Question

some residuals for a scatterplot are given
for x = 3, the residual is -5
for x = 5, the residual is -1
for x = 7, the residual is 3
for x = 9, the residual is 0
for which value of x is the data point farthest from the
line of best fit?
3
5
7
9

Explanation:

Step1: Recall residual definition

Residual is the vertical distance (in absolute value) between a data point and the line of best fit. So we need to find the absolute value of each residual.

• For \( x = 3 \), residual is \( - 5 \), absolute value is \( |-5|=5 \).
• For \( x = 5 \), residual is \( - 1 \), absolute value is \( |-1| = 1 \).
• For \( x = 7 \), residual is \( 3 \), absolute value is \( |3|=3 \).
• For \( x = 9 \), residual is \( 0 \), absolute value is \( |0| = 0 \).

Step2: Compare absolute values

We compare the absolute values: \( 5>3>1>0 \). The largest absolute value of the residual is for \( x = 3 \), which means the data point at \( x = 3 \) is farthest from the line of best fit.

Answer:

A. 3