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Regression with Graphics 
by Lawrence Hamilton
Table of Contents

This page was adapted from a page at the Stata Bookstore page.  We thank Stata for their permission to adapt and distribute this page via our web site.  We are very grateful to Professor Lawrence Hamilton for granting us permission to distribute the data files for Regression with Graphics.

Regression with Graphics provides a unique treatment of regression by integrating graphical and regression methods for performing exploratory data analysis. More emphasis is given to practical issues and troubleshooting than statistical theory. Techniques are illustrated using real data with environmental themes from diverse disciplines, thus making it interesting and understandable to readers in any field. Stata graphs and output are used throughout the book.

Click here for descriptions and optionally to download the datasets used in Regression with Graphics.

Contents

    1 Variable Distributions

    The Concord Water Study
    Mean, Variance, and Standard Deviation
    Normal Distributions
    Median and Interquartile Range
    Boxplots
    Symmetry Plots
    Quantile Plots
    Quantile-Quantile Plots
    Quantile-Normal Plots
    Power Transformations
    Selecting an Appropriate Power
    Conclusion
    Exercises
    Notes

    2 Bivariate Regression Analysis

    The Basic Linear Model
    Ordinary Least Squares
    Scatterplots and Regression
    Predicted Values and Residuals
    R2, Correlation, and Standardized Regression Coefficients
    Reading Computer Output
    Hypothesis Tests for Regression Coefficients
    Confidence Intervals
    Regression Through the Origin
    Problems with Regression
    Residual Analysis
    Power Transformations in Regression
    Understanding Curvilinear Regression
    Conclusion
    Exercises
    Notes

    3 Basics of Multiple Regression

    Multiple Regression Models
    A Three-Variable Example
    Partial Effects
    Variable Selection
    A Seven-Variable Example
    Standardized Regression Coefficients
    t-Tests and Confidence Intervals for Individual Coefficients
    F-Tests for Sets of Coefficients
    Multicollinearity
    Search Strategies
    Interaction Effects
    Intercept Dummy Variables
    Slope Dummy Variables
    Oneway Analysis of Variance
    Twoway Analysis of Variance
    Conclusion
    Exercises
    Notes

    4 Regression Criticism

    Assumptions of Ordinary Least Squares
    Correlation and Scatterplot Matrices
    Residual Versus Predicted Y Plots
    Autocorrelation
    Nonnormality
    Influence Analysis
    More Case Statistics
    Symptoms of Multicollinearity
    Conclusion
    Exercises
    Notes

    5 Fitting curves

    Exploratory Band Regression
    Regression with Transformed Variables
    Curvilinear Regression Models
    Choosing Transformations
    Evaluating Consequences of Transformation
    Conditional Effect Plots
    Comparing Effects
    Nonlinear Models
    Estimating Nonlinear Models
    Interpretation
    Conclusion
    Exercises
    Notes

    6 Robust regression

    A Two-Variable Example
    Goals of Robust Estimation
    M-Estimation and Iteratively Reweighted Least Squares
    Calculation by IRLS
    Standard Errors and Tests for M-Estimates
    Using Robust Estimation
    A Robust Multiple Regression
    Bounded-Influence Regression
    Conclusion
    Exercises
    Notes

    7 Logit regression

    Limitations of Linear Regression
    The Logit Regression Model
    Estimation
    Hypothesis Tests and Confidence Intervals
    Interpretation
    Statistical Problems
    Influence Statistics for Logit Regression
    Diagnostic Graphs
    Conclusion
    Exercises
    Notes

    8 Principal Components and Factor Analysis

    Introduction to Components and Factor Analysis
    A Principal Components Analysis
    How Many Components?
    Rotation
    Factor Scores
    Graphical Applications: Detecting Outliers and Clusters
    Principal Factor Analysis
    An Example of Principal Factor Analysis
    Maximum-Likelihood Factor Analysis
    Conclusion
    Exercises
    Notes

    Appendix 1 Population and sampling distributions

    Expected Values
    Covariance
    Variance
    Further Definitions
    Properties of Sampling Distributions
    Ordinary Least Squares
    Some Theoretical Distributions
    Exercises
    Notes

    Appendix 2 Computer-Intensive Methods

    Monte Carlo Simulation
    Bootstrap Methods
    Bootstrap Distributions
    Residual Versus Data Resampling
    Bootstrap Confidence Intervals
    Evaluating Confidence Intervals
    Computer-Intensive Methods in Research
    Exercises
    Notes

    Appendix 3 Matrix Algebra

    Basic Ideas
    Matrix Addition and Multiplication
    Regression in Matrix Form
    An Example
    Regression from Correlation Matrices
    Further Definitions
    Exercises
    Notes

    Appendix 4 Statistical tables

    A4.1: Critical Values for Student's t-Distribution
    A4.2: Critical Values for the F-Distribution
    A4.3: Critical Values for the Chi-Square Distribution
    A4.4: Critical Values for the Durbin–Watson Test for Autocorrelation

    References

    Index

This page was adapted from a page at the Stata Bookstore page.  We thank Stata for their permission to adapt and distribute this page via our web site.  We are very grateful to Professor Lawrence Hamilton for granting us permission to distribute the data files for Regression with Graphics.

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