Question

A line of best fit is calculated for a dataset with a correlation coefficient of 0.58. Later, a point is removed from the dataset, and the line of best fit is recalculated. The new correlation coefficient is 0.89. Was the point that got removed an outlier of the dataset? Explain your reasoning

Answer 1

Yes — very likely. Correlation r measures the linear association of the whole dataset; a single point that does not follow the prevailing linear pattern can pull the fitted line and reduce |r|. If removing that one point raises r from 0.58 to 0.89, that point had a large influence on the fit and was acting as an outlier (or at least an influential observation).

Brief reasoning:
- A large change in r from deleting one observation means that observation weakened the linear relationship.
- Such observations are either vertical outliers (large residuals) or high‑leverage points (far out in x) that disproportionately affect the slope and correlation.

Caveat / next steps:
- "Outlier" should be confirmed by diagnostic checks (scatterplot, studentized residuals, leverage and Cook’s distance) and by investigating whether the point is a measurement error or legitimately part of a different population. Only then should you decide whether to exclude it from analysis.