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: Observe the scatter - plot

The points in the scatter - plot show a negative linear trend. A correlation coefficient of 1 represents a perfect positive linear relationship, so option A is incorrect. A correlation coefficient of 0 represents no linear relationship, so option B is incorrect.

Step2: Evaluate the strength of the negative relationship

The points do not have a very strong negative linear relationship. A correlation coefficient of - 0.8 represents a strong negative linear relationship, and the points here are more scattered than what would be expected for a - 0.8 correlation. A correlation coefficient of - 0.2 is too weak for the visible negative trend. The points show a moderate negative linear relationship, and a correlation coefficient of - 0.5 is a reasonable estimate.

Answer:

D. -0.5