High-Leverage Point vs Influential Point
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
High-leverage point
Regression and correlation
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 (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 , so the point at 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 , 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.
Influential point
Regression and correlation
An influential point is an observation that, if removed, would markedly change the regression line's slope, intercept, or correlation.
An influential point pulls the least-squares line noticeably toward itself, so dropping it shifts the fit by a lot. Points with extreme x-values, called high-leverage points, tend to be the most influential, often more than a point that is simply a vertical outlier. For example, one house priced far above the rest at a large size can tilt the whole price-versus-size line. You check for influential points by refitting the line without the suspect point and comparing the slope and correlation.