Question

use the data set in the scatter plot shown to answer the question.
what is the best estimate of the correlation coefficient for the data set?
a. -0.9
b. -0.5
c. 0.5
d. 0.9

Explanation:

Step1: Determine the sign of the correlation coefficient

Since the data points in the scatter - plot show a downward trend (as \(x\) increases, \(y\) decreases), the correlation coefficient \(r\) is negative. So we can eliminate options C (\(r = 0.5\)) and D (\(r=0.9\)).

Step2: Determine the strength of the correlation

The data points are closely clustered around an imaginary line (a strong linear relationship). A correlation coefficient of \(r=-0.5\) indicates a moderate negative correlation, while \(r = - 0.9\) indicates a strong negative correlation. The data points in the scatter - plot are more consistent with a strong negative correlation.

Answer:

A. \(-0.9\)