A Second Course in Statistics: Regression Analysis 8th Edition

A Second Course in Statistics Regression Analysis
Contents
Preface
Overview
Introductory Statistics Course
Applied Regression for Graduates
Features
New to the 8th Edition
Supplements
Chapter 1 A Review of Basic Concepts (Optional)
Contents
Objectives
1.1 Statistics and Data
Solution
1.1 Exercises
1.2 Populations, Samples, and Random Sampling
Solution
1.2 Exercises
1.3 Describing Qualitative Data
1.3 Exercises
1.4 Describing Quantitative Data Graphically
Solution
Solution
1.4 Exercises
1.5 Describing Quantitative Data Numerically
Solution
Solution
Solution
1.5 Exercises
1.6 The Normal Probability Distribution
Solution
Solution
1.6 Exercises
1.7 Sampling Distributions and the Central Limit Theorem
Solution
1.8 Estimating a Population Mean
Solution
Solution
Solution
1.8 Exercises
1.9 Testing a Hypothesis About a Population Mean
Solution
Solution
1.9 Exercises
1.10 Inferences About the Difference Between Two Population Means
Solution
Solution
1.10 Exercises
1.11 Comparing Two Population Variances
Solution
1.11 Exercises
Quick Summary/Guides
Key Ideas
Types of statistical applications
Descriptive statistics
Inferential statistics
Types of data
Graphs for qualitative data
Graphs for quantitative data
Measure of central tendency
Measures of variation
Percentage of measurements within 2 standard deviations of the mean
Properties of the sampling distribution of ȳ
Central Limit Theorem
Formulation of Confidence Intervals for a Population Parameter θ and Test Statistics for H0: θ=θ0, where θ=μ or (μ1−μ2)
Population Parameters and Corresponding Estimators and Standard Errors
Supplementary Exercises
References
Chapter 2 Introduction to Regression Analysis
Contents
Objectives
2.1 Modeling a Response
2.2 Overview of Regression Analysis
2.3 Regression Applications
2.4 Collecting the Data for Regression
Quick Summary
Key Ideas
Regression analysis
Regression variables
Probabilistic model
Steps in regression
Types of regression data
Chapter 3 Simple Linear Regression
Contents
Objectives
3.1 Introduction
3.2 The Straight-Line Probabilistic Model
Steps in Regression Analysis
3.2 Exercises
3.3 Fitting the Model: The Method of Least Squares
3.3 Exercises
3.4 Model Assumptions
3.5 An Estimator of σ2
3.5 Exercises
3.6 Assessing the Utility of the Model: Making Inferences About the Slope β1
3.6 Exercises
3.7 The Coefficient of Correlation
Solution
Solution
3.8 The Coefficient of Determination
Solution
3.8 Exercises
3.9 Using the Model for Estimation and Prediction
Solution
Solution
3.9 Exercises
3.10 A Complete Example
3.10 Exercises
3.11 Regression Through the Origin (Optional)
Solution
Solution
3.11 Exercises
Quick Summary/Guides
Guide to Simple Linear Regression
Key Symbols/Notation
Key Ideas
Simple Linear Regression Variables
Method of Least Squares Properties
Practical Interpretation of y-Intercept
Practical Interpretation of Slope
First-Order (Straight-Line) Model
Coefficient of Correlation, r
Coefficient of Determination, r2
Practical Interpretation of Model Standard Deviation, s
Confidence Interval vs. Prediction Interval
Regression through the origin model
Supplementary Exercises
References
Case Study 1 Legal Advertising—Does it Pay?
