If one found that the sum of the residuals from a regression line (with an intercept) was a large negative
value, one could conclude that there is a negative relationship between the independent and dependent
variables.
There must have been a calculation error since the residuals sum to 0 (apart from rounding error).

Question

If one found that the sum of the residuals from a regression line (with an intercept) was a large negative
value, one could conclude that there is a negative relationship between the independent and dependent
variables. 
There must have been a calculation error since the residuals sum to 0 (apart from rounding error).

Quizplus · Accepted Answer

The sum of the residuals always equals 0 (apart from rounding error). Therefore, if one found a large negative value, it would indicate a calculation error. It is not an indication of a negative relationship between the independent and dependent variables.

If One Found That the Sum of the Residuals from a Regression