Week 7 - Hypothesis Tests with Multiple Regressions
Overview
And now, we’re back to hypothesis testing. The big thing we’re going to learn about is testing more complicated hypotheses, like whether two coefficients are equal, and whether a whole bunch of coefficients equal zero.
Reading Guide
Chapter 7: Hypothesis Tests and Confidence Intervals with Multiple Regressions
SW 7.1 Hypothesis Tests and Confidence Intervals for a Single Coefficient
Here, we want to test hypothesis of this form: \(H_0: \beta_j = \beta_{j,0}\) vs. \(H_a: \beta_j \neq \beta_{j,0}\)
If you want another take on hypothesis testing with regression coefficients, go ahead and read this. I’m not going to cover this in class, because we’ve hit this in Chapter 5.
SW 7.2 Tests of Joint Hypotheses
Here, we test hypothesis with lots of coefficients, of this form: \(H_0: \beta_j = \beta_{j,0}, \beta_m = \beta_{m,0}, ...\), for \(q\) restrictions, vs \(H_a\): any one of those \(q\) restrictions does not hold.
SW 7.3 Testing Single Restrictions Involving Multiple Coefficients
Here, we test one restriction, but with multiple coefficients, like this: \(H_0: \beta_j = \beta_m\) vs. \(H_a: \beta_j \neq \beta_m\)
That’s it!
7.5 is a good review of things we’ve already discussed, and 7.6 walk us through an example. I encourage you to read them, but not mandatory. And we’re skipping 7.4
