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- Kuchibhotla, Brown, Buja, [Model-free study of ordinary least squares linear regression](https://arxiv.org/pdf/1809.10538.pdf)

Jan 19
: **Lecture**{: .label .label-green } Inference in linear models
: [[PPTX]](https://github.com/stanford-msande228/winter23/raw/main/MSANDE228_Lecture3_Inference_in_Linear_Models.pptx)
: [[PDF]](https://github.com/stanford-msande228/winter23/raw/main/MSANDE228_Lecture3_Inference_in_Linear_Models.pdf)
: [[Demo Code]](https://github.com/stanford-msande228/winter23/blob/main/Lecture2-Demo.ipynb)
: Basics of statistical inference in linear models; confidence intervals for p « n; interpretation of coefficient as partialling out; inference on ATE from trials via regression; Revisiting the role of covariates in randomized trials: precision and heterogeneity: variance characterization and comparisons
: **Lecture**{: .label .label-green } Prediction in high dimensional linear models
: [[PPTX]](https://github.com/stanford-msande228/winter23/raw/main/MSANDE228_Lecture4_Inference_in_High_Dimensional_Linear_Models.pptx)
: [[PDF]](https://github.com/stanford-msande228/winter23/raw/main/MSANDE228_Lecture4_Inference_in_High_Dimensional_Linear_Models.pdf)
: [[Demo Code]](https://github.com/stanford-msande228/winter23/blob/main/Lecture3-Demo.ipynb)
: High dimensional methods and prediction; regularization; lasso; elasticnet;
: ***Reading Materials***
- Chapter 1 of [Textbook](https://canvas.stanford.edu/courses/168439/files/folder/Readings)
- Chapter 3 of [Textbook](https://canvas.stanford.edu/courses/168439/files/folder/Readings)
: ***Coding Materials***
- [Predicting Wages](https://github.com/CausalAIBook/MetricsMLNotebooks/blob/main/PM1/PM1_prediction.ipynb)
- [Predictive Inference on Wage Gap](https://github.com/CausalAIBook/MetricsMLNotebooks/blob/main/PM1/inference.ipynb)
: ***Further Reading***
- Lovell, [A Simple Proof of the FWL Theorem](https://www.jstor.org/stable/41426805)
- Cattaneo, Jansson, Newey, [Inference in Linear Regression Models with Many Covariates and Heteroscedasticity](https://www.tandfonline.com/doi/full/10.1080/01621459.2017.1328360)
- Kuchibhotla, Brown, Buja, [Model-free study of ordinary least squares linear regression](https://arxiv.org/pdf/1809.10538.pdf)

- [Penalized Linear Regressions: Simulated Data](https://github.com/CausalAIBook/MetricsMLNotebooks/blob/main/PM2/linear-penalized-regs.ipynb)
- [Predicting Wages with Penalized Regressions](https://github.com/CausalAIBook/MetricsMLNotebooks/blob/main/PM2/ml-for-wage-prediction.ipynb)

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