Question

1. for which data set does the correlation coefficient r appear to be equal to -1? select
2. for which data set is the correlation coefficient r closest to 1? select
3. which data set shows the least evidence of a linear relationship? select

Explanation:

Step1: Recall Correlation Coefficient Concepts

• \( r = -1 \): Perfect negative linear relationship (points lie on a straight line with negative slope).
• \( r = 1 \): Perfect positive linear relationship (points lie on a straight line with positive slope).
• Least linear relationship: Points are most scattered, no clear linear trend.

Step2: Analyze Each Figure

Sub - Question 1: \( r = -1 \)

• Figure 4: Points seem to lie on a straight line with negative slope (as \( x \) increases, \( y \) decreases), indicating a perfect negative linear relationship, so \( r = -1 \) here.

Sub - Question 2: \( r \) closest to 1

• Figure 1: Points seem to lie on a straight line with positive slope (as \( x \) increases, \( y \) increases), indicating a strong positive linear relationship, so \( r \) is closest to 1 here.

Sub - Question 3: Least Linear Relationship

• Figure 3: Points are most scattered, with no clear linear trend (neither positive nor negative straight - line pattern), so it shows the least evidence of a linear relationship.

Answer:

1. Figure 4
2. Figure 1
3. Figure 3