In AP Statistics, an influential point is any data point that, if removed from the dataset, substantially changes the regression relationship, such as the slope, y-intercept, or correlation of the least-squares regression line (LSRL). Outliers and high-leverage points are often influential.
An influential point is defined by what happens when you take it away. If removing one point substantially changes the regression relationship (a much different slope, y-intercept, and/or correlation), that point is influential. That's the exact definition in the AP Stats CED (2.9.A), and the "remove it and see what changes" framing is how the exam wants you to think about it.
The trick is that influence usually comes from one of two sources. A point with an extreme x-value (a high-leverage point) acts like a hand on the far end of a seesaw, so even a small pull there can swing the whole LSRL. A point with a large residual (an outlier) sits far from the trend the rest of the data follows. The CED is careful here. Outliers and high-leverage points are often influential, but neither label automatically means influential. The only way to confirm influence is to compare the regression with and without the point.
Influential points live in Topic 2.9, Analyzing Departures from Linearity, in Unit 2 (Exploring Two-Variable Data). Learning objective 2.9.A asks you to identify influential points in regression, and the essential knowledge spells out the three-term family you need to keep straight: outlier (large residual), high-leverage point (extreme x-value), and influential point (removal changes the relationship). This matters because the LSRL minimizes squared residuals, so a single weird point can drag the line toward itself and wreck your slope, your r, and every prediction you make. Spotting influential points is part of the bigger Unit 2 skill of judging whether a linear model is actually appropriate, which also connects to residual plots and transformations (2.9.B).
Keep studying AP Statistics Unit 2
Outlier (Unit 2)
An outlier in regression has a large residual because it doesn't follow the trend of the rest of the data. Outliers are often influential, but not always. An outlier near the middle of the x-values may barely move the line at all.
Leverage (Unit 2)
A high-leverage point has an x-value much larger or smaller than the rest of the data. Think of the LSRL as a seesaw balanced at the mean of x. A point far out on the end has a long lever arm, so it can tilt the entire line, which is why high-leverage points are prime suspects for influence.
Residual (Unit 2)
Residuals are how you measure 'doesn't follow the trend.' A point can have a small residual and still be influential, because a high-leverage point can pull the line toward itself so hard that its own residual ends up tiny. That's a classic MCQ trap.
y-intercept (Unit 2)
Influence isn't only about slope. The CED explicitly says removal can produce a much different y-intercept too. When the slope pivots, the intercept usually shifts with it, so check both when you compare the with-and-without regressions.
This shows up almost entirely as multiple-choice and regression-analysis FRQ reasoning. MCQs typically describe a point's characteristics (extreme x-value, large or small residual) and ask which combination makes it most influential. The strongest answer usually pairs high leverage with a large residual, because that point both sits at the end of the seesaw and pulls away from the trend. You should also be ready for 'what happens if this point is removed' questions, where you predict how the slope, correlation, or intercept would change. Some practice questions reference Cook's distance (values above about 1 flag a highly influential point), which is a diagnostic worth recognizing, but the AP exam itself grades you on the removal logic, not the formula. No released FRQ uses 'influential point' verbatim, but FRQs about regression appropriateness reward you for noticing a single point that distorts the LSRL.
These overlap but are not the same. An outlier is defined by its residual (it doesn't follow the trend), while an influential point is defined by its effect (removing it substantially changes the slope, intercept, or correlation). An outlier in the middle of the x-range may not be influential, and a high-leverage point that follows the trend perfectly is influential on r but might have almost no residual. To check influence, you have to actually compare the regression with and without the point.
An influential point is any point that, if removed, substantially changes the regression relationship, such as the slope, y-intercept, or correlation.
An outlier has a large residual, a high-leverage point has an extreme x-value, and either one is often (but not automatically) influential.
The most influential points usually combine high leverage with a large residual, like a heavy hand at the far end of a seesaw.
A high-leverage point can have a small residual precisely because it dragged the LSRL toward itself, so a small residual does not rule out influence.
The only way to confirm a point is influential is to run the regression with and without it and compare the slope, intercept, and r.
It's a data point that, if removed, substantially changes the regression results, like the slope, y-intercept, or correlation of the LSRL. This definition comes straight from learning objective 2.9.A in Unit 2.
No. An outlier has a large residual, but if it sits near the middle of the x-values, removing it may barely change the slope. The CED says outliers and high-leverage points are often influential, not always.
A high-leverage point is defined by its position (an x-value much larger or smaller than the rest), while an influential point is defined by its effect (removal substantially changes the relationship). High leverage is a warning sign for influence, not proof of it.
Calculate the LSRL with the point and without it, then compare the slope, y-intercept, and correlation. If they change substantially, the point is influential. Some software reports Cook's distance, where values above about 1 flag strong influence.
It's not required by the CED, but it's useful to recognize. The exam tests the underlying idea, which is comparing the regression with and without a point, and that's the reasoning you should show.