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 direction of the correlation

The scatter - plot shows a negative correlation (as \(x\) increases, \(y\) decreases). So the correlation coefficient \(r<0\). Options A (\(r = 1\)) and B (\(r=0\)) can be eliminated.

Step2: Analyze the strength of the correlation

A correlation coefficient of \(r=-0.2\) indicates a very weak negative correlation. A correlation coefficient of \(r = - 0.5\) indicates a moderate negative correlation. A correlation coefficient of \(r=-0.8\) indicates a strong negative correlation.
Looking at the scatter - plot, the points are not extremely scattered (so it's not a very weak correlation) and not extremely close to a straight line (so it's not a very strong correlation). The pattern is more in line with a moderate negative correlation.

Answer:

D. \(-0.5\)