (Balanced)
Exercises 8c
Two-Way Classification (One Observation per Mean)
Underlying Assumptions
Higher-Way Classifications with Equal Numbers per Mean
Definition of Interactions
Hypothesis Testing
Missing Observations
Exercises 8d
Designs with Simple Block Structure
Analysis of Covariance
Exercises 8e
Miscellaneous Exercises 8
Departures from Underlying Assumptions
Introduction
Bias
Bias Due to Underfitting
Bias Due to Overfitting
Exercises 9a
Incorrect Variance Matrix
Exercises 9b
Effect of Outliers
Robustness of the F-Test to Nonnormality
Effect of the Regressor Variables
Quadratically Balanced F-Tests
Exercises 9c
Effect of Random Explanatory Variables
Random Explanatory Variables Measured without Error
Fixed Explanatory Variables Measured with Error
Round-off Errors
Some Working Rules
Random Explanatory Variables Measured with Error
Controlled Variables Model
Collinearity
Effect on the Variances of the Estimated Coefficients
Variance Inflation Factors
Variances and Eigenvalues
Perturbation Theory
Collinearity and Prediction
Exercises 9d
Miscellaneous Exercises 9
Departures from Assumptions: Diagnosis and Remedies
Introduction
Residuals and Hat Matrix Diagonals
Exercises 10a
Dealing with Curvature
Visualizing Regression Surfaces
Transforming to Remove Curvature
Adding and Deleting Variables
Exercises 10b
Nonconstant Variance and Serial Correlation
Detecting Nonconstant Variance
Estimating Variance Functions
Transforming to Equalize Variances
Serial Correlation and the Durbin-Watson Test
Exercises 10c
Departures from Normality
Normal Plotting
Transforming the Response
Transforming Both Sides
Exercises 10d
Detecting and Dealing with Outliers
Types of Outliers
Identifying High-Leverage Points
Leave-One-Out Case Diagnostics
Test for Outliers
Other Methods
Exercises 10e
Diagnosing Collinearity
Drawbacks of Centering
Detection of Points Influencing Collinearity
Remedies for Collinearity
Exercises 10f
Miscellaneous Exercises 10
Computational Algorithms for Fitting a Regression
Introduction
Basic Methods
Direct Solution of the Normal Equations
Calculation of the Matrix X'X
Solving the Normal Equations
Exercises 11a
QR Decomposition
Calculation of Regression Quantities
Algorithms for the QR and WU Decompositions
Exercises 11b
Singular Value Decomposition
Regression Calculations Using the SVD
Computing the SVD
Weighted Least Squares
Adding and Deleting Cases and Variables
Updating Formulas
Connection with the Sweep Operator
Adding and Deleting Cases and Variables Using QR
Centering the Data
Comparing Methods
Resources
Efficiency
Accuracy
Two Examples
Summary
Exercises 11c
Rank-Deficient Case
Modifying the QR Decomposition
Solving the Least Squares Problem
Calculating Rank in the Presence of Round-off Error
Using the Singular Value Decomposition
Computing the Hat Matrix Diagonals
Using the Cholesky Factorization
Using the Thin QR Decomposition
Calculating Test Statistics
Robust Regression Calculations
Algorithms for L[subscript 1] Regression
Algorithms for M- and GM-Estimation
Elemental Regressions
Algorithms for High-Breakdown Methods
Exercises 11d
Miscellaneous Exercises 11
Prediction and Model Selection
Introduction
Why Select?
Exercises 12a
Choosing the Best Subset
Goodness-of-Fit Criteria
Criteria Based on Prediction Error
Estimating Distributional Discrepancies
Approximating Posterior Probabilities
Exercises 12b
Stepwise Methods
Forward Selection
Backward Elimination
Stepwise Regression
Exercises 12c
Shrinkage Methods
Stein Shrinkage
Ridge Regression
Garrote and Lasso Estimates
Exercises 12d
Bayesian Methods
Predictive Densities
Bayesian Prediction
Bayesian Model Averaging
Exercises 12e
Effect of Model Selection on Inference
Conditional and Unconditional Distributions
Bias
Conditional Means and Variances
Estimating Coefficients Using Conditional Likelihood
Other Effects of Model Selection
Exercises 12f
Computational Considerations
Methods for All Possible Subsets
Generating the Best Regressions
All Possible Regressions Using QR Decompositions
Exercises 12g
Comparison of Methods
Identifying the Correct Subset
Using Prediction Error as a Criterion
Exercises 12h
Miscellaneous Exercises 12
Some Matrix Algebra
Trace and Eigenvalues
Rank
Positive-Semidefinite Matrices
Positive-Definite Matrices
Permutation Matrices
Idempotent Matrices
Eigenvalue Applications
Vector Differentiation
Patterned Matrices
Generalized Inverse
Some Useful Results
Singular Value Decomposition
Some Miscellaneous Statistical Results
Fisher Scoring
Orthogonal Projections
Orthogonal Decomposition of Vectors
Orthogonal Complements
Projections on Subspaces
Tables
Percentage Points of the Bonferroni t-Statistic
Distribution of the Largest Absolute Value of k Student t Variables
Working-Hotelling Confidence Bands for Finite Intervals
Outline Solutions to Selected Exercises
References
Index

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