Question

question 15
consider the given table.

x	y
2	4
3	3
4	2
5	1

which statement is valid for the correlation coefficient of the data?

a the correlation coefficient of -1 indicates that the x and y values have a perfect linear relationship.

b the correlation coefficient of 1 indicates that the x and y values have a perfect linear relationship.

c the correlation coefficient of -1 indicates that the x and y values have a weak linear relationship

d the correlation coefficient of 1 indicates that the x and y values have a weak linear relationship.

Explanation:

Step1: Identify trend of x and y

As $x$ increases by 1, $y$ decreases by 1.

Step2: Determine correlation coefficient

This is a perfect negative linear relationship, so $r=-1$.

Step3: Match to valid statement

A coefficient of -1 means perfect linear relationship, which matches option A.

Answer:

A. The correlation coefficient of -1 indicates that the x and y values have a perfect linear relationship.