A study reports a correlation coefficient of r = -0.82 between two quantitative variables. Describe the direction and strength of the linear relationship.

Step 1: Determine the direction from the sign of r.

The correlation coefficient is:
r = -0.82

Because r is negative, the variables have a negative linear association.

This means that as one variable tends to increase, the other tends to decrease.

Step 2: Determine the strength from the magnitude of r.

The magnitude is:
|r| = 0.82

A correlation coefficient with magnitude relatively close to 1 indicates a strong linear relationship.

Step 3: Combine the direction and strength.

Because r is negative and has a magnitude of 0.82, the data show a strong negative linear relationship.

Step 4: Remember what correlation does not establish.

A strong correlation does not by itself prove that changes in one variable cause changes in the other.

Therefore, r = -0.82 indicates a strong negative linear relationship.