PART ONE SIMPLE LINEAR REGRESSION
  Chapter Linear Regression with One Predictor Variable
   1.1 Relations between Variables
    Functional Relation between Two
    Variables
    Statistical Relation between Two Variables
   1.2 Regression Models and Their Uses
    Historical Origins
    Basic Concepts
    Construction of Regression Models
    Uses of Regression Analysis
    Regression and Causality
    Use of Computers
   1.3 Simple Linear Regression Model with Distribution of Error Terms Unspecified
    Formal Statement of Model
    Important Features of Model
    Meaning of Regression Parameters
    Alternative Versions of Regression Model
   1.4 Data for Regression Analysis
    Observational Data
    Experimental Data
    Completely Randomized Design
   1.5 Overview of Steps in Regression Analysis
   1.6 Estimation of Regression Function
    Method of Least Squares
    Point Estimation of Mean Response
    Residuals
    Properties of Fitted Regression Line
   1.7 Estimation of Error Terms Variance σ2
    Point Estimator of σ2
   1.8 Normal Error Regression Model
    Model
    Estimation of Parameters by Method of Maximum Likelihood
   Cited References
   Problems
   Exercises
   Projects
  Chapter 2 Inferences in Regression and Correlation Analysis
   2.1 Inferences Concerning β1
    Sampling Distribution of b1
    Sampling Distribution of(b1—β1)/s {b1}
    Confidence Interval for β1
    Tests Concerning β1
   2.2 Inferences Concerning β0
    Sampling Distribution of b0
    Sampling Distribution of (b0—β0)/s{b0}
    Confidence Interval for β0
   2.3 Some Considerations on Making Inferences Concerning β0 and β1
    Effects of Departures from Normality
    Interpretation of Confidence Coefficient and Risks of Errors
    Spacing of the X Levels
    Power of Tests
   2.4 Interval Estimation of E{Yh}
    Sampling Distribution of ●h
    Sampling Distribution of (●h-E{Yh})/s{●h}
    Confidence Interval for E{Yh}
   2.5 Prediction of New Observation
    Prediction Interval for Yh(new) when
    Parameters Known
    Prediction Interval for Yh(new) when
    Parameters Unknown
    Prediction of Mean of m New Observations for Given Xh
   2.6 Confidence Band for Regression Line
   2.7 Analysis of Variance Approach to Regression Analysis
    Partitioning of Total Sum of Squares
    Breakdown of Degrees of Freedom
    Mean Squares
    Analysis of Variance Table
    Expected Mean Squares
    F Test of β1=0 versus β≠0
   2.8 General Linear Test Approach
    Full Model
    Reduced Model
    Test Statistic
    Summary
   2.9 Descriptive Measures of Linear Association between X and Y
    Coefficient of Determination
    Limitations of R2
    Coefficient of Correlation
   2.10 Considerations in Applying Regression Analysis
   2.11 Normal Correlation Models
    Distinction between Regression and
    Correlation Model
    Bivariate Normal Distribution
    Conditional Inferences
    Inferences on Correlation Coefficients
    Spearman Rank Correlation Coefficient
   Cited References
   Problems
   Exercises
   Projects
  Chapter 3 Diagnostics and Remedial Measures
   3.1 Diagnostics for Predictor Variable
   3.2 Residuals
    Properties of Residuals
    Semistudentized Residuals
    Departures from Model to Be Studied by Residuals
   3.3 Diagnostics for Residuals
    Nonlinearity of Regression Function
    Nonconstancy of Error Variance
    Presence of Outliers
    Nonindependence of Error Terms
    Nonnormality of Error Terms
    Omission of Important Predictor
    Variables
    Some Final Comments
   3.4 Overview of Tests Involving Residuals
    Tests for Randomness
    Tests for Constancy of Variance
    Tests for Outliers
    Tests for Normality
   3.5 Correlation Test for Normality
   3.6 Tests for Constancy of Error Variance
    Brown-Forsythe Test
    Breusch-Pagan Test
   3.7 F Test for Lack of Fit
    Assumptions
    Notation
    Full Model
    Reduced Model
    Test Statistic
    ANOVA Table
   3.8 Overview of Remedial Measures
    Nonlinearity of Regression
    Function
    Nonconstancy of Error Variance
    Nonindependence of Error Terms
    Nonnormality of Error Terms
    Omission of Important Predictor
    Variables
    Outlying Observations
   3.9 Transformations
    Transformations for Nonlinear
    Relation Only
    Transformations for Nonnormality and Unequal Error Variances
    Box-Cox Transformations
   3.10 Exploration of Shape of Regression Function
    Lowess Method
    Use of Smoothed Curves to Confirm Fitted
    Regression Function
   3.11 Case Example—Plutonium Measurement
   Cited References
   Problems
   Exercises
   Projects
   Case Studies
