Question

A student measures the amount of water, x, that his classmates drink during one day and compares it to the amount of sleep, y, that they get. When he computes the correlation coefficient, he gets 1.18. What does that say about the relationship between the amount of water and amount of sleep?

Answer 1

The correlation coefficient gives information about the behavior of two variables and it should always be between -1 and 1.

Since the value of the correlation coefficient is 1.18, then the student made an error computing the correlation coefficient, because the number has to be between -1 and 1.

When the coefficient is near the value of 1, it means that there is a strong positive relationship between the variables (y increases as x increases).

When the coefficient is near the value of -1, it means that there is a strong negative relationship between the variables (y decreases as x increases).

When the value is not near 1 or -1, and it's rather near to 0, then there is a weak relationship (it will be a positive or negative relationship depending on the sign).

Either case, the coefficient cannot be greater than 1 or lower than -1.