Which of the following is closest to the correlation coefficient of the five data pairs (x, y) = (1, 2), (2, 4), (3, 5), (4, 4), (5, 5)?

Answer: C. 0.77

The mean of x is 3 and the mean of y is 4. The sum of the products of the differences from the means is (−2) × (−2) + (−1) × 0 + 0 × 1 + 1 × 0 + 2 × 1 = 6, the sum of the squared differences of x from its mean is 10, and that of y is 6. The correlation coefficient is 6 ÷ √(10 × 6) = 6 ÷ √60 ≈ 0.77, a fairly strong positive correlation.

• A. This divides the covariance 6 ÷ 5 = 1.2 by the product of the variances of x and y, 2 × 1.2. The correlation coefficient divides by the product of the standard deviations, which are square roots.
• B. 6 ÷ 10 = 0.6 is the slope of the regression line predicting y from x.
• C. Correct. 6 ÷ √60 ≈ 0.77.