The Problem
The Data
Research Questions
The Models
Model 1
Model 2
Descriptive Analysis
Testing the Models
More Supporting Evidence
Conclusion
Follow-up Questions
Chapter 4 Multiple Regression Models
Contents
Objectives
4.1 General Form of a Multiple Regression Model
4.2 Model Assumptions
4.3 A First-Order Model with Quantitative Predictors
4.4 Fitting the Model: The Method of Least Squares
Solution
Solution
4.5 Estimation of σ2, the Variance of ε
4.6 Testing the Utility of a Model: The Analysis of Variance F-Test
Solution
4.7 Inferences About the Individual β Parameters
Solution
4.8 Multiple Coefficients of Determination: R2 and R2a
4.8 Exercises
4.9 Using the Model for Estimation and Prediction
Solution
4.9 Exercises
4.10 An Interaction Model with Quantitative Predictors
Solution
4.10 Exercises
4.11 A Quadratic (Second-Order) Model with a Quantitative Predictor
Solution
4.11 Exercises
4.12 More Complex Multiple Regression Models (Optional)
Solution
Solution
Solution
4.12 Exercises
4.13 A Test for Comparing Nested Models
Solution
4.13 Exercises
4.14 A Complete Example
Quick Summary/Guides
Key Formulas
Estimator of σ2 for a model with k independent variables
Test statistic for testing H0: βi
100(1−α)% confidence interval for βi
Multiple coefficient of determination
Adjusted multiple coefficient of determination
Test statistic for testing H0: β1 = β2 = ... = βk = 0
Test statistic for comparing reduced and complete models
Key Symbols
Key Ideas
Multiple Regression Variables
First-Order Model in k Quantitative x’s
Interaction Model in 2 Quantitative x’s
Quadratic Model in 1 Quantitative x
Complete Second-Order Model in 2 Quantitativex’s
Dummy Variable Model for 1 Qualitative x
Multiplicative Model in Quantitative x’s
Adjusted Coefficient of Determination, R2a
Interaction between x1 and x2
Parsimonious Model
Recommendation for Assessing Model Adequacy
Recommendation for Testing Individual β’s
Extrapolation
Nested Models
Guide To Multiple Regression
Supplementary Exercises
References
Case Study 2 Modeling the Sale Prices of Residential Properties in Four Neighborhoods
The Problem
The Data
The Theoretical Model
The Hypothesized Regression Models
Model 1
Model 2
Model 3
Model 4
Model Comparisons
Test # 1
Test # 2
Test # 3
Interpreting the Prediction Equation
Predicting the Sale Price of a Property
Chapter 5 Principles of Model Building
Contents
Objectives
5.1 Introduction: Why Model Building Is Important
5.2 The Two Types of Independent Variables: Quantitative and Qualitative
Solution
5.2 Exercises
5.3 Models with a Single Quantitative Independent Variable
Solution
5.3 Exercises
5.4 First-Order Models with Two or More Quantitative Independent Variables
5.5 Second-Order Models with Two or More Quantitative Independent Variables
Solution
5.5 Exercises
5.6 Coding Quantitative Independent Variables (Optional)
Solution
5.6 Exercises
5.7 Models with One Qualitative Independent Variable
Solution
5.8 Models with Two Qualitative Independent Variables
Solution
Solution
Solution
Solution
Solution
5.8 Exercises
5.9 Models with Three or More Qualitative Independent Variables
Solution
Solution
Solution
5.10 Models with Both Quantitative and Qualitative Independent Variables
Solution
Solution
Solution
Solution
5.10 Exercises
5.11 External Model Validation (Optional)
Solution
Quick Summary/Guides
Key Formulas
Coding Quantitative x’s
Cross-validation
Key Ideas
Steps in Model Building
Procedure for Writing a Complete Second-Order Model
Models with One Quantitative x
Models with Two Quantitative x’s
Model with Three Qualitative x’s
Model with One Qualitative x (k levels)
Models with Two Qualitative x’s (one at two levels, one at three levels)
Models with One Quantitative x and One Qualitative x (at three levels)
Models with Two Quantitative x’s and Two Qualitative x’s (both at two levels)
Supplementary Exercises
References
Chapter 6 Variable Screening Methods
Contents
Objectives
6.1 Introduction: Why Use a Variable Screening Method?
