A silly psychology student gathers data on the shoe size of 30 of his classmates and their GPA’s. The correlation coefficient between these two variables is most likely to be
A) exactly –1.0
B) near -0.6
C) near 0
D) near +0.6
E) exactly +1.0
The correct answer and explanation is :
The correct answer is C) near 0.
Here’s why: The scenario involves a psychology student collecting data on the shoe sizes and GPAs of 30 classmates. In this case, we’re looking at the correlation between two variables: shoe size and GPA. Correlation measures the strength and direction of the linear relationship between two variables, and it ranges from -1.0 to +1.0.
- A correlation of +1.0 would indicate a perfect positive relationship, meaning that as one variable increases, the other increases in a perfectly linear fashion.
- A correlation of -1.0 would indicate a perfect negative relationship, meaning that as one variable increases, the other decreases in a perfectly linear fashion.
- A correlation of 0 would indicate no linear relationship, meaning that the two variables do not affect each other in any systematic way.
Given the nature of the two variables in this case—shoe size and GPA—it’s highly unlikely that there is any meaningful or systematic linear relationship between them. Shoe size is primarily determined by physical factors such as age, gender, and genetics, while GPA is influenced by academic performance, effort, and other cognitive or behavioral factors. The two factors don’t have a causal or linear connection.
Therefore, we would expect the correlation to be near 0, reflecting the absence of a meaningful relationship between the two variables. The data points would likely be scattered without forming any clear upward or downward trend, which is characteristic of a low or no correlation.
In conclusion, a correlation coefficient near 0 best fits the scenario, suggesting that shoe size and GPA are unrelated in this particular dataset.