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