while the scatter plot and the correlation coefficient provide valuable information about the relationship between free throws and total points scored, they do not establish a causal relationship.
Noah's scatter plot showing the relationship between the number of free throws made in a basketball game and the number of points scored, with a correlation coefficient of 0.76, indicates a strong positive correlation between these two variables. However, it's important to understand that correlation does not imply causation.
Here's why:
1. Correlation Indicates Association, Not Causation: A correlation coefficient of 0.76 suggests that there is a strong association between the number of free throws made and the number of points scored. This means that, typically, as the number of free throws increases, the number of points scored also tends to increase.
2. Causation Requires More Evidence: To establish causation, one would need to demonstrate that changes in one variable (like the number of free throws made) directly cause changes in the other variable (points scored). While it's reasonable to assume that scoring free throws contributes to the total points, the relationship is not exclusively causal. There are many factors in a basketball game that contribute to the total points scored.
3. Other Contributing Factors: Points in a basketball game can be scored in various ways, not just through free throws. Field goals and three-point shots also contribute to the total points. Hence, even if there's a strong correlation with free throws, they are not the sole factor in determining the total points scored.
4. Potential Confounding Variables: There might be other variables at play that affect both free throws and total points, such as the skill level of the players, the strategy employed by the team, or the defense of the opposing team.