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​​Syllabus

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​​Module 1. Classical Linear Regression 

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• ​​Ordinary Least Squares (OLS)

• ​​Estimation

• ​​BLUE, Gauss-Markov Theorem

• ​​Confidence

• ​​Confidence Interval for a single Linear Parametric Function (LPF)

• ​​Confidence Regions for multiple LPFs

• ​​Simultaneous Confidence Intervals for multiple LPFs

• ​​Prediction Interval

• ​​Hypothesis Testing

• ​​Testing for the significance of a single LPF

• ​​Testing for the significance of individual predictors: t-test

• ​​ANOVA Table and testing hypothesis involving several LPFs

• ​​Testing for the significance of the entire model/testing for lack of fit: F-test

• ​​Categorical Predictors, Interaction models

• ​​Least Squares in Heteroskedastic Models

• ​​Generalized Least Squares

• ​​Weighted Least Squares

• ​​Residual Diagnostics

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​​Additional Readings:

• ​​Read chapter 12 of PRA by J. Faraway for a complete linear regression example 

• ​​tidyverse from ModernDive for reducing unstructured data to a regression framework. 

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​​Module 2. Beyond Least Squares

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• ​​Non-Linear Regression

• ​​Transforming the Response: Box-Cox method

• ​​Transforming the Predictors

• ​​Polynomial Regression

• ​​Regression Splines*

• ​​Local Regression

• ​​Generalized Additive Models (GAM)

• ​​Bootstrapping methods

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• ​​Additional Readings: 

• ​​Ch 6 slides from ISLR for more information on the above methods 

• ​​Ch 5 slides from ISLR for cross validation and bootstrap

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• ​​Robust Regression

• ​​Quantile Regression

• ​​M-Estimation

• ​​Huber loss, Robustness and rlm R package

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