Final answer:
The sum of residuals in a regression model is zero. With two known residuals of -12 and 6, the third residual must be 6 to balance out to zero. Therefore, the answer is option A.
Step-by-step explanation:
In statistics, the sum of the residuals within a dataset always equals zero when you are working with a linear regression model. This is because residuals are calculated as the differences between the actual values and the predicted values obtained from the regression line, and the line of best fit is positioned in such a way that these differences (or errors) cancel each other out.
Given that we already have two residuals from a dataset with three data points, -12 and 6, we can calculate the third residual by adding the known residuals and setting the sum equal to zero:
-12 + 6 + third residual = 0.
The third residual can then be solved for by rearranging the equation:
third residual = 12 - 6 = 6
Therefore, the third residual has to be 6, which makes option A correct.