Question

a set of data pairs (x, y) have a correlation coefficient of r = 0.35. which statement best describes the relationship between x and y?
a. x and y show a strong, negative association
b. x and y show a weak, negative association
c. x and y show a weak, positive association
d. x and y show a strong, positive association

Explanation:

The correlation coefficient \( r \) ranges from -1 to 1. A positive \( r \) indicates a positive association, and a negative \( r \) indicates a negative association. The magnitude of \( |r| \) determines the strength: values close to 0 (e.g., \( |r| < 0.5 \)) are weak, and values close to 1 (or -1) are strong. Here, \( r = 0.35 \), which is positive (so positive association) and has a small magnitude (so weak association).

Answer:

C. \( x \) and \( y \) show a weak, positive association