High-leverage point

A high-leverage point has an x-value far from the mean of x, which gives it unusual pull on the slope and intercept of the regression line.

Leverage is about the x-direction only: the further a point sits from xˉ\bar{x} (read x-bar, the mean of the explanatory variable), the more the line pivots to accommodate it. For the x-values 2, 3, 4, 5, and 20, the mean is 34/5=6.834/5 = 6.8, so the point at x=20x = 20 sits 13.2 units from the center while no other point is more than 4.8 units away. Keep three labels apart: an outlier in regression has a large residual, a high-leverage point has an extreme xx, and an influential point is one whose removal visibly changes the fit. A high-leverage point that happens to follow the pattern has a small residual and shifts the line very little, which is why leverage on its own is not a verdict.

Where this comes up

More regression and correlation terms, or browse the full statistics glossary.