(1 mark) If the sum of three positive residuals is 15 , what would be the sum of the negative residuals after fitting a least square regression line?

In the context of least squares regression, the sum of the residuals (the differences between observed and predicted values) is always equal to zero. This means that the sum of the positive residuals must equal the absolute value of the sum of the negative residuals.

Step 1: Understand the Relationship

If we denote the sum of the positive residuals as $S^+$ and the sum of the negative residuals as $S^-$, we have: $S^+ + S^- = 0$ This implies: $S^- = -S^+$

Step 2: Given Information

We are given that the sum of the positive residuals is 15: $S^+ = 15$

Step 3: Calculate the Sum of Negative Residuals

Using the relationship derived in Step 1: $S^- = -S^+ = -15$

Final Answer

The sum of the negative residuals after fitting a least squares regression line would be $-15$.