The image contains four scatter plots labeled as Figure 1 through Figure 4 and three corresponding questions. Here's an interpretation of the questions and how to approach them:

1. Which data set has an apparent positive, but not perfect, linear relationship between its two variables?

   • Look for a scatter plot where the data points show a general upward trend (i.e., as one variable increases, the other tends to increase) but does not form a perfect straight line.

2. For which data set does the correlation coefficient $r$ appear to be equal to -1?

   • The correlation coefficient $r$ is -1 when there is a perfect negative linear relationship, meaning the points lie exactly on a straight line with a negative slope.

3. Which data set indicates the strongest linear relationship between its two variables?

   • Identify the scatter plot where the points are closest to forming a straight line, whether positive or negative.

Answers Based on the Scatter Plots:

• Figure 1: Data points seem scattered with no strong relationship, probably no linear correlation.
• Figure 2: Shows a strong negative linear relationship, where the points are nearly on a straight line. This would likely have $r = -1$.
• Figure 3: Also shows a negative linear trend but less tight compared to Figure 2. Still a moderately strong negative correlation.
• Figure 4: Displays a weak positive linear trend, where the points are spread out but generally increasing.

Suggested Answers:

1. Positive, but not perfect, linear relationship: Figure 4.
2. $r = -1$: Figure 2.
3. Strongest linear relationship: Figure 2.

Do you need further explanation or have any questions?

Related Questions:

1. How do you calculate the correlation coefficient $r$ mathematically?
2. What does a positive or negative correlation coefficient signify?
3. How can outliers affect the correlation coefficient?
4. What is the difference between a strong and weak linear relationship?
5. How can you use the line of best fit to estimate correlation strength?

Tip:

A correlation coefficient of $r = 1$ means a perfect positive linear relationship, while $r = -1$ indicates a perfect negative one.