Week 6 - Multiple Linear Regression

Overview

Let’s model!

Now, we can build powerful models with heaps of dependent variables. Want to predict wages? Let’s control for education, for experience, for gender, for age, for age squared (yes!). YES. Only our degrees of freedom can hold us back.

Reading Guide

Chapter 6: Linear Regression with Multiple Regressors

SW 6.1 Omitted Variable Bias

A discussion that connects nicely with our previous discussion of the zero conditional mean discussion and causal inference.

SW 6.2 The Multiple Regression Model

Hooray!

SW 6.3 The OLS Estimator in Multiple Regression

This section doesn’t get into derivation, and neither do we!

SW 6.4 Measures of Fit in Multiple Regression

The only new thing here is a revised $SER$ forumla and the introduction of the Adjusted $R^2$. Note that the lecture video also discusses the root mean standard error, $RMSE$, which is a lot like the $SER$ except that it uses $n$ rather than degrees of freedom as a denominator.

SW 6.5 The Least Squares Assumptions in Multiple Regression

Take the three from univariate regression and add … no multicollinearity. Sorted.

SW 6.6 Distribution of the OLS Estimators in Multiple Regression

Just the intuition, don’t worry about the appendix.

SW 6.7 Multicollinearity

Make sure you understand the examples, but remember that in practice, any statistical package will fix perfect multicollinearity on its own. Imperfect multicollinearity, on the other hand, is something to think about when crafting your models.

SW 6.8 Conclusion

Treat yourself.

Slides

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Other resources

As requested, slower graphs! Also added a graph on collider bias, the webpage explanation helps there.

These graphs are intended to show what standard causal inference methods actually *do* to data, and how they work.

This is what controlling for a binary variable looks like: pic.twitter.com/dTZxqY5JxA

— Nick HK (@nickchk) November 29, 2018