# Second Course in Statistics, A: Regression Analysis, 8th edition

• William Mendenhall,
• Terry T Sincich

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## Overview

A Second Course in Statistics: Regression Analysis, 8th Edition gives you the background and confidence to apply regression analysis techniques. The authors focus on readability to provide a learning experience rather than a reference, explaining concepts in a logical, intuitive manner with worked-out examples. Applications to engineering, sociology, psychology, science and business are demonstrated throughout. Real data and scenarios extracted from news articles, journals and actual consulting problems are used to apply the concepts, helping you utilize the techniques outlined in the text. Case studies throughout focus on specific problems and are suitable for class discussion. This text is ideal for the second half of a 2-semester introductory statistics sequence, or a graduate course in applied regression analysis.

ISBN-13: 9780137515264

Subject: Introductory Statistics

Category: Second Course in Statistics, A: Regression Analysis

## Overview

### 1. A Review of Basic Concepts (Optional)

• 1.1 Statistics and Data
• 1.2 Populations, Samples, and Random Sampling
• 1.3 Describing Qualitative Data
• 1.4 Describing Quantitative Data Graphically
• 1.5 Describing Quantitative Data Numerically
• 1.6 The Normal Probability Distribution
• 1.7 Sampling Distributions and the Central Limit Theorem
• 1.8 Estimating a Population Mean
• 1.9 Testing a Hypothesis About a Population Mean
• 1.10 Inferences About the Difference Between Two Population Means
• 1.11 Comparing Two Population Variances

### 2. Introduction to Regression Analysis

• 2.1 Modeling a Response
• 2.2 Overview of Regression Analysis
• 2.3 Regression Applications
• 2.4 Collecting the Data for Regression

### 3. Simple Linear Regression

• 3.1 Introduction
• 3.2 The Straight-Line Probabilistic Model
• 3.3 Fitting the Model: The Method of Least Squares
• 3.4 Model Assumptions
• 3.5 An Estimator of σ2
• 3.6 Assessing the Utility of the Model: Making Inferences About the Slope β1
• 3.7 The Coefficient of Correlation
• 3.8 The Coefficient of Determination
• 3.9 Using the Model for Estimation and Prediction
• 3.10 A Complete Example
• 3.11 Regression Through the Origin (Optional)
• Case Study 1: Legal Advertising–Does It Pay?

### 4. Multiple Regression Models

• 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
• 4.5 Estimation of σ2, the Variance of ε
• 4.6 Testing Overall Model Utility: The Analysis of Variance F-Test
• 4.7 Inferences About the Individual β Parameters
• 4.8 Multiple Coefficients of Determination: R2 and R2adj
• 4.9 Using the Model for Estimation and Prediction
• 4.10 An Interaction Model with Quantitative Predictors
• 4.11 A Quadratic (Second-Order) Model with a Quantitative Predictor
• 4.12 More Complex Multiple Regression Models (Optional)
• 4.13 A Test for Comparing Nested Models
• 4.14 A Complete Example
• Case Study 2: Modeling the Sale Prices of Residential Properties in Four Neighborhoods

### 5. Principles of Model-Building

• 5.1 Introduction: Why Model Building is Important
• 5.2 The Two Types of Independent Variables: Quantitative and Qualitative
• 5.3 Models with a Single Quantitative Independent Variable
• 5.4 First-Order Models with Two or More Quantitative Independent Variables
• 5.5 Second-Order Models with Two or More Quantitative Independent Variables
• 5.6 Coding Quantitative Independent Variables (Optional)
• 5.7 Models with One Qualitative Independent Variable
• 5.8 Models with Two Qualitative Independent Variables
• 5.9 Models with Three or More Qualitative Independent Variables
• 5.10 Models with Both Quantitative and Qualitative Independent Variables
• 5.11 External Model Validation

### 6. Variable Screening Methods

• 6.1 Introduction: Why Use a Variable-Screening Method?
• 6.2 Stepwise Regression
• 6.3 All-Possible-Regressions-Selection Procedure
• 6.4 Caveats
• Case Study 3: Deregulation of the Intrastate Trucking Industry

### 7. Some Regression Pitfalls

• 7.1 Introduction
• 7.2 Observational Data Versus Designed Experiments
• 7.3 Parameter Estimability and Interpretation
• 7.4 Multicollinearity
• 7.5 Extrapolation: Predicting Outside the Experimental Region
• 7.6 Variable Transformations

