Week 7 - Hypothesis Tests with Multiple Regressions

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. $H_a:{\beta }_j\ne {\beta }_{j,0}$

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. $H_a:{\beta }_j\ne {\beta }_m$

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

Video: Hypothesis Tests with Multiple Linear Regression

Class Video