Question

In the least-squares regression line, the desired sum of the errors (residuals) should be a) zero b) positive c) 1 d) negative e) maximized

Answer 1

Answer: a) zero

Step-by-step explanation:

The key word here is "desired". We wish to make the errors as small as possible. The smallest any individual error can get is 0. Adding the entire collection of zeros will sum in a total of zero.

An error of zero means we hit the mark exactly. The unfortunate reality is that error is going to happen, so we'll have some positive error values with any regression line (or curve). It's only when all points are on the same line is when we have zero error and perfect interpolation rather than regression.

Again, the question is asking about desired error and the ultimate goal is to make the error zero. The next best thing is to minimize it as small as possible.