  Chapter 4 Simultaneous Inferences and Other Topics in Regression Analysis
   4.1 Joint Estimation of β0 and β1
    Need for Joint Estimation
    Bonferroni Joint Confidence Intervals
   4.2 Simultaneous Estimation of Mean Responses
    Working-Hotelling Procedure
    Bonferroni Procedure
   4.3 Simultaneous Prediction Intervals for New Observations
   4.4 Regression through Origin
    Model
    Inferences
    Important Cautions for Using Regression through Origin
   4.5 Effects of Measurement Errors
    Measurement Errors in Y
    Measurement Errors in X
    Berkson Model
   4.6 Inverse Predictions
   4.7 Choice of X Levels
   Cited References
   Problems
   Exercises
   Projects
  Chapter 5 Matrix Approach to Simple Linear Regression Analysis
   5.1 Matrices
    Definition of Matrix
    Square Matrix
    Vector
    Transpose
    Equality of Matrices
   5.2 Matrix Addition and Subtraction
   5.3 Matrix Multiplication
    Multiplication of a Matrix by a Scalar
    Multiplication of a Matrix by a Matrix
   5.4 Special Types of Matrices
    Symmetric Matrix
    Diagonal Matrix
    Vector and Matrix with All Elements
    Unity
    Zero Vector
   5.5 Linear Dependence and Rank of Matrix
    Linear Dependence
    Rank of Matrix
   5.6 Inverse of a Matrix
    Finding the Inverse
    Uses of Inverse Matrix
   5.7 Some Basic Results for Matrices
   5.8 Random Vectors and Matrices
    Expectation of Random Vector or Matrix
    Variance-Covariance Matrix of Random Vector
    Some Basic Results
    Multivariate Normal Distribution
   5.9 Simple Linear Regression Model in Matrix Terms
   5.10 Least Squares Estimation of Regression Parameters
    Normal Equations
    Estimated Regression Coefficients
   5.11 Fitted Values and Residuals
    Fitted Values
    Residuals
   5.12 Analysis of Variance Results
    Sums of Squares
    Sums of Squares as Quadratic
    Forms
   5.13 Inferences in Regression Analysis
    Regression Coefficients
    Mean Response
    Prediction of New Observation
   Cited Reference
   Problems
   Exercises
 PART TWO MULTIPLE LINEAR REGRESSION
  Chapter 6 Multiple Regression I
   6.1 Multiple Regression Models
    Need for Several Predictor Variables
    First-Order Model with Two Predictor Variables
    First-Order Model with More than Two Predictor Variables
    General Linear Regression Model
   6.2 General Linear Regression Model in Matrix Terms
   6.3 Estimation of Regression Coefficients
   6.4 Fitted Values and Residuals
   6.5 Analysis of Variance Results
    Sums of Squares and Mean Squares
    F Test for Regression Relation
    Coefficient of Multiple Determination
    Coefficient of Multiple Correlation
   6.6 Inferences about Regression Parameters
    Interval Estimation of βa
    Tests for βa
    Joint Inferences
   6.7 Estimation of Mean Response and Prediction of New Observation
    Interval Estimation of E{Yh}
    Confidence Region for Regression
    Surface
    Simultaneous Confidence Intervals for Several
    Mean Responses
    Prediction of New Observation Yh(new)
    Prediction of Mean of m New Observations at Xh
    Predictions of g New Observations
    Caution about Hidden Extrapolations
   6.8 Diagnostics and Remedial Measures
    Scatter Plot Matrix
    Three-Dimensional Scatter Plots
    Residual Plots
    Correlation Test for Normality
    Brown-Forsythe Test for Constancy of Error Variance
    Breusch-Pagan Test for Constancy of Error Variance
    F Test for Lack of Fit
    Remedial Measures
   6.9 An Example—Multiple Regression with Two Predictor Variables
    Setting
    Basic Calculations
    Estimated Regression Function
    Fitted Values and Residuals
    Analysis of Appropriateness of Model
    Analysis of Variance
    Estimation of Regression Parameters
    Estimation of Mean Response
    Prediction Limits for New Observations
   Cited Reference
   Problems
   Exercises
   Projects
  Chapter 7 Multiple Regression II
   7.1 Extra Sums of Squares
    Basic Ideas
    Definitions
    Decomposition of SSR into Extra Sums of Squares
    ANOVA Table Containing Decomposition of SSR
   7.2 Uses of Extra Sums of Squares in Tests for Regression Coefficients
    Test whether a Single βk=0
    Test whether Several βk=0
   7.3 Summary of Tests Concerning Regression Coefficients
    Test whether All βk=0
    Test whether a Single βk=0
    Test whether Some βk=0
    Other Tests
   7.4 Coefficients of Partial Determination
    Two Predictor Variables
    General Case
    Coefficients of Partial Correlation
   7.5 Standardized Multiple Regression Model
    Roundoff Errors in Normal Equations
    Calculations
