Worksheet #4 FWL

We will keep using the data shown in that example and can be found here: https://github.com/dstellotri/rmda

Before we were trying to under how to obtain beta from this model:

Now, we want to understand how $\beta_1$ changes once we add a covariate. In this case the full model will be:

Let’s go through several methods. Each of this inspire different ways of understanding what a covariate is really doing. What I recommend is going through this and trying to understand from your own perspective the intuition of what “controlling for a variable” is doing.

Regression

• First run the regression using the data and report what the value of $\beta_1$ is.
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Answer

Mean Comparison

• How would we obtain the value if we were to use averages?
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Answer

Using the formula

• Now obtain the value of beta 1 using the following Formula $\beta_1=\frac{Cov(Batten,Income)}{Var(Batten)}$
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Answer

FWL Way

• Here is another method (similar to the one before) in which it shows how obtain the same beta and provides similar intuition. It’s called using the Frisch–Waugh–Lovell theorem.