Correlation Coefficient Formula

The Formula

r = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum(x_i-\bar{x})^2 \sum(y_i-\bar{y})^2}}

When to use: r = 1 means perfect positive line, r = โˆ’1 means perfect negative line, r = 0 means no linear pattern.

Quick Example

Height and weight: r โ‰ˆ 0.7, a moderate positive correlation โ€” taller people tend to weigh more.

What This Formula Means

A number between โˆ’1 and 1 that measures the strength and direction of the linear relationship between two variables.

r = 1 means perfect positive line, r = โˆ’1 means perfect negative line, r = 0 means no linear pattern.

Why This Formula Matters

Widely used in science, social science, and business to measure how strongly two variables are related.

Frequently Asked Questions

What is the Correlation Coefficient formula?

A number between โˆ’1 and 1 that measures the strength and direction of the linear relationship between two variables.

How do you use the Correlation Coefficient formula?

r = 1 means perfect positive line, r = โˆ’1 means perfect negative line, r = 0 means no linear pattern.

Why is the Correlation Coefficient formula important in Statistics?

Widely used in science, social science, and business to measure how strongly two variables are related.

What do students get wrong about Correlation Coefficient?

Correlation does not imply causation โ€” two variables can be correlated for unrelated reasons.

What should I learn before the Correlation Coefficient formula?

Before studying the Correlation Coefficient formula, you should understand: correlation intro, line of best fit.