    Lack of Comparability in Regression
    Coefficients
    Correlation Transformation
    Standardized Regression Model
    XX Matrix for Transformed Variables
    Estimated Standardized Regression
    Coefficients
   7.6 Multicollinearity and Its Effects
    Uncorrelated Predictor Variables
    Nature of Problem when Predictor Variables
    Ant Perfectly Correlated
    Effects of Multicollinearity
    Need for More Powerful Diagnostics for
    Multicollinearity
   Cited Reference
   Problems
   Exercise
   Projects
  Chapter 8 Regression Models for Quantitative and Qualitative Predictors
   8.1 Polynomial Regression Models
    Uses of Polynomial Models
    One Predictor Variable-Second Order
    One Predictor Variable-Third Order
    One Predictor Variable-Higher Orders
    Two Predictor Variables-Second Order
    Three Predictor Variables-Second
    Order
    Implementation of Polynomial Regression
    Models
    Case Example
    Some Further Comments on Polynomial
    Regression
   8.2 Interaction Regression Models
    Interaction Effects
    Interpretation of Interaction Regression Models with Linear Effects
    Interpretation of Interaction Regression Models with Curvilinear Effects
    Implementation of Interaction Regression Models
   8.3 Qualitative Predictors
    Qualitative Predictor with Two Classes
    Interpretation of Regression Coefficients
    Qualitative Predictor with More than Two Classes
    Time Series Applications
   8.4 Some Considerations in Using Indicator Variables
    Indicator Variables versus Allocated Codes
    Indicator Variables versus Quantitative Variables
    Other Codings for Indicator Variables
   8.5 Modeling Interactions between Quantitative and Qualitative Predictors
    Meaning of Regression Coefficients
   8.6 More Complex Models
    More than One Qualitative Predictor Variable
    Qualitative Predictor Variables Only
   8.7 Comparison of Two or More Regression Functions
    Soap Production Lines Example
    Instrument Calibration Study Example
   Cited Reference
   Problems
   Exercises
   Projects
   Case Study
  Chapter 9 Building the Regression Model I: Model Selection and Validation
   9.1 Overview of Model-Building Process
    Data Collection
    Data Preparation
    Preliminary Model Investigation
    Reduction of Explanatory Variables
    Model Refinement and Selection
    Model Validation
   9.2 Surgical Unit Example
   9.3 Criteria for Model Selection
    R2 or SSEp Criterion
    R2a.p or MSEp Criterion
    Mallows' Cp Criterion
    A1CP and SBCp Criteria
    PRESSp Criterion
   9.4 Automatic Search Procedures for Model Selection
    "Best" Subsets Algorithm
    Stepwise Regression Methods
    Forward Stepwise Regression
    Other Stepwise Procedures
   9.5 Some Final Comments on Automatic Model Selection Procedures
   9.6 Model Validation
    Collection of New Data to Check Model
    Comparison with Theory, EmpiricalEvidence, or Simulation Results Data Splitting
   Cited References
   Problems
   Exercise
   Projects
   Case Studies
  Chapter 10 Building the Regression Model II: Diagnostics
   10.1 Model Adequacy for a Predictor Variable-Added-Variable Plots
   10.2 Identifying Outlying Y Observations?Studentized Deleted Residuals
    Outlying Cases
    Residuals and Semistudentized
    Residuals
    Hat Matrix
    Studentized Residuals
    Deleted Residuals
    Studentized Deleted Residuals
   10.3 Identifying Outlying X Observations-Hat Matrix Leverage Values
    Use of Hat Matrix for Identifying Outlying X Observations
    Use of Hat Matrix to Identify Hidden Extrapolation
   10.4 Identifying Influential Cases-DFFITS, Cook's Distance, and DFBETAS Measures
    Influence on Single Fitted Value-DFFITS
    Influence on All Fitted Values-Cook's Distance
    Influence on the Regression Coefficients-DFBETAS
    Influence on Inferences Some Final Comments
   10.5 Multicollinearity Diagnostics-Variance Inflation Factor
    Informal Diagnostics
    Variance Inflation Factor
   10.6 Surgical Unit Example-Continued
   Cited References
   Problems
   Exercises
   Projects
   Case Studies
  Chapter Building the Regression Model III: Remedial Measures
   11.1 Unequal Error Variances Remedial Measures-Weighted Least Squares
    Error Variances Known
    Error Variances Known up to Proportionality Constant
    Error Variances Unknown
   11.2 Multicollinearity Remedial Measures桼idge Regression
    Some Remedial Measures
    Ridge Regression
   11.3 Remedial Measures for Influential Cases桼obust Regression
    Robust Regression
    IRIS Robust Regression
   11.4 N on parametric Regression: Lowess Method and Regression Trees
