A second course in statistics : regression analyisis

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