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El. knyga: Linear Models with R

4.10/5 (100 ratings by Goodreads)
(University of Bath, UK)
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Linear models describe a quantitative response in terms of linear combinations of predictors, and R--open-source, powerful, and de facto standard language for statistical computation--provides many tools to utilize them. In this second edition of the standard text on the applications of linear models in R, much of the material has been reorganized. New material includes elementary causality, splines, additive models, and false discovery rates, among other things. The discussion is not introductory, but suitable to those with some knowledge of programming in R and at least one or two classes in introductory statistics. It is a stated goal of the author to integrate three languages--English, Mathematics, and R--seamlessly, and he largely succeeds. The discussion emphasizes intuition over rigorous proof, but does not lack in fundamental rigor. Much of the discussion concerns the issues of problem setup and formulation. A website with datasets and errata accompanies the text, and R packages containing data under discussion are available from standard CRAN sites. Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)

A Hands-On Way to Learning Data Analysis

Part of the core of statistics, linear models are used to make predictions and explain the relationship between the response and the predictors. Understanding linear models is crucial to a broader competence in the practice of statistics. Linear Models with R, Second Edition explains how to use linear models in physical science, engineering, social science, and business applications. The book incorporates several improvements that reflect how the world of R has greatly expanded since the publication of the first edition.

New to the Second Edition

  • Reorganized material on interpreting linear models, which distinguishes the main applications of prediction and explanation and introduces elementary notions of causality
  • Additional topics, including QR decomposition, splines, additive models, Lasso, multiple imputation, and false discovery rates
  • Extensive use of the ggplot2 graphics package in addition to base graphics

Like its widely praised, best-selling predecessor, this edition combines statistics and R to seamlessly give a coherent exposition of the practice of linear modeling. The text offers up-to-date insight on essential data analysis topics, from estimation, inference, and prediction to missing data, factorial models, and block designs. Numerous examples illustrate how to apply the different methods using R.

Recenzijos

"After 10 years, a new edition of Faraways excellent Linear Models with R is now available.. . There are several major changes in this edition. The material on interpreting linear models has been reorganized to emphasize the distinction between prediction and explanation; this was done with the addition of two new chapters . . . Several other chapters benefit from the addition of new material. . . Finally, most chapters conclude with more exercises than in the previous edition." The American Statistician, 2016

"This book is a must-have tool for anyone interested in understanding and applying linear models. The logical ordering of the chapters is well thought out and portrays Faraways wealth of experience in teaching and using linear models. The reorganization of the material in this second edition presents linear models with R in a coherent and easy-to-follow way. In summary, this book provides an excellent basis for understanding and applying linear models. It lays down the material in a logical and intricate manner and makes linear modeling appealing to researchers from virtually all fields of study." Biometrical Journal, 2015

"The book provides an excellent introduction of the various aspects of linear models with many interesting examples. The explanations are clear enough for beginners with little statistical background and are accompanied by worked examples with associated R code. This is an important contribution since it provides readers/students an opportunity to replicate the analyses and results of an example. There are many books written on the topic of linear models, but this book takes an applied approach and explains the concepts intuitively using graphical explanations and examples. Overall, this is a nicely written book, which can lay a strong foundation for senior undergraduate and beginning graduate students. This book can be recommended as a textbook for computational linear regression courses. It will also be useful for practitioners who want to get started on applying regression models for studying associations among different variables, estimation of regression coefficients, and prediction. It offers insightful interpretations and discussions with examples worked using the R software." MAA Reviews, January 2015

Praise for the First Edition:"One danger with applied books such as this is that they become recipe lists of the kind 'press this key to get that result.' This is not so with Faraway's book. Throughout, it gives plenty of insight on what is going on, with comments that even the seasoned practitioner will appreciate. Interspersed with R code and the output that it produces one can find many little gems of what I think is sound statistical advice, well epitomized with the examples chosenI read it with delight and think that the same will be true with anyone who is engaged in the use or teaching of linear modelsI find this book a valuable buy for anyone who is involved with R and linear models, and it is essential in any university library where those topics are taught." -Journal of the Royal Statistical Society "Linear Models with R is well written and, given the increasing popularity of R, it is an important contribution." -Technometrics, Vol. 47, No. 3, August 2005

"There are many books on regression and analysis of variance on the market, but this one is unique and has a novel approach to these statistical methods. The author uses R throughout the text to teach data analysisThe text also contains a wealth of references for the reader to pursue on related issues. This book is recommended for all who wish to use R for statistical investigations." -Short Book Reviews of the International Statistical Institute "The book is very comprehensibly written and can therefore be recommended for beginners in linear models. It is clearly and simply explained how to use R and which packages are necessary to analyze linear models. All in all, this book is recommendable as a textbook for computational linear regression courses and therefore for students and lecturers, but also for applied statisticians who want to get started on regression analysis using the software R." -Biometrics "Dr. Faraway uses many examples and graphical procedures to illustrate the methods. This is a great strength of the book. Linear Models with R is one of several books appearing to make R more accessible by bringing together functions from a number of packages and illustrating their use. From this perspective alone it is an important contribution. I feel this book does a nice job of describing the methods available in linear modeling and illustrating the realistic implementation of these methods in a careful data analysis. " -Statistics in Medicine, 2006

