In the least-squares regression line, the desired sum of the errors (residuals) should bea) zero...
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Answered
2022-11-24
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
a) zero
b) positive
c) 1
d) negative
e) maximized
Answer & Explanation
Henry Arellano
Expert
2022-11-25Added 12 answers
Answer: a) zero
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.
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.
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