Question

which of the following graphs shows a negative linear relationship with a correlation coefficient, r, relatively close to -1? a. b. c. d. a. graph a b. graph b c. graph c d. graph d

Explanation:

Step1: Analyze the sign of the correlation coefficient

A negative linear relationship means that as one variable increases, the other variable decreases. Graphs A and C show no or positive relationships (A has no clear trend, C has a positive trend), so we can eliminate A and C.

Step2: Analyze the closeness to - 1

The correlation coefficient \(r=-1\) represents a perfect negative linear relationship. The closer \(r\) is to \(-1\), the more closely the data points follow a straight - line negative trend. Graph D has more scattered points compared to Graph B. Graph B has data points that are more closely clustered around an imaginary negative - slope line.

Answer:

B. Graph B