Introduction to Linear Regression Analysis

Name: Introduction to Linear Regression Analysis
Price: 4.82 USD
Availability: InStock
ISBN: 9780471754954

ISBN-10: 0471754951

ISBN-13: 9780471754954

Edition: 4th 2006 (Revised)

Authors: Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining

List price: $150.00

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Description:

A comprehensive and up-to-date introduction to the fundamentals of regression analysis The Fourth Edition of Introduction to Linear Regression Analysis describes both the conventional and less common uses of linear regression in the practical context of today's mathematical and scientific research. This popular book blends both theory and application to equip the reader with an understanding of the basic principles necessary to apply regression model-building techniques in a wide variety of application environments. It assumes a working knowledge of basic statistics and a familiarity with hypothesis testing and confidence intervals, as well as the normal, t, x2, and F distributions. …

Book details

List price: $150.00
Edition: 4th
Copyright year: 2006
Publisher: John Wiley & Sons, Incorporated
Publication date: 7/21/2006
Binding: Hardcover
Pages: 640
Size: 7.25" wide x 10.25" long x 1.25" tall
Weight: 2.948
Language: English



Preface


Introduction


Regression and Model Building


Data Collection


Uses of Regression


Role of the Computer


Simple Linear Regression


Simple Linear Regression Model


Least-Squares Estimation of the Parameters


Estimation of [beta subscript 0] and [beta subscript 1]


Properties of the Least-Squares Estimators and the Fitted Regression Model


Estimation of [sigma superscript 2]


Alternate Form of the Model


Hypothesis Testing on the Slope and Intercept


Use of t Tests


Testing Significance of Regression


Analysis of Variance


Interval Estimation in Simple Linear Regression


Confidence Intervals on [beta superscript 0], [beta superscript 1], and [sigma subscript 2]


Interval Estimation of the Mean Response


Prediction of New Observations


Coefficient of Determination


Using SAS for Simple Linear Regression


Some Considerations in the Use of Regression


Regression Through the Origin


Estimation by Maximum Likelihood


Case Where the Regressor x is Random


x and y Jointly Distributed


x and y Jointly Normally Distributed: Correlation Model


Problems


Multiple Linear Regression


Multiple Regression Models


Estimation of the Model Parameters


Least-Squares Estimation of the Regression Coefficients


Geometrical Interpretation of Least Squares


Properties of the Least-Squares Estimators


Estimation of [sigma superscript 2]


Inadequacy of Scatter Diagrams in Multiple Regression


Maximum-Likelihood Estimation


Hypothesis Testing in Multiple Linear Regression


Test for Significance of Regression


Tests on Individual Regression Coefficients


Special Case of Orthogonal Columns in X


Testing the General Linear Hypothesis


Confidence Intervals in Multiple Regression


Confidence Intervals on the Regression Coefficients


Confidence Interval Estimation of the Mean Response


Simultaneous Confidence Intervals on Regression Coefficients


Prediction of New Observations


Using SAS for Basic Multiple Linear Regression


Hidden Extrapolation in Multiple Regression


Standardized Regression Coefficients


Multicollinearity


Why Do Regression Coefficients Have the Wrong Sign?


Problems


Model Adequacy Checking


Introduction


Residual Analysis


Definition of Residuals


Methods for Scaling Residuals


Residual Plots


Partial Regression and Partial Residual Plots


Using MINITAB and SAS for Residual Analysis


Other Residual Plotting and Analysis Methods


PRESS Statistic


Detection and Treatment of Outliers


Lack of Fit of the Regression Model


Formal Test for Lack of Fit


Estimation of Pure Error from Near Neighbors


Problems


Transformations and Weighting to Correct Model Inadequacies


Introduction


Variance-Stabilizing Transformations


Transformations to Linearize the Model


Analytical Methods for Selecting a Transformation


Transformations on y: The Box-Cox Method


Transformations on the Regressor Variables


Generalized and Weighted Least Squares


Generalized Least Squares


Weighted Least Squares


Some Practical Issues


Problems


Diagnostics for Leverage and Influence


Importance of Detecting Influential Observations


Leverage


Measures of Influence: Cook's D


Measures of Influence: DFFITS and DFBETAS


A Measure of Model Performance


Detecting Groups of Influential Observations


Treatment of Influential Observations


Problems


Polynomial Regression Models


Introduction


Polynomial Models in One Variable


Basic Principles


Piecewise Polynomial Fitting (Splines)


