Question

what is the correlation coefficient for the data shown in the table?
o 1
o -1
o 5
o 10
x y
0 15
5 10
10 5
15 0

Explanation:

Step1: Recall correlation - coefficient concept

The correlation coefficient $r$ measures the strength and direction of a linear relationship between two variables. If as one variable increases, the other decreases in a perfectly linear fashion, $r=- 1$. If as one variable increases, the other increases in a perfectly linear fashion, $r = 1$.

Step2: Analyze the data

In the given table, when $x = 0,y = 15$; when $x=5,y = 10$; when $x = 10,y=5$; when $x = 15,y = 0$. As $x$ increases by 5 each time, $y$ decreases by 5 each time. This is a perfectly - linear negative relationship.

Answer:

B. -1