Question

1. for which data set is the correlation coefficient ( r ) closest to 0?
2. for which data set is the correlation coefficient ( r ) closest to 1?
3. which data set indicates the strongest negative linear relationship between its two variables?

Explanation:

Step1: Understand correlation coefficient

The correlation coefficient \(r\) measures the strength and direction of a linear relationship. \(r = 0\) means no linear relationship. \(r=1\) means a perfect positive linear relationship. \(r = - 1\) means a perfect negative linear relationship.

Step2: Analyze each figure

• Figure 1: Shows a negative linear trend. Points follow a line - like pattern going downwards, so \(r\) is close to \(-1\) (strong negative).
• Figure 2: Shows a positive linear trend. Points follow a line - like pattern going upwards, so \(r\) is close to \(1\) (strong positive).
• Figure 3: Points are scattered with no clear linear pattern. So \(r\) is close to \(0\).
• Figure 4: Shows a weak negative trend, but not as strong as Figure 1.

Answer:

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