Suppose Figure 1 shows a scatterplot of two variables with points closely clustered around a straight line that slopes upward. Which of the following best describes the statistical relationship indicated in Figure 1?

• A. There is a nonlinear relationship between the two variables.
• B. There is no correlation between the two variables.
• C. There is a strong negative linear correlation between the two variables.
• D. There is a strong positive linear correlation between the two variables.

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the meaning of a scatterplot. A scatterplot displays points representing pairs of values for two variables, allowing us to visually assess the relationship between them.
2. Step 2: Identify the pattern of the points. If the points are closely clustered around a straight line that slopes upward, this suggests a linear relationship where one variable increases as the other increases.
3. Step 3: Recall the types of correlation: a positive linear correlation means both variables increase together, a negative linear correlation means one variable increases while the other decreases, and no correlation means no apparent pattern.
4. Step 4: Since the points cluster tightly around an upward sloping line, this indicates a strong positive linear correlation between the two variables.
5. Step 5: Therefore, the best description of the relationship shown in the scatterplot is that there is a strong positive linear correlation between the two variables.