The question asks whether the data shown in Figure 4.1 suggests that an increase in shoe size causes an increase in height.

Looking at the scatter plot in Figure 4.1:

• The horizontal axis represents shoe size, and the vertical axis represents height in inches.
• The data points suggest a positive correlation between shoe size and height: as shoe size increases, height tends to increase as well.

However, correlation does not imply causation. The plot shows a relationship between the two variables, but it does not necessarily indicate that an increase in shoe size directly causes an increase in height. Instead, it is more likely that both shoe size and height are influenced by other factors, such as age, genetics, or general body growth.

The correct answer to the question, "Does this indicate that an increase in shoe size causes an increase in height?" is:

• No. The plot indicates a relationship, but not causality.

Would you like a more detailed explanation, or have any questions about correlation vs. causation?

Here are 5 related questions to think about:

1. What is the difference between correlation and causation in data analysis?
2. How can we determine if one variable truly causes another to change?
3. Can a third variable influence both shoe size and height, explaining their correlation?
4. What statistical tests can help us verify the strength of a correlation?
5. In what scenarios might a positive correlation be misleading?

Tip: Always be cautious when interpreting correlations; a relationship between two variables does not automatically mean that one causes the other.