Correlation Coefficient

Statistics
definition

Also known as: r, Pearson's r, r-value

Grade 9-12

A number between −1 and 1 that measures the strength and direction of the linear relationship between two variables. Widely used in science, social science, and business to measure how strongly two variables are related.

Definition

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

💡 Intuition

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

🎯 Core Idea

The correlation coefficient quantifies only linear relationships; nonlinear patterns can have r ≈ 0.

Example

Height and weight: r ≈ 0.7, a moderate positive correlation — taller people tend to weigh more.

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}}

🌟 Why It Matters

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

🚧 Common Stuck Point

Correlation does not imply causation — two variables can be correlated for unrelated reasons.

Frequently Asked Questions

What is Correlation Coefficient in Statistics?

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

Why is Correlation Coefficient important?

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

What do students usually get wrong about Correlation Coefficient?

Correlation does not imply causation — two variables can be correlated for unrelated reasons.

What should I learn before Correlation Coefficient?

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

How Correlation Coefficient Connects to Other Ideas

To understand correlation coefficient, you should first be comfortable with correlation intro and line of best fit. Once you have a solid grasp of correlation coefficient, you can move on to linear regression.

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