When you first hear about **regression****s**, you may think that **correlation** and **regression** are synonyms or at least they related to the same concept. This statement is somewhat supported by the fact that many academic papers in the past were based solely on correlations.

However, correlation and regression are far from the same concept. So, let’s see what the relationship is between **correlation analysis** and **regression analysis**.

There is a single expression that sums it up nicely: correlation does not imply causation!

With that in mind, it’s time to start exploring the various differences between **correlation** and **regression**.

**1. The Relationship between Variables**

First, **correlation** measures the degree of relationship between two variables. **Regression analysis** is about how one variable affects another or what changes it triggers in the other.

*For more on variables and regression, check out our tutorial How to Include Dummy Variables into a Regression*.

**2. Causality**

Second, **correlation** doesn’t capture *causality* but the degree of interrelation between the two variables. **Regression** is based on *causality*. It shows no degree of connection, but cause and effect.

**3. Are X and Y Interchangeable?**

Third, a property of **correlation** is that the **correlation** between *x* and *y* is the same as between *y* and *x*. You can easily spot that from the formula, which is symmetrical. **Regressions** of *y* on *x* and *x* on *y* yield different results. Think about income and education. Predicting income, based on education makes sense, but the opposite does not.

## 4. Graphical Representation of Correlation and Regression Analysis

Finally, the two methods have a very different graphical representation. **Linear regression analysis** is known for the best fitting line that goes through the data points and minimizes the distance between them. Whereas, **correlation** is a single point.

*Want to learn how to visualize statistical data? Check out our tutorials