What happens when an influential point is removed from a data set regarding the regression line?

When an influential point is removed from a data set, it typically has a significant effect on the regression line. An influential point is defined as a data point that has a considerable impact on the slope and position of the regression line due to its position in the data set.

When such a point is removed, it can lead to changes in the overall data distribution, which often results in a different slope and intercept of the regression line. This is especially true if the influential point lies significantly away from the overall trend of the data or has extreme values for either the independent or dependent variable. The alteration can make the regression line fit the remaining data points better or change the relationship that was previously depicted.

In contrast, other choices do not accurately capture the dynamics at play. For example, stating that the regression line remains unchanged ignores the very definition of an influential point and how critical it is in determining the line’s properties. Additionally, the slope increasing or decreasing is conditional and cannot be guaranteed; it ultimately depends on the data points in question. Lastly, defining the point as a vertical outlier is a limitation, as influential points can be outliers in several forms, not strictly vertical. Thus, the removal of an influential point is indeed likely to alter the