Residual vs Outlier

A residual measures how far off the line is for a single point, so a positive residual sits above the line and a negative one below. It equals $\text{residual} = y - \hat{y}$, the observed response minus the predicted response $\hat{y}$ (read y-hat). For example, if the line predicts 72 but a student actually scored 80, the residual is $80 - 72 = 8$. Least-squares regression chooses the line that makes the sum of the squared residuals as small as possible.

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.