Book contents
- Frontmatter
- Dedication
- Contents
- Figures
- Preface
- 1 Learning from Data, and Tools for the Task
- 2 Generalizing from Models
- 3 Multiple Linear Regression
- 4 Exploiting the Linear Model Framework
- 5 Generalized Linear Models, and Survival Analysis
- 6 Time Series Models
- 7 Multilevel Models, and Repeated Measures
- 8 Tree-Based Classification and Regression
- 9 Multivariate Data Exploration and Discrimination
- Appendix A The R System: a Brief Overview
- References
- References to R Packages
- Index of R Functions
- Index of Terms
3 - Multiple Linear Regression
Published online by Cambridge University Press: 11 May 2024
- Frontmatter
- Dedication
- Contents
- Figures
- Preface
- 1 Learning from Data, and Tools for the Task
- 2 Generalizing from Models
- 3 Multiple Linear Regression
- 4 Exploiting the Linear Model Framework
- 5 Generalized Linear Models, and Survival Analysis
- 6 Time Series Models
- 7 Multilevel Models, and Repeated Measures
- 8 Tree-Based Classification and Regression
- 9 Multivariate Data Exploration and Discrimination
- Appendix A The R System: a Brief Overview
- References
- References to R Packages
- Index of R Functions
- Index of Terms
Summary
Multiple linear regression generalizes straight line regression to allow multiple explanatory (or predictor) variables, in this chapter under the normal errors assumption. The focus may be on accurate prediction. Or it may, alternatively or additionally, be on the regression coefficients themselves. Simplistic interpretations of coefficients can be grossly misleading. Later chapters elaborate on the ideas and methods developed in this chapter, applying them in new contexts. The attaching of causal interpretations to model coefficients must be justified both by reference to subject area knowledge and by careful checks to ensure that they are not artefacts of the correlation structure. There is attention to regression diagnostics, to assessment, and comparison of models. Variable selection strategies can readily over-fit. Hence the importance of training/test approaches and cross-validation. The potential is demonstrated for errors in x to seriously bias regression coefficients. Strong multicollinearity leads to large variance inflation factors.
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- A Practical Guide to Data Analysis Using RAn Example-Based Approach, pp. 144 - 207Publisher: Cambridge University PressPrint publication year: 2024