Influential Point vs Outlier

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.

An outlier is a point that stands apart from the overall pattern of the data. A common rule flags a value as an outlier when it falls below $Q_1 - 1.5 \times \text{IQR}$ or above $Q_3 + 1.5 \times \text{IQR}$, using the first quartile $Q_1$, the third quartile $Q_3$, and the interquartile range. For example, with $Q_1 = 3$, $Q_3 = 9$, and IQR $= 6$, any value below $3 - 9 = -6$ or above $9 + 9 = 18$ is an outlier. Outliers can be genuine extreme cases or data-entry errors, so you investigate before removing them.