Question

interpreting the strength of correlation
bretts teacher observed bretts behavior in class for a
week and compared the minutes he stayed on task in
class to the grade he earned on the homework that night.
she found that the correlation coefficient was r = 0.97.
what type of relationship has his teacher discovered?
positive correlation, likely causal
positive correlation, not likely causal
negative correlation, likely causal
negative correlation, not likely causal

Explanation:

Step1: Analyze the sign of the correlation coefficient

The correlation coefficient \(r = 0.97\) is positive. A positive \(r\) value indicates a positive correlation (as one variable increases, the other variable also tends to increase).

Step2: Consider the concept of causation

Just because there is a strong positive correlation (\(r = 0.97\) is close to \(1\), indicating a strong linear relationship) between minutes on - task in class and homework grade, it doesn't necessarily mean that the minutes on - task causes the good homework grade. There could be other factors (e.g., Brett could be more focused in general, and that focus helps both in - class task completion and homework performance).

Answer:

positive correlation, not likely causal