Respuesta :
Answer: True
The errors represent how far off the guess is to the true value. The points on the residual plot must be scattered randomly around 0, in both positive and negative regions. Ideally, the smaller the errors, the better the fit. So we want these errors to be as close to 0 as possible. This is why we try to minimize the sum of the squared error (SSE) when trying to find the linear regression equation. The r and r^2 value are related to this idea as well.
If we don't have randomly scattered errors, and some pattern shows up, then this means a linear equation is not a good fit. Another model such as a quadratic model may be the better option.
As for the "why" this works, try to think of a person throwing darts. Their accuracy isn't perfect so they'll likely miss on the left and right sides of the target. Stuff on the left is negative territory, while stuff on the right is positive. Each side is fairly equal assuming the thrower isn't biased in some way. That's why we have randomly scattered points in both regions. In the case of a regression line, that's where our guess goes while the actual data point is the observed value. The difference between the two is the error.