### 8. Residual Analysis

• 8.1 Introduction
• 8.2 Plotting Residuals and Detecting Lack of Fit
• 8.3 Detecting Unequal Variances
• 8.4 Checking the Normality Assumption
• 8.5 Detecting Outliers and Identifying Influential Observations
• 8.6 Detection of Residual Correlation: The Durbin-Watson Test
• Case Study 4: An Analysis of Rain Levels in California
• Case Study 5: Factors Affecting the Sale Price of Condominium Units Sold at Public Auction

### 9. Special Topics in Regression (Optional)

• 9.1 Introduction
• 9.2 Piecewise Linear Regression
• 9.3 Inverse Prediction
• 9.4 Weighted Least Squares
• 9.5 Modeling Qualitative Dependent Variables
• 9.6 Logistic Regression
• 9.7 Poisson Regression
• 9.8 Ridge and Lasso Regression
• 9.9 Robust Regression
• 9.10 Nonparametric Regression Models

### 10. Time Series Modeling and Forecasting

• 10.1 What is a Time Series?
• 10.2 Time Series Components
• 10.3 Forecasting Using Smoothing Techniques (Optional)
• 10.4 Forecasting: The Regression Approach
• 10.5 Autocorrelation and Autoregressive Error Models
• 10.6 Other Models for Autocorrelated Errors (Optional)
• 10.7 Constructing Time Series Models
• 10.8 Fitting Time Series Models with Autoregressive Errors
• 10.9 Forecasting with Time Series Autoregressive Models
• 10.10 Seasonal Time Series Models: An Example
• 10.11 Forecasting Using Lagged Values of the Dependent Variable (Optional)
• Case Study 6: Modeling Daily Peak Electricity Demands

### 11. Principles of Experimental Design

• 11.1 Introduction
• 11.2 Experimental Design Terminology
• 11.3 Controlling the Information in an Experiment
• 11.4 Noise-Reducing Designs
• 11.5 Volume-Increasing Designs
• 11.6 Selecting the Sample Size
• 11.7 The Importance of Randomization

### 12. The Analysis of Variance for Designed Experiments

• 12.1 Introduction
• 12.2 The Logic Behind an Analysis of Variance
• 12.3 One-Factor Completely Randomized Designs
• 12.4 Randomized Block Designs
• 12.5 Two-Factor Factorial Experiments
• 12.6 More Complex Factorial Designs (Optional)
• 12.7 Follow-Up Analysis: Tukey's Multiple Comparisons of Means
• 12.8 Other Multiple Comparisons Methods (Optional)
• 12.9 Checking ANOVA Assumptions
• Case Study 7: Voice Versus Face Recognition -- Does One Follow the Other?

### Appendices

• A: Derivation of the Least Squares Estimates of β0 and β1 in Simple Linear Regression
• A.1 Introduction
• A.2 Matrices and Matrix Multiplication
• A.3 Identity Matrices and Matrix Inversion
• A.4 Solving Systems of Simultaneous Linear Equations
• A.5 The Least Squares Equations and Their Solution
• A.6 Calculating SSE and s2
• A.7 Standard Errors of Estimators, Test Statistics, and Confidence Intervals for β0, β1, ... , βk
• A.8 A Confidence Interval for a Linear Function of the β Parameters and for E(y)
• A.9 A Prediction Interval for Some Value of y to be Observed in the Future
• B: The Mechanics of a Multiple Regression Analysis
• C: A Procedure for Inverting a Matrix
• D: Statistical Tables
• Table 1: Normal Curve Areas
• Table 2: Critical Values for Student's t
• Table 3: Critical Values for the F Statistic: F.10
• Table 4: Critical Values for the F Statistic: F.05
• Table 5: Critical Values for the F Statistic: F.025
• Table 6: Critical Values for the F Statistic: F.01
• Table 7: Critical Values for the Durbin-Watson d Statistic (α=.05)
• Table 8: Critical Values for the Durbin-Watson d Statistic (α=.01)
• Table 9: Critical Values for the X2-Statistic
• Table 10: Percentage Points of the Studentized Range, q(p,v), Upper 5%
• Table 11: Percentage Points of the Studentized Range, q(p,v), Upper 1%
• E: File Layouts for Case Study Data Sets

#### Online:

• SAS Tutorial
• SPSS Tutorial
• MINITAB Tutorial
• R Tutorial

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