Raymond B. answered • 06/26/19
Math, microeconomics or criminal justice
The regression line minimizes the distances between actual data points and the estimated data points. The regression line is the estimated data points. Take a simple example. You have four points (1,1), (1,3), (2,2), (2,4) The regression line runs in the middle of those points, y=x+1, going through the points exactly in the middle, (1,2) and (2,3). The residuals are actual y values minus estimated y values: 1-2, 3-2, 2-3 and 4-3. That's -1, 1, -1 and 1. They sum to zero, because you're trying to get exactly in the middle, where half the residuals will equal exactly half the other residuals. Half are plus, half are minus, and they cancel each other. Residuals are like errors, and you want to minimize error. You err on the negative side exactly as much as you err on the positive side, much like aiming at the bull's eye of a target, but missing a little to each side.
