APEX AP Stats 3.4.1 Influential Points and Outliers Study Guide

What are outliers in a dataset?

Points that are a sizeable distance from other points or have unusual y-values, which may or may not change the direction of the line of best fit.

How are outliers distinguished?

By the size of their residuals and their distance from the other data points in the y-direction.

What defines an influential point?

Points with unusual x-values that greatly affect the slope or direction of the regression line if removed.

Can an influential point also be an outlier?

Yes, an influential point may or may not be part of the linear pattern and can also be classified as an outlier.

What effect do influential points have on the regression line?

They have a dramatic effect on the residual correlation and can significantly influence the slope of the line.

What happens to the regression line when an influential point is removed?

The removal can make the new line appear completely unrelated to the original line, especially if the influential point is also an outlier.

How do outliers affect the regression line?

Outliers affect the regression line, but not as dramatically as influential points.

What is the relationship between the correlation coefficient and influential points?

The correlation coefficient (r) and the slope of the regression line (b1) are linearly related and are affected by outliers and influential points.

What is the effect of removing an influential point on the linear relationship?

It can either strengthen or weaken the linear relationship, depending on the influential point's position relative to other points.

What is the impact of removing an outlier on correlation?

Removal of an outlier will almost always strengthen the correlation.

Why is it important to interpret influential points and outliers?

They can cause the least-squares regression line to not accurately represent the sample or population.

What should be examined when encountering an outlier or influential point?

Consider why they are present, whether there was an error, if it's a random occurrence, and if they can be ignored in analysis.

What is the definition of residual in the context of regression?

The difference between the observed value and the predicted value from the regression line.

What does it mean if a point is farther to the right in a dataset?

It typically indicates more influence on the regression line if it is an influential point.

What is the primary distinction between an outlier and an influential point?

An outlier is primarily defined by its unusual y-value, while an influential point is defined by its potential to significantly affect the regression line's slope.

What is the significance of examining outliers and influential points?

They help ensure that the regression analysis accurately reflects the underlying data trends.