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E-raamat: Linear Models with Python

(University of Bath, United Kingdom)
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Praise for Linear Models with R:

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 Faraway’s wealth of experience in teaching and using 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

Throughout, it gives plenty of insight … 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 chosen…I read it with delight and think that the same will be true with anyone who is engaged in the use or teaching of linear models… -Journal of the Royal Statistical Society

Like its widely praised, best-selling companion version, Linear Models with R, this book replaces R with Python to seamlessly give a coherent exposition of the practice of linear modeling. Linear Models with Python 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 Python.

Features:

  • Python is a powerful, open source programming language increasingly being used in data science, machine learning and computer science. Python and R are similar, but R was designed for statistics while Python is multi-talented.
  • This version replaces R with Python to make it accessible to a greater number of users outside of statistics including those from Machine Learning.
  • A reader coming to this book from an ML background will learn new statistical perspectives on learning from data.
  • Topics include Model Selection, Shrinkage, Experiments with Blocks and Missing Data.
  • Includes an Appendix on Python for beginners.

Linear Models with Python explains how to use linear models in physical science, engineering, social science, and business applications. It is ideal as a textbook for linear models or linear regression courses.

Arvustused

'Multiple Python program scripts and screenshots of the outcomes fill the book, and each chapter suggests numerous exercises for training in coding. The book presents an amazingly valuable source of knowledge on statistical modeling and Python tools for students and practitioners.'

- Stan Lipovetsky, Technometrics, Vol 63, Issue 3 2021

'Therefore, this book is very valuable for understanding paired and multivariate linear regressions.[ ...] The book is clearly structured, containing all the necessary theoretical calculations and theoretical results on which the calculations are based'

- Igor Malyk, International Society for Clinical Biostatistics, 72, 2021

Preface ix
1 Introduction
1(14)
1.1 Before You Start
1(1)
1.2 Initial Data Analysis
2(4)
1.3 When to Use Linear Modeling
6(1)
1.4 History
7(8)
2 Estimation
15(22)
2.1 Linear Model
15(1)
2.2 Matrix Representation
16(1)
2.3 Estimating β
17(1)
2.4 Least Squares Estimation
18(1)
2.5 Examples of Calculating β
19(1)
2.6 Example
19(3)
2.7 Computing Least Squares Estimates
22(2)
2.8 Gauss--Markov Theorem
24(2)
2.9 Goodness of Fit
26(2)
2.10 Identifiability
28(3)
2.11 Orthogonality
31(6)
3 Inference
37(16)
3.1 Hypothesis Tests to Compare Models
37(2)
3.2 Testing Examples
39(5)
3.3 Permutation Tests
44(1)
3.4 Sampling
45(2)
3.5 Confidence Intervals for β
47(1)
3.6 Bootstrap Confidence Intervals
48(5)
4 Prediction
53(8)
4.1 Confidence Intervals for Predictions
53(1)
4.2 Predicting Body Fat
54(2)
4.3 Autoregression
56(2)
4.4 What Can Go Wrong with Predictions?
58(3)
5 Explanation
61(14)
5.1 Simple Meaning
61(2)
5.2 Causality
63(1)
5.3 Designed Experiments
64(1)
5.4 Observational Data
65(2)
5.5 Matching
67(3)
5.6 Covariate Adjustment
70(1)
5.7 Qualitative Support for Causation
71(4)
6 Diagnostics
75(26)
6.1 Checking Error Assumptions
75(10)
6.1.1 Constant Variance
75(5)
6.1.2 Normality
80(3)
6.1.3 Correlated Errors
83(2)
6.2 Finding Unusual Observations
85(8)
6.2.1 Leverage
85(2)
6.2.2 Outliers
87(4)
6.2.3 Influential Observations
91(2)
6.3 Checking the Structure of the Model
93(3)
6.4 Discussion
96(5)
7 Problems with the Predictors
101(14)
7.1 Errors in the Predictors
101(4)
7.2 Changes of Scale
105(3)
7.3 Collinearity
108(7)
8 Problems with the Error
115(20)
8.1 Generalized Least Squares
115(2)
8.2 Weighted Least Squares
117(4)
8.3 Testing for Lack of Fit
121(4)
8.4 Robust Regression
125(10)
8.4.1 M-Estimation
125(3)
8.4.2 High Breakdown Estimators
128(7)
9 Transformation
135(20)
9.1 Transforming the Response
135(5)
9.2 Transforming the Predictors
140(1)
9.3 Broken Stick Regression
140(2)
9.4 Polynomials
142(6)
9.5 Splines
148(2)
9.6 Additive Models
150(2)
9.7 More Complex Models
152(3)
10 Model Selection
155(18)
10.1 Hierarchical Models
156(1)
10.2 Hypothesis Testing-Based Procedures
156(4)
10.3 Criterion-Based Procedures
160(3)
10.4 Sample Splitting
163(4)
10.5 Crossvalidation
167(2)
10.6 Summary
169(4)
11 Shrinkage Methods
173(24)
11.1 Principal Components
173(11)
11.2 Partial Least Squares
184(3)
11.3 Ridge Regression
187(4)
11.4 Lasso
191(3)
11.5 Other Methods
194(3)
12 Insurance Redlining --- A Complete Example
197(14)
12.1 Ecological Correlation
197(2)
12.2 Initial Data Analysis
199(3)
12.3 Full Model and Diagnostics
202(2)
12.4 Sensitivity Analysis
204(3)
12.5 Discussion
207(4)
13 Missing Data
211(10)
13.1 Types of Missing Data
211(1)
13.2 Representation and Detection of Missing Values
212(1)
13.3 Deletion
213(2)
13.4 Single Imputation
215(2)
13.5 Multiple Imputation
217(2)
13.6 Discussion
219(2)
14 Categorical Predictors
221(20)
14.1 A Two-Level Factor
221(4)
14.2 Factors and Quantitative Predictors
225(3)
14.3 Interpretation with Interaction Terms
228(2)
14.4 Factors with More Than Two Levels
230(5)
14.5 Alternative Codings of Qualitative Predictors
235(6)
15 One-Factor Models
241(12)
15.1 The Model
241(1)
15.2 An Example
242(3)
15.3 Diagnostics
245(1)
15.4 Pairwise Comparisons
246(2)
15.5 False Discovery Rate
248(5)
16 Models with Several Factors
253(20)
16.1 Two Factors with No Replication
253(4)
16.2 Two Factors with Replication
257(5)
16.3 Two Factors with an Interaction
262(4)
16.4 Larger Factorial Experiments
266(7)
17 Experiments with Blocks
273(16)
17.1 Randomized Block Design
274(4)
17.2 Latin Squares
278(4)
17.3 Balanced Incomplete Block Design
282(7)
A About Python 289(2)
Bibliography 291(4)
Index 295
Julian J. Faraway is a professor of statistics in the Department of Mathematical Sciences at the University of Bath. His research focuses on the analysis of functional and shape data with particular application to the modeling of human motion. He earned a PhD in statistics from the University of California, Berkeley.