Question 1

What is the Pearson correlation coefficient?

Accepted Answer

The Pearson correlation coefficient (r) measures the strength and direction of a linear relationship between two variables. It ranges from -1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive).

Question 2

What is the correlation coefficient formula?

Accepted Answer

r = [ n×Σ(xy) − Σx×Σy ] / √( [n×Σx² − (Σx)²] × [n×Σy² − (Σy)²] ). Sum x, y, xy, x² and y², plug them into the formula with n (number of pairs) and simplify.

Question 3

How do I interpret the value of r?

Accepted Answer

Use the absolute value: 0 to 0.19 very weak, 0.20 to 0.39 weak, 0.40 to 0.59 moderate, 0.60 to 0.79 strong, 0.80 to 1.00 very strong. The sign shows direction: positive means both rise together, negative means one rises as the other falls.

Question 4

Does correlation mean causation?

Accepted Answer

No. Correlation only shows that two variables move together linearly. It does not prove that one causes the other. There may be hidden confounding variables, or the relationship may be coincidental. Always combine r with domain knowledge and study design.