Extrapolation 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.
Extrapolation
Regression and correlation
Extrapolation is using a regression line to predict outside the range of x-values the data covered, where the pattern may no longer hold.
Extrapolation stretches a fitted line beyond the interval of explanatory values you actually observed, where there is no evidence the linear trend continues. Predictions there can be badly wrong because the relationship may bend, flatten, or reverse. For example, a line fit to children's ages 5 to 12 might predict a 40-year-old is 12 feet tall. Keep predictions within the observed range of the explanatory variable to stay on safe ground.
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.