Question

what is the correlation coefficient for the data shown in the table? 1 -1 5 10

Explanation:

Step1: Analyze the relationship between x and y

As x increases by 5 each time (from 0 to 5 to 10 to 15), y decreases by 5 each time (from 15 to 10 to 5 to 0). This is a perfect linear relationship.

Step2: Determine the sign of the correlation coefficient

Since as x increases, y decreases, the relationship is negative.

Step3: Confirm the magnitude of the correlation coefficient

For a perfect linear relationship (all points lie on a straight - line), the magnitude of the correlation coefficient \(r\) is 1.

Answer:

-1