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Regression with Graphics: A Second Course in Applied Statistics

Author:
Lawrence C. Hamilton
Publisher: Brooks/Cole
Copyright: 1992
ISBN-13: 978-0-534-15900-9
Pages: 363; hardcover
Price: $198.00
Supplements:descriptions and datasets
examples

Comment from the Stata technical group

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 to 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.


Table of 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
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