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02 Regression and Statistical Testing
This is a very important content-heavy block, in which the lectures are longer than usual, and the workshop is shorter to make up for it.
In Block 02, we cover:
- Classical Regression:
- How to implement regression in practice
- How to interpret regression outputs
- Standard and Logistic regression
- Modern Regression:
- Matrix formulation of multivariate regression.
- Elements of multivariate calculus
- Statistical Testing:
- Classical statistical testing
- Resampling approaches to statistical testing
- Model evaluation using Cross Validation
- Implementations in R:
- Regression for time series
- Regression for feature matrices
Lectures:
Regression:
Statistical Testing and Model Selection:
Preparation:
If you have not completed the Block 1 Preparation, please do so.
Workshop:
Assessments:
- The full Portfolio will be set in this week; see Assessments. This is a summative assessment (i.e. does contribute to your grade) and will be due in Week 12, but contains material to work on each week.
- Portfolio 02 of the full Portfolio.
- Block02 on Noteable via Blackboard
Reference material:
For Regression:
- Cosma Shalizi’s Modern Regression Lectures (Lectures 4-9 for basic material; Lectures 13-14 for Linear Algebra approach)
- Matrix Multiplication Cheat Sheet
- A complete reference is The Matrix Cookbook
- Sam Roweis’ Matrix Identities
- Cosma Shalizi’s Modern Regression Lectures
- Further reading in chapters 2.3 and 3.2 of The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Friedman, Hastie and Tibshirani)
For Statistical testing:
- Cosma Shalizi’s Modern Regression Lectures (Lecture 21)
- Chapter 4 of Statistical Data Analysis by Glen Cowan
- Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations by Greenland et al.
For Model Comparison:
- Cosma Shalizi’s Modern Regression Lectures (Lectures 26,28)
- Further reading in Chapters 2.3 and 7.10 of The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Friedman, Hastie and Tibshirani).