13.5 Hypothesis testing in OLS

author strongly dislikes it, since choice of rejection value is arbitrary and sharp

1. Pick a theoretical distribution
2. Estimate $\beta_1$ using OLS in observed data: $\hat{\beta_1}$
3. Use that theoretical distribution to see how unlikely it would be to get $\hat{\beta_1}$
4. If it’s super unlikely, that initial value is probably wrong

Alternative: hpyothesis testing

1. Pick null hypothesis (typically $\beta_1 = 0$)
2. Pick rejection value $\alpha$
3. Check probability against rejection value
4. Possibly reject null: we think it’s unlikely that the value is 0.

• Type I error rate (“false positive rate”): rejection of something that’s true

• Type II error rate (“false negative rate”): not rejecting something that’s false

• p-value: double percentile (2-sided test)

• t-statistic: $\frac{\hat{\beta_1}}{se(\hat{\beta_1})}$ to use with standard normal distribution