6.2 Stepwise Regression
Solution
6.3 All-Possible-Regressions Selection Procedure
R2 Criterion
Adjusted R2 or MSE Criterion
Cp Criterion
PRESS Criterion
Solution
6.4 Caveats
Quick Summary/Guides
KEY FORMULAS
Key Ideas
Variable Screening Methods
All-Possible-Regressions Selection Criteria
Potential Caveats in Using Variable Screening Methods to Determine the “Final” Model
Supplementary Exercises
Reference
Case Study 3 Deregulation of the Intrastate Trucking Industry
The Problem
The Data
Variable Screening
Model Building
Test for Significance of All Quadratic Terms (Model 1 vs. Model 2)
Test for Significance of All Quantitative–Qualitative Interaction Terms (Model 1 vs. Model 3)
Test for Significance of Qualitative–Quadratic Interaction (Model 1 vs. Model 4)
Test for Significance of All Origin Terms (Model 4 vs. Model 5)
Test for Significance of All Deregulation Terms (Model 4 vs. Model 6)
Test for Significance of All Deregulation–Origin Interaction Terms (Model 4 vs. Model 7)
Impact of Deregulation
Follow-up Questions
Chapter 7 Some Regression Pitfalls
Contents
Objectives
7.1 Introduction
7.2 Observational Data versus Designed Experiments
Solution
Solution
7.3 Parameter Estimability and Interpretation
Solution
Solution
7.4 Multicollinearity
Solution
7.5 Extrapolation: Predicting Outside the Experimental Region
Solution
7.6 Variable Transformations
Solution
Solution
Quick Summary
Key Formulas
pth-order polynomial
Standardized beta for xi
Variance inflation factor for xi
Key Ideas
Establishing cause and effect
Parameter estimability
Multicollinearity
Extrapolation
Variable transformations
Supplementary Exercises
References
Chapter 8 Residual Analysis
Contents
Objectives
8.1 Introduction
8.2 Regression Residuals
Solution
8.3 Detecting Lack of Fit
Solution
Solution
Solution
8.3 Exercises
8.4 Detecting Unequal Variances
Solution
Solution
Solution
8.4 Exercises
8.5 Checking the Normality Assumption
8.5 Exercises
8.6 Detecting Outliers and Identifying Influential Observations
Solution
Leverage
The Jackknife
Cook’s Distance:
Solution
8.6 Exercises
8.7 Detecting Residual Correlation: The Durbin–Watson Test
8.7 Exercises
Quick Summary
Key Symbols & Formulas
Residual
Partial residuals for xj
Standardized residual
Studentized residual
Leverage for xj
Jackknifed predicted value
Deleted residual
Standard deviation of deleted residual sdi
Studentized deleted residual
Cook’s distance
Durbin–Watson statistic
Key Ideas
Properties of residuals
Outlier:
Detecting influence
Testing for residual correlation
Supplementary Exercises
References
Case Study 4 An Analysis of Rain Levels in California
The problem
The Data
A Model for Average Annual Precipitation
Model 1
A Residual Analysis of the Model
Adjustments to the Model
Model 2
Model 3
Conclusions
Follow-up Questions
Reference
Case Study 5 An Investigation of Factors Affecting the Sale Price of Condominium Units Sold at Public Auction
The Problem
The Data
The Models
Model 1
Model 2
Model 3
Model 4
The Regression Analyses
An Analysis of the Residuals from Model 3
What the Model 3 Regression Analysis Tells Us
Comparing the Mean Sale Price for Two Types of Units (Optional)
Conclusions
Follow-up Questions
Reference
Chapter 9 Special Topics in Regression (Optional)
Contents
Objectives
9.1 Introduction
9.2 Piecewise Linear Regression
Solution
Solution
9.2 Exercises
9.3 Inverse Prediction
Solution
9.3 Exercises
9.4 Weighted Least Squares
Solution
9.4 Exercises
9.5 Modeling Qualitative Dependent Variables
9.5 Exercises
9.6 Logistic Regression
Solution
Solution
9.6 Exercises
9.7 Poisson Regression
Solution
9.7 Exercises
9.8 Ridge and LASSO Regression
9.9 Robust Regression
Solution
9.10 Nonparametric Regression Models
Quick Summary
Key Formulas
Piecewise Linear Regression Models
Inverse Prediction–Prediction Interval for x when y = yp
Weighted Least Squares
Logistic Regression Model
Poisson Regression Model
Inverse Prediction
Weighted Least Squares (WLS)
