Question

1. which data set indicates the strongest linear relationship between its two variables? 2. which data set has an apparent negative, but not perfect, linear relationship between its two variables? 3. for which data set does the correlation coefficient r appear to be equal to 1?

Explanation:

Step1: Recall correlation concept

The closer the data points are to a straight - line, the stronger the linear relationship.

Step2: Analyze Figure 1

In Figure 1, the data points are more scattered.

Step3: Analyze Figure 2

In Figure 2, the data points form a better - defined linear pattern compared to others.

Step4: Analyze Figure 3

In Figure 3, the data points show a negative linear trend but are not perfectly aligned.

Step5: Analyze Figure 4

In Figure 4, the data points are highly scattered.

1. The data set in Figure 2 has the strongest linear relationship as the points are more closely aligned to a straight - line compared to the other figures.
2. The data set in Figure 3 has an apparent negative, but not perfect, linear relationship as the points generally slope downwards but are not exactly on a single straight - line.
3. A correlation coefficient $r = 1$ indicates a perfect positive linear relationship. None of the given figures show a perfect positive linear relationship where all points lie exactly on an upward - sloping straight - line.

Answer:

1. The data set in Figure 2
2. The data set in Figure 3
3. None of the above figures