Question

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

Explanation:

Step1: Understand linear relationship

A linear relationship in a scatter - plot shows points that roughly follow a straight line. The least evidence of a linear relationship is when the points are most scattered. In Figure 2, the points are more spread out compared to the other figures.

Step2: Understand correlation coefficient close to - 1

A correlation coefficient \(r\) close to - 1 indicates a strong negative linear relationship. In Figure 3, the points show a strong negative trend (as \(x\) increases, \(y\) decreases in a relatively straight - line fashion).

Step3: Understand correlation coefficient close to 1

A correlation coefficient \(r\) close to 1 indicates a strong positive linear relationship. In Figure 4, the points show a strong positive trend (as \(x\) increases, \(y\) increases in a relatively straight - line fashion).

Answer:

1. The data set in Figure 2
2. The data set in Figure 3
3. The data set in Figure 4