Mean absolute error (MAE) measures how far predictions are from observed values on average. For a line fitted to points, it is the average of the absolute vertical distances from the points to the line. section 3.4
Averages make errors easier to compare across datasets of different sizes: a sum can grow simply because one dataset contains more points. Mean square error also averages errors, but squares the distances instead. section 3.4
Figure 3.18 The absolute error is the sum of the vertical distances from the points to the line. Note that the absolute error is large for the bad model on the left and small for the good model on the right.
See how absolute vertical distances distinguish a poor-fitting line from a better-fitting one; MAE averages those distances. section 3.4
