Linear Models with R (Chapman & Hall/CRC Texts in Statistical Science)

Faraway, Julian J.

ISBN 10: 1584884258 / ISBN 13: 9781584884255

Editore: Chapman and Hall/CRC, 2004

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Dati bibliografici

• Titolo: Linear Models with R (Chapman & Hall/CRC Texts in Statistical Science)
• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2004
• Lingua: Inglese
• ISBN 10: 1584884258
• ISBN 13: 9781584884255
• Rilegatura: Rilegato
• Condizione: new

Descrizione articolo

Riassunto

Books on regression and the analysis of variance abound―many are introductory, many are theoretical. While most of them do serve a purpose, the fact remains that data analysis cannot be properly learned without actually doing it, and this means using a statistical software package. There are many of these to choose from, all with their particular strengths and weaknesses. Lately, however, one such package has begun to rise above the others thanks to its free availability, its versatility as a programming language, and its interactivity. That software is R.

In the first book that directly uses R to teach data analysis, Linear Models with R focuses on the practice of regression and analysis of variance. It clearly demonstrates the different methods available and, more importantly, in which situations each one applies. It covers all of the standard topics, from the basics of estimation to missing data, factorial designs, and block designs. It also discusses topics, such as model uncertainty, rarely addressed in books of this type. The presentation incorporates numerous examples that clarify both the use of each technique and the conclusions one can draw from the results. All of the data sets used in the book are available for download from http://people.bath.ac.uk/jjf23/LMR/

The author assumes that readers know the essentials of statistical inference and have a basic knowledge of data analysis, linear algebra, and calculus. The treatment reflects his view of statistical theory and his belief that qualitative statistical concepts, while somewhat more difficult to learn, are just as important because they enable us to practice statistics rather than just talk about it.

Contenuti

INTRODUCTION
Before b
Initial Data Analysis
When to Use Regression Analysis
History
ESTIMATION
Linear Model
Matrix Representation
Estimating b
Least b
Examples of Calculating
Gauss-Markov Theorem
Goodness of Fit
Example
Identifiability
INFERENCE
Hypothesis Tests to compare models
Testing Examples
Permutation tests
Confidence Intervals for b
Confidence Intervals for Predictions
Designed Experiments
Observational Data
Practical Difficulties
DIAGNOSTICS
Checking Error Assumptions
Finding Unusual Observations
Checking the Structure of the Model
PROBLEMS WITH THE PREDICTORS
Errors in Predictors
Changes of Scale
Collinearity
PROBLEMS WITH THE ERROR
Generalized Least Squares
Weighted Least Squares
Testing for Lack of Fit
Robust Regression
TRANSFORMATION
Transforming the Response
Transforming the Predictors
VARIABLE SELECTION
Hierarchical Models
Testing-based Procedures
Criterion-based procedures
Summary
SHRINKAGE METHODS
Principal Components
Partial Least Squares
Ridge Regression
STATISTICAL STRATEGY AND MODEL UNCERTAINTY
Strategy
An Experiment in Model Building
Discussion
CHICAGO INSURANCE REDLINING - A COMPLETE EXAMPLE
Ecological Correlation
Initial Data Analysis
Initial model and Diagnostics
Transformation and Variable Selection
Discussion
MISSING DATA
ANALYSIS OF COVARIANCE
A Two-Level Example
Coding Qualitative Predictors
A Multi-Level Factor Example
ONE-WAY ANOVA
The Model
An Example
Diagnostics
Pairwise Comparisons
FACTORIAL DESIGNS
Two-Way Anova
Two-Way Anova with One Observation per Cell
Two-Way Anova with more than One Observation per Cell
Larger Factorial Experiments
BLOCK DESIGNS
Randomized Block design
Latin Squares
Balanced Incomplete Block design
APPENDICES
R installation, Functions and Data
Quick Introduction to R
BIBLIOGRAPHY
INDEX