    Lowess Method
    Regression Trees
   11.5 Remedial Measures for Evaluating Precision in Nonstandard Situations-Bootstrapping
    General Procedure
    Bootstrap Sampling
    Bootstrap Confidence Intervals
   11.6 Case Example-MNDOT Traffic Estimation
    The AADT Database
    Model Development
    Weighted Least Squares Estimation
   Cited References
   Problems
   Exercises
   Projects
   Case Studies
  Chapter 12 Autocorrelation in Time Series Data
   12.1 Problems of Autocorrelation
   12.2 First-Order Autoregressive Error Model
    Simple Linear Regression
    Multiple Regression
    Properties of Error Terms
   12.3 Durbin-Watson Test for Autocorrelation
   12.4 Remedial Measures for Autocorrelation
    Addition of Predictor Variables
    Use of Transformed Variables
    Cochrane-Orcutt Procedure
    Hildreth-Lu Procedure
    First Differences Procedure
    Comparison of Three Methods
   12.5 Forecasting with Autocorrelated Error Terms
   Cited References
   Problems
   Exercises
   Projects
   Case Studies
 PART THREE NONLINEAR REGRESSION
  Chapter 13 Introduction to Nonlinear Regression and Neural Networks
   13.1 Linear and Nonlinear Regression Models
    Linear Regression Models
    Nonlinear Regression Models
    Estimation of Regression Parameters
   13.2 Least Squares Estimation in Nonlinear Regression
    Solution of Normal Equations
    Direct Numerical Search—Gauss-Newton Method
    Other Direct Search Procedures
   13.3 Model Building and Diagnostics
   13.4 Inferences about Nonlinear Regression Parameters
    Estimate of Error Term Variance
    Large-Sample Theory
    When Is Large-Sample Theory Applicable?
    Interval Estimation of a Single γk
    Simultaneous Interval Estimation of Several γk
    Test Concerning a Single γk
    Test Concerning Several γk
   13.5 Learning Curve Example
   13.6 Introduction to Neural Network Modeling
    Neural Network Model
    Network Representation
    Neural Network as Generalization of Linear Regression
    Parameter Estimation: Penalized Least Squares
    Example: Ischemic Heart Disease
    Model Interpretation and Prediction
    Some Final Comments on Neural Network Modeling
   Cited References
   Problems
   Exercises
   Projects
   Case Studies
  Chapter 14 Logistic Regression, Poisson Regression,and Generalized Linear Models
   14.1 Regression Models with Binary Response Variable
    Meaning of Response Function when Outcome Variable Is Binary
    Special Problems when Response Variable Is Binary
   14.2 Sigmoidal Response Functions for Binary Responses
    Probit Mean Response Function
    Logistic Mean Response Function
    Complementary Log-Log Response Function
   14.3 Simple Logistic Regression
    Simple Logistic Regression Model
    Likelihood Function
    Maximum Likelihood Estimation
    Interpretation of b1
    Use of Probit and Complementary Log-Log Response Functions
    Repeat Observations—Binomial Outcomes
   14.4 Multiple Logistic Regression
    Multiple Logistic Regression Model
    Fitting of Model
    Polynomial Logistic Regression
   14.5 Inferences about Regression Parameters
    Test Concerning a Single βk: Wald Test
    Interval Estimation of a Single βa
    Test whether Several βk=0: Likelihood
    Ratio Test
   14.6 Automatic Model Selection Methods
    Model Selection Criteria
    Best Subsets Procedures
    Stepwise Model Selection
   14.7 Tests for Goodness of Fit
    Pearson Chi-Square Goodness of Fit Test
    Deviance Goodness of Fit Test
    Hosmer-Lemeshow Goodness of Fit Test
   14.8 Logistic Regression Diagnostics
    Logistic Regression Residuals
    Diagnostic Residual Plots
    Detection of Influential
    Observations
   14.9 Inferences about Mean Response
    Point Estimator
    Interval Estimation
    Simultaneous Confidence Intervals for Several Mean Responses
   14.10 Prediction of a New Observation Choice of Prediction Rule Validation of Prediction Error Rate
   14.11 Polytomous Logistic Regression for Nominal Response
    Pregnancy Duration Data
    with Polytomous Response
    J—1 Baseline-Category Logits for
    Nominal Response
    Maximum Likelihood Estimation
   14.12 Polytomous Logistic Regression for Ordinal Response
   14.13 Poisson Regression
    Poisson Distribution
    Poisson Regression Model
    Maximum Likelihood Estimation
    Model Development
    Inferences
   14.14 Generalized Linear Models
   Cited References
   Problems
   Exercises
   Projects
   Case Studies
 Appendix A
  Some Basic Results in Probability and Statistics
 Appendix B
  Tables
 Appendix C
  Data Sets
 Appendix D
  Selected Bibliography
 Index