High-Leverage Point vs Outlier

Leverage is about the x-direction only: the further a point sits from $\bar{x}$ (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 $34/5 = 6.8$, so the point at $x = 20$ 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 $x$, 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.

An outlier is a point that stands apart from the overall pattern of the data. A common rule flags a value as an outlier when it falls below $Q_1 - 1.5 \times \text{IQR}$ or above $Q_3 + 1.5 \times \text{IQR}$, using the first quartile $Q_1$, the third quartile $Q_3$, and the interquartile range. For example, with $Q_1 = 3$, $Q_3 = 9$, and IQR $= 6$, any value below $3 - 9 = -6$ or above $9 + 9 = 18$ is an outlier. Outliers can be genuine extreme cases or data-entry errors, so you investigate before removing them.