Deviation vs Residual

A deviation describes a single observation rather than the whole data set, and you write it as $x_i - \bar{x}$, where $\bar{x}$ (x-bar) is the mean. A positive deviation puts the value above the mean and a negative deviation puts it below. In the data 2, 4, 6, 8 the mean is 5, so the four deviations are -3, -1, 1, and 3. They add to zero, which is true for every data set and is exactly why the variance squares the deviations before adding them up.

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.