Final answer:
The sum of the residuals in any least-squares regression analysis is indeed always zero because the regression line is calculated with the aim of minimizing these residuals to the least possible value.
Step-by-step explanation:
The statement 'the sum of the residuals in any given regression analysis is always zero' is true. Residuals are the differences between the observed values and the values predicted by the regression line.
In the context of least-squares regression, the regression line is calculated in such a way that the sum of the residuals is minimized to the least possible value, which mathematically results in a sum of zero.
The calculation of a regression line includes the constraint that the sum of the positive residuals (the amounts by which the observed values are above the predicted values) must equal the sum of the negative residuals (the amounts by which the observed values are below the predicted values).