In this task, you are asked to match each scatterplot to one of the four specified correlation coefficients provided:

• a. -0.29
• b. 0.53
• c. -0.91
• d. 0.97

To solve this, I'll analyze each scatterplot in terms of correlation:

1. Scatterplot with a very strong positive relationship: If the points are closely aligned in a straight line going upwards, this would correspond to the highest positive correlation, which is d. 0.97.

2. Scatterplot with a strong negative relationship: If the points are closely aligned in a straight line going downwards, this would correspond to the strongest negative correlation, which is c. -0.91.

3. Scatterplot with a moderate positive relationship: This scatterplot shows a generally upward trend, but with more spread out points, which corresponds to b. 0.53.

4. Scatterplot with a weak negative relationship: The points show a slight downward trend, but with more spread, corresponding to a. -0.29.

Let me now match these to the scatterplots in your image:

1. The first scatterplot (from the top) appears to have a weak negative trend, so this should be a. -0.29.
2. The second scatterplot shows a moderate positive trend, so this should be b. 0.53.
3. The third scatterplot clearly has a strong negative trend, so this should be c. -0.91.
4. The fourth scatterplot has a very strong positive trend, so this should be d. 0.97.

Final Matchings:

• 1st scatterplot → a. -0.29
• 2nd scatterplot → b. 0.53
• 3rd scatterplot → c. -0.91
• 4th scatterplot → d. 0.97

Would you like more details on understanding correlations or scatterplots?

Here are 5 related questions to expand your knowledge:

1. What is the difference between positive and negative correlation?
2. How do you calculate a correlation coefficient?
3. What is the interpretation of a correlation of 0?
4. Can two variables have a perfect correlation of 1 or -1 in real-world data?
5. What are the assumptions behind using correlation as a measure of association?

Tip: Always visually inspect scatterplots to ensure the correlation coefficient makes sense with the data's trend and spread.