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 (\(0\to5\to10\to15\)), \(y\) decreases by \(5\) each time (\(15\to10\to5\to0\)). This is a perfect linear relationship.

Step2: Determine the sign of the correlation coefficient

Since \(y\) decreases as \(x\) increases, the correlation is negative.

Step3: Recall the value for a perfect linear relationship

The correlation coefficient \(r\) for a perfect linear relationship is either \(1\) (perfect positive) or \(- 1\) (perfect negative). Here, it is a perfect negative linear relationship.

Answer:

-1