Determining the Weights in WLS
Problems with a Least Squares Binary Regression Model
Interpreting Betas in a Logistic Regression Model
Interpreting Betas in a Poisson Regression Model
Ridge Regression
Estimating the Biasing Constant c in Ridge Regression
LASSO Regression
Robust Regression
Methods of Estimation with Robust Regression
Nonparametric Regression
References
Chapter 10 Introduction to Time Series Modeling and Forecasting
Contents
Objectives
10.1 What Is a Time Series?
10.2 Time Series Components
10.3 Forecasting Using Smoothing Techniques (Optional)
Moving Average Method
Exponential Smoothing
Holt–Winters Forecasting Model
Solution
Solution
10.3 Exercises
10.4 Forecasting: The Regression Approach
Solution
10.4 Exercises
10.5 Autocorrelation and Autoregressive Error Models
10.5 Exercises
10.6 Other Models for Autocorrelated Errors (Optional)
10.7 Constructing Time Series Models
Choosing the Deterministic Component
Choosing the Residual Component
10.7 Exercises
10.8 Fitting Time Series Models with Autoregressive Errors
10.8 Exercises
10.9 Forecasting with Time Series Autoregressive Models
Solution
10.9 Exercises
10.10 Seasonal Time Series Models: An Example
10.11 Forecasting Using Lagged Values of the Dependent Variable (Optional)
Quick Summary
Key Formulas
Time series model
Exponential smoothing
Holt–Winter’s method
Moving average
Mean absolute deviation
Mean absolute percentage error
Root mean squared error
AR(p) error model
MA(q) error model
95% forecast limits using AR(1) error model
Key Symbols
Key Ideas
Time series components
Time series forecasting methods
Measures of forecast accuracy
Problems with least squares regression forecasting
Autocorrelation
Supplementary Exercises
References
Case Study 6 Modeling Daily Peak Electricity Demands
The Problem
The Data
The Models
Model 1
Model 2
Model 3
The Regression and Autoregression Analyses
Forecasting Daily Peak Electricity Demand
Conclusions
Follow-up Questions
References
Chapter 11 Principles of Experimental Design
Contents
Objectives
11.1 Introduction
11.2 Experimental Design Terminology
Solution
11.3 Controlling the Information in an Experiment
11.4 Noise-Reducing Designs
Solution
Solution
11.4 Exercises
11.5 Volume-Increasing Designs
Solution
Solution
11.5 Exercises
11.6 Selecting the Sample Size
Solution
11.6 Exercises
11.7 The Importance of Randomization
Quick Summary
Key Formulas
Key Ideas
Steps in Experimental Design
Two Methods for Assigning Treatments
Supplementary Exercises
References
Chapter 12 The Analysis of Variance for Designed Experiments
Contents
Objectives
12.1 Introduction
12.2 The Logic Behind an Analysis of Variance
12.3 One-Factor Completely Randomized Designs
Solution
Solution
Solution
Solution
Solution
Solution
12.3 Exercises
12.4 Randomized Block Designs
Solution
Solution
Solution
12.4 Exercises
12.5 Two-Factor Factorial Experiments
Solution
Solution
Solution
Solution
Solution
Solution
Solution
12.5 Exercises
12.6 More Complex Factorial Designs (Optional)
Solution
Solution
Solution
12.6 Exercises
12.7 Follow-Up Analysis: Tukey’s Multiple Comparisons of Means
Solution
Solution
12.7 Exercises
12.8 Other Multiple Comparisons Methods (Optional)
Scheffé Method
Solution
Bonferroni Approach
Solution
12.8 Exercises
12.9 Checking ANOVA Assumptions
Detecting Nonnormal Populations
Detecting Unequal Variances
Solution
12.9 Exercises
Quick Summary
Key Symbols/Notation
Key Ideas
Key Elements of a Designed Experiment
Balanced Design
Tests for Main Effects in a Factorial Design
Robust Method
Conditions Required for Valid F-test in a Completely Randomized Design
Conditions Required for Valid F-tests in a Randomized Block Design
Conditions Required for Valid F-tests in a Complete Factorial Design
Multiple Comparisons of Means Methods
Linear Model for a Completely Randomized Design with p Treatments
Linear Model for a Randomized Block Design with p Treatments and> b Blocks
Linear Model for a Complete Factorial Block Design with Factor A at a levels and Factor B at b levels
Guide to Selecting the Experimental Design
Guide To Conducting Anova F-Tests
Supplementary Exercises
References
Case Study 7 Voice Versus Face Recognition—Does One Follow the Other?
The Problem
The Design of Experiment #1
Research Questions
ANOVA Models and Results
Multiple Comparisons of Means
Conclusions
Reference
Appendix A Derivation of the Least Squares Estimates of β0 and β1 in Simple Linear Regression
Appendix B The Mechanics of a Multiple Regression Analysis
Contents
B.1 Introduction
B.2 Matrices and Matrix Multiplication
Solution
Solution
B.2 Exercises
B.3 Identity Matrices and Matrix Inversion
Solution
B.3 Exercises
B.4 Solving Systems of Simultaneous Linear Equations
Solution
B.4 Exercises
B.5 The Least Squares Equations and Their Solutions
Solution
Solution
B.5 Exercises
B.6 Calculating SSE and s2
Solution
B.7 Standard Errors of Estimators, Test Statistics, and Confidence Intervals for β0, β1, ..., βk
Solution
Solution
B.7 Exercises
B.8 A Confidence Interval for a Linear Function of the β Parameters; a Confidence Interval for E(y)
Solution
Solution
B.9 A Prediction Interval for Some Value of y to be Observed in the Future
Solution
B.9 Exercises
Summary
Supplementary Exercises
References
Appendix C A Procedure for Inverting a Matrix
Solution
Solution
C.0 Exercise
Appendix D Useful Statistical Tables
Contents
Appendix E File Layouts for Case Study Data Sets
Case Study 1: Legal Advertising—Does It Pay?
Case Study 2: Modeling the Sales Prices of Properties in Four Neighborhoods
Case Study 3: Deregulation of the Intrastate Trucking Industry
Case Study 4: An Analysis of Rain Levels in California
Case Study 5: An Investigation of Factors Affecting the Sales Price of Condominium Units Sold at Public Auction
Case Study 7: Voice Vs. Face Recognition—Does One Follow the Other?
Answers to Selected Exercises
Chapter 1
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Chapter 12
Credits
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 12
Chapter APP B
Chapter APP D
Chapter Cover
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y