Question

question 1 of 10
a data set contains three points, and two of the residuals are -12 and 6. what is the third residual?
a. 6
b. -12
c. -6
d. 12

Explanation:

Step1: Recall residual sum property

The sum of residuals in a simple - linear regression (or in general for a set of data points) is zero when using the least - squares method. Let the three residuals be $r_1$, $r_2$, and $r_3$. So $r_1 + r_2+r_3 = 0$.

Step2: Substitute known values

We know that $r_1=-12$ and $r_2 = 6$. Substitute these values into the equation $r_1 + r_2+r_3 = 0$. We get $-12 + 6+r_3=0$.

Step3: Solve for $r_3$

First, simplify the left - hand side of the equation: $-6 + r_3=0$. Then, add 6 to both sides of the equation to isolate $r_3$. So $r_3=6$.

Answer:

A. 6