Question

Correlation coefficients such as r, consist of two components, a numerical value and a sign.

a) What is the range of possible values for r?

b) What does the sign tell you about the relationship between the two variables?

c) What information can you derive from the numerical value?

Answer 1

Solution

(a) Range of r = -1<=r<=1

i.e from -1 to 1

(b) A positive sign indicates a positive association; that is, as the value of one variable increases, so does the value of the other variable. A negative sign indicates a negative association; that is, as the value of one variable increases, the value of the other variable decreases.

(c) A value of exactly 1.0 means there is a perfect positive relationship between the two variables. For a positive increase in one variable, there is also a positive increase in the second variable. A value of -1.0 means there is a perfect negative relationship between the two variables. This shows that the variables move in opposite directions - for a positive increase in one variable, there is a decrease in the second variable. If the correlation is 0, there is no relationship between the two variables.