Let's solve the questions based on the given scatter plots:

Question 1:

Which scatter plot shows a positive association for the data?

• Positive association means as $x$ increases, $y$ increases. From the graphs:
  • A: As $x$ increases, $y$ remains mostly constant.
  • B: As $x$ increases, $y$ increases, showing a positive trend.
  • C: As $x$ increases, $y$ decreases, indicating a negative trend.
  • D: The relationship is nonlinear and does not represent a clear positive trend.

Answer: B

Question 2:

Which scatter plot shows a nonlinear association for the data?

• Nonlinear association means the data does not follow a straight line (neither positive nor negative linear trends). From the graphs:
  • A: Linear association with a positive trend.
  • B: Linear association with a negative trend.
  • C: Nonlinear, as the data forms a curved pattern.
  • D: Also linear with a slight negative trend.

Answer: C

Would you like further explanations or need assistance with more questions?

Here are five related questions for practice:

1. How can you determine the strength of a linear association in a scatter plot?
2. What are some examples of real-world data that might show a positive association?
3. How do outliers affect the relationship in scatter plots?
4. What tools can you use to fit a nonlinear association in data analysis?
5. Can a scatter plot show no association? What would it look like?

Tip: Always check the overall trend in scatter plots by observing how $y$ changes as $x$ increases or decreases. This helps in identifying patterns or relationships easily!