Preface xi
1 Introduction
1(12)
1.1 Before You Start
1(1)
1.2 Initial Data Analysis
2(5)
1.3 When to Use Linear Modeling
7(1)
1.4 History
8(5)
2 Estimation
13(20)
2.1 Linear Model
13(1)
2.2 Matrix Representation
14(1)
2.3 Estimating β
15(1)
2.4 Least Squares Estimation
16(1)
2.5 Examples of Calculating β
17(1)
2.6 Example
17(3)
2.7 QR Decomposition
20(2)
2.8 Gauss--Markov Theorem
22(1)
2.9 Goodness of Fit
23(3)
2.10 Identifiability
26(2)
2.11 Orthogonality
28(5)
3 Inference
33(18)
3.1 Hypothesis Tests to Compare Models
33(2)
3.2 Testing Examples
35(5)
3.3 Permutation Tests
40(2)
3.4 Sampling
42(1)
3.5 Confidence Intervals for β
43(3)
3.6 Bootstrap Confidence Intervals
46(5)
4 Prediction
51(8)
4.1 Confidence Intervals for Predictions
51(1)
4.2 Predicting Body Fat
52(2)
4.3 Autoregression
54(2)
4.4 What Can Go Wrong with Predictions?
56(3)
5 Explanation
59(14)
5.1 Simple Meaning
59(2)
5.2 Causality
61(1)
5.3 Designed Experiments
62(1)
5.4 Observational Data
63(2)
5.5 Matching
65(3)
5.6 Covariate Adjustment
68(1)
5.7 Qualitative Support for Causation
69(4)
6 Diagnostics
73(26)
6.1 Checking Error Assumptions
73(10)
6.1.1 Constant Variance
73(5)
6.1.2 Normality
78(3)
6.1.3 Correlated Errors
81(2)
6.2 Finding Unusual Observations
83(9)
6.2.1 Leverage
83(2)
6.2.2 Outliers
85(4)
6.2.3 Influential Observations
89(3)
6.3 Checking the Structure of the Model
92(4)
6.4 Discussion
96(3)
7 Problems with the Predictors
99(14)
7.1 Errors in the Predictors
99(4)
7.2 Changes of Scale
103(3)
7.3 Collinearity
106(7)
8 Problems with the Error
113(20)
8.1 Generalized Least Squares
113(3)
8.2 Weighted Least Squares
116(3)
8.3 Testing for Lack of Fit
119(4)
8.4 Robust Regression
123(10)
8.4.1 M-Estimation
123(3)
8.4.2 Least Trimmed Squares
126(7)
9 Transformation
133(16)
9.1 Transforming the Response
133(4)
9.2 Transforming the Predictors
137(1)
9.3 Broken Stick Regression
137(2)
9.4 Polynomials
139(2)
9.5 Splines
141(3)
9.6 Additive Models
144(1)
9.7 More Complex Models
145(4)
10 Model Selection
149(12)
10.1 Hierarchical Models
150(1)
10.2 Testing-Based Procedures
151(2)
10.3 Criterion-Based Procedures
153(6)
10.4 Summary
159(2)
11 Shrinkage Methods
161(22)
11.1 Principal Components
161(11)
11.2 Partial Least Squares
172(2)
11.3 Ridge Regression
174(3)
11.4 Lasso
177(6)
12 Insurance Redlining --- A Complete Example
183(14)
12.1 Ecological Correlation
183(2)
12.2 Initial Data Analysis
185(3)
12.3 Full Model and Diagnostics
188(2)
12.4 Sensitivity Analysis
190(4)
12.5 Discussion
194(3)
13 Missing Data
197(8)
13.1 Types of Missing Data
197(1)
13.2 Deletion
198(2)
13.3 Single Imputation
200(2)
13.4 Multiple Imputation
202(3)
14 Categorical Predictors
205(18)
14.1 A Two-Level Factor
205(4)
14.2 Factors and Quantitative Predictors
209(3)
14.3 Interpretation with Interaction Terms
212(1)
14.4 Factors With More Than Two Levels
213(6)
14.5 Alternative Codings of Qualitative Predictors
219(4)
15 One Factor Models
223(12)
15.1 The Model
223(1)
15.2 An Example
224(3)
15.3 Diagnostics
227(1)
15.4 Pairwise Comparisons
228(2)
15.5 False Discovery Rate
230(5)
16 Models with Several Factors
235(16)
16.1 Two Factors with No Replication
235(4)
16.2 Two Factors with Replication
239(4)
16.3 Two Factors with an Interaction
243(3)
16.4 Larger Factorial Experiments
246(5)
17 Experiments with Blocks
251(14)
17.1 Randomized Block Design
252(4)
17.2 Latin Squares
256(3)
17.3 Balanced Incomplete Block Design
259(6)
A About R 265(2)
Bibliography 267(4)
Index 271
Julian J. Faraway