Question

interpreting the magnitude of residuals
points and their residual values are shown in the table. which point is farthest from the line of best fit?

x	y	residual
2	5	0.04
3	6.2	-1.1
4	9	-0.64
5	13	1.02

Explanation:

Step1: Recall the concept of residual

The magnitude of the residual represents the distance of a point from the line of best - fit. We need to find the largest absolute value of the residuals.

Step2: Calculate the absolute values of residuals

For the first point: $|0.68| = 0.68$; for the second point: $|0.04|=0.04$; for the third point: $|- 1.1| = 1.1$; for the fourth point: $|-0.64| = 0.64$; for the fifth point: $|1.02| = 1.02$.

Step3: Compare the absolute values

We compare $0.68,0.04,1.1,0.64,1.02$. The largest value is $1.1$, which corresponds to the point with $x = 3$.

Answer:

$(3,6.2)$