Question

which value is the best estimate for the correlation coefficient of the data set?
a. 1
b. 0
c. −0.2
d. −0.5
e. −0.8

Explanation:

Step1: Analyze the scatter plot trend

The scatter plot shows a negative correlation (as \( x \) increases, \( y \) generally decreases). So the correlation coefficient should be negative, eliminating options A (1, positive perfect) and B (0, no correlation).

Step2: Analyze the strength of correlation

The points don't lie perfectly on a line, but there's a noticeable negative trend. A correlation coefficient of -0.5 indicates a moderate negative correlation, which fits the scatter plot better than -0.2 (weak) or -0.8 (strong, points would be closer to a line).

Answer:

D. \(-0.5\)