Polynomial and Trigonometric Terms


Nonparametric Regression


Kernel Regression


Locally Weighted Regression (Loess)


Final Cautions


Polynomial Models in Two or More Variables


Orthogonal Polynomials


Problems


Indicator Variables


General Concept of Indicator Variables


Comments on the Use of Indicator Variables


Indicator Variables versus Regression on Allocated Codes


Indicator Variables as a Substitute for a Quantitative Regressor


Regression Approach to Analysis of Variance


Problems


Variable Selection and Model Building


Introduction


Model-Building Problem


Consequences of Model Misspecification


Criteria for Evaluating Subset Regression Models


Computational Techniques for Variable Selection


All Possible Regressions


Stepwise Regression Methods


Strategy for Variable Selection and Model Building


Case Study: Gorman and Toman Asphalt Data Using SAS


Problems


Validation of Regression Models


Introduction


Validation Techniques


Analysis of Model Coefficients and Predicted Values


Collecting Fresh Data-Confirmation Runs


Data Splitting


Data from Planned Experiments


Problems


Multicollinearity


Introduction


Sources of Multicollinearity


Effects of Multicollinearity


Multicollinearity Diagnostics


Examination of the Correlation Matrix


Variance Inflation Factors


Eigensystem Analysis of X'X


Other Diagnostics


SAS Code for Generating Multicollinearity Diagnostics


Methods for Dealing with Multicollinearity


Collecting Additional Data


Model Respecification


Ridge Regression


Principal-Component Regression


Comparison and Evaluation of Biased Estimators


Using SAS to Perform Ridge and Principal-Component Regression


Problems


Robust Regression


Need for Robust Regression


M-Estimators


Properties of Robust Estimators


Breakdown Point


Efficiency


Survey of Other Robust Regression Estimators


High-Breakdown-Point Estimators


Bounded Influence Estimators


Other Procedures


Computing Robust Regression Estimators


Problems


Introduction to Nonlinear Regression


Linear and Nonlinear Regression Models


Linear Regression Models


Nonlinear Regression Models


Origins of Nonlinear Models


Nonlinear Least Squares


Transformation to a Linear Model


Parameter Estimation in a Nonlinear System


Linearization


Other Parameter Estimation Methods


Starting Values


Computer Programs


Statistical Inference in Nonlinear Regression


Examples of Nonlinear Regression Models


Using SAS PROC NLIN


Problems


Generalized Linear Models


Introduction


Logistic Regression Models


Models with a Binary Response Variable


Estimating the Parameters in a Logistic Regression Model


Interpretation of the Parameters in a Logistic Regression Model


Statistical Inference on Model Parameters


Diagnostic Checking in Logistic Regression


Other Models for Binary Response Data


More Than Two Categorical Outcomes


Poisson Regression


The Generalized Linear Model


Link Functions and Linear Predictors


Parameter Estimation and Inference in the GLM


Prediction and Estimation with the GLM


Residual Analysis in the GLM


Overdispersion


Problems


Other Topics in the Use of Regression Analysis


Regression Models with Autocorrelated Errors


Source and Effects of Autocorrelation


Detecting the Presence of Autocorrelation


Parameter Estimation Methods


Effect of Measurement Errors in the Regressors


Simple Linear Regression


Berkson Model


Inverse Estimation-The Calibration Problem


Bootstrapping in Regression


Bootstrap Sampling in Regression


Bootstrap Confidence Intervals


Classification and Regression Trees (CART)


Neural Networks


Designed Experiments for Regression


Problems


Statistical Tables


Data Sets For Exercises


Supplemental Technical Material


Background on Basic Test Statistics


Background from the Theory of Linear Models


Important Results on SS[subscript R] and SS[subscript Res]


Gauss-Markov Theorem, Var([epsilon]) = [sigma superscript 2]I


Computational Aspects of Multiple Regression


Result on the Inverse of a Matrix


Development of the PRESS Statistic


Development of S[superscript 2 subscript (i)]


Outlier Test Based on R-Student


Independence of Residuals and Fitted Values


The Gauss-Markov Theorem, Var([epsilon]) = V


Bias in MS[subscript Res] When the Model Is Underspecified


Computation of Influence Diagnostics


Generalized Linear Models


Introduction to SAS


Basic Data Entry


Creating Permanent SAS Data Sets


Importing Data from an EXCEL File


Output Command


Log File


Adding Variables to an Existing SAS Data Set


References


Index