Book contents
- Frontmatter
- Contents
- Preface
- Notation Used
- Abbreviations
- 1 Introduction
- 2 Basics
- 3 Probability Distributions
- 4 Statistical Inference
- 5 Linear Regression
- 6 Neural Networks
- 7 Non-linear Optimization
- 8 Learning and Generalization
- 9 Principal Components and Canonical Correlation
- 10 Unsupervised Learning
- 11 Time Series
- 12 Classification
- 13 Kernel Methods
- 14 Decision Trees, Random Forests and Boosting
- 15 Deep Learning
- 16 Forecast Verification and Post-processing
- 17 Merging of Machine Learning and Physics
- Appendices
- References
- Index
5 - Linear Regression
Published online by Cambridge University Press: 23 March 2023
Book contents
- Frontmatter
- Contents
- Preface
- Notation Used
- Abbreviations
- 1 Introduction
- 2 Basics
- 3 Probability Distributions
- 4 Statistical Inference
- 5 Linear Regression
- 6 Neural Networks
- 7 Non-linear Optimization
- 8 Learning and Generalization
- 9 Principal Components and Canonical Correlation
- 10 Unsupervised Learning
- 11 Time Series
- 12 Classification
- 13 Kernel Methods
- 14 Decision Trees, Random Forests and Boosting
- 15 Deep Learning
- 16 Forecast Verification and Post-processing
- 17 Merging of Machine Learning and Physics
- Appendices
- References
- Index
Summary
Simple linear regression is extended to multiple linear regression (for multiple predictor variables) and to multivariate linear regression for (multiple response variables). Regression with circular data and/or categorical data is covered. How to select predictors and how to avoid overfitting with techniques such as ridge regression and lasso are followed by quantile regression. The assumption of Gaussian noise or residual is removed in generalized least squares, with applications to optimal fingerprinting in climate change.
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- Introduction to Environmental Data Science , pp. 137 - 172Publisher: Cambridge University PressPrint publication year: 2023
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