The image shows a scatterplot along with several correlation coefficient options (a. 0.85, b. 0.09, c. -0.35, d. -0.79). The task is to match the scatterplot with the correct correlation coefficient based on the pattern of the points.

To determine the correlation coefficient (often denoted as r), you can visually inspect how the points are arranged:

1. Positive or negative trend: A positive correlation means that as one variable increases, the other also increases, while a negative correlation means that as one variable increases, the other decreases.
2. Strength of the correlation: The closer the points are to forming a straight line, the stronger the correlation. A value near +1 or -1 indicates a strong correlation, while a value near 0 indicates a weak or no correlation.

Analysis of the Scatterplot:

• The scatterplot in the image does not exhibit a clear trend, as the points seem to be widely scattered.
• The spread of the points around both axes, without a visible upward or downward slope, suggests a weak correlation.

Based on these observations, the correlation coefficient is likely close to zero, indicating a weak relationship. Therefore, the correct correlation is b. 0.09, as this option represents a very weak positive correlation, which aligns with the scattered nature of the data.

Would you like further details or have any questions?

Here are 5 follow-up questions that expand on this:

1. How do you calculate correlation coefficients mathematically?
2. What does it mean when the correlation coefficient is exactly zero?
3. Can correlation coefficients above 1 or below -1 exist?
4. How does a correlation of -1 differ from +1 in scatterplots?
5. Why is it important to distinguish between correlation and causation?

Tip: Correlation only measures the strength of a linear relationship between two variables. It does not imply causation.