Question
Lisa is not sure if m causes n, n causes m, or neither. In an attempt to come to a conclusion, she first plotted m on the x-axis, n on the y-axis, and used the linear regression feature of her graphing calculator. When she did this, she got a correlation coefficient (r) of 0.962 and a line with a slope of 2.3. She then plotted n on the x-axis, m on the y-axis, and used the linear regression feature of her graphing calculator. When she did this, she got a correlation coefficient (r) of 0.962 and a line with a slope of 0.4. Which conclusion is the most valid?
Responses
A m causes n.m causes n .
B n causes m.n causes m .
C m might cause n, or n might cause m.m might cause n , or n might cause m .
D m doesn’t cause n, and n doesn’t cause m.
Responses
A m causes n.m causes n .
B n causes m.n causes m .
C m might cause n, or n might cause m.m might cause n , or n might cause m .
D m doesn’t cause n, and n doesn’t cause m.
Answers
GPT-4o mini
The most valid conclusion based on Lisa's analysis is:
C. m might cause n, or n might cause m.
Here's the reasoning:
1. **Correlation and Causation**: The presence of a high correlation coefficient (0.962) in both scenarios indicates a very strong linear relationship between the two variables (m and n). However, correlation does not imply causation. Therefore, we cannot conclude definitively that one causes the other based solely on the correlation.
2. **Different Slope Interpretations**: The slope of the regression line differs based on which variable is plotted on the x-axis and which is plotted on the y-axis. This suggests that the relationship between the two variables may not be one-way; thus, it does not provide clear evidence to assert a singular cause-and-effect relationship.
3. **Ambiguity in Direction of Influence**: Since the correlation is strong regardless of the axis chosen, it indicates a relationship, but does not clarify which variable is influencing the other, or if they are mutually influencing each other.
Considering these points, the conclusion that "m might cause n, or n might cause m" encapsulates the uncertainty about the direction of the relationship.
C. m might cause n, or n might cause m.
Here's the reasoning:
1. **Correlation and Causation**: The presence of a high correlation coefficient (0.962) in both scenarios indicates a very strong linear relationship between the two variables (m and n). However, correlation does not imply causation. Therefore, we cannot conclude definitively that one causes the other based solely on the correlation.
2. **Different Slope Interpretations**: The slope of the regression line differs based on which variable is plotted on the x-axis and which is plotted on the y-axis. This suggests that the relationship between the two variables may not be one-way; thus, it does not provide clear evidence to assert a singular cause-and-effect relationship.
3. **Ambiguity in Direction of Influence**: Since the correlation is strong regardless of the axis chosen, it indicates a relationship, but does not clarify which variable is influencing the other, or if they are mutually influencing each other.
Considering these points, the conclusion that "m might cause n, or n might cause m" encapsulates the uncertainty about the direction of the relationship.