Question

answer the questions that follow. the same response may be the correct answer for more than one question. 1. for which data set is the correlation coefficient r closest to 1? 2. for which data set is the correlation coefficient r closest to 0? 3. which data set indicates the strongest negative linear

Explanation:

Step1: Recall correlation coefficient properties

The correlation coefficient $r$ ranges from - 1 to 1. $r = 1$ indicates a perfect positive - linear relationship, $r=-1$ indicates a perfect negative - linear relationship, and $r = 0$ indicates no linear relationship.

Step2: Analyze Figure 1

The points in Figure 1 are scattered randomly, so the correlation coefficient $r$ is close to 0.

Step3: Analyze Figure 2

The points in Figure 2 show a weak positive - linear trend, but not a very strong one.

Step4: Analyze Figure 3

The points in Figure 3 show a negative - linear trend. As the $x$ - values increase, the $y$ - values decrease.

Step5: Analyze Figure 4

The points in Figure 4 follow a very clear positive - linear pattern. So the correlation coefficient $r$ for Figure 4 is closest to 1.

Step6: Determine the data - set with $r$ close to 0

Since the points in Figure 1 are randomly scattered, the correlation coefficient $r$ for Figure 1 is closest to 0.

Step7: Determine the data - set with the strongest negative linear relationship

Figure 3 has the most distinct negative - linear pattern among the four figures, so it has the strongest negative linear relationship.

Answer:

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