Correlation vs Regression 🥊

While Correlation and Regression are closely related and often used together, they serve different purposes. Understanding the distinction is crucial for statistical analysis.

The Core Difference 💡

• Correlation: Tells us "How strongly" two variables are related. It yields a number (r) between -1 and +1.
• Regression: Tells us "The nature" of the relationship. It gives us an equation (Y = a + bX) used for prediction.

[!NOTE] Think of it this way:

• Correlation says: "Height and Weight are strongly related."
• Regression says: "If Height is 170cm, predicted Weight is 65kg."

Detailed Comparison 📋

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When to use what? 🛠️

Use Correlation when:

• You just want to know if two things move together.
• You want to check the strength of association.
• Example: Is study time related to exam marks?

Use Regression when:

• You want to predict or forecast.
• You want to quantify the impact of one variable on another.
• Example: How much will sales increase if I spend $100 more on ads?

Relationship between Coefficient of Correlation and Regression Coefficients 🤝

An interesting mathematical relationship exists between the two:

r = √(b_xy * b_yx)

Where:

• r = Coefficient of Correlation
• b_xy = Regression coefficient of X on Y
• b_yx = Regression coefficient of Y on X

Note: The sign of r is the same as the sign of regression coefficients.

Summary

Correlation is the diagnosis; Regression is the prescription. Correlation identifies the connection, while Regression models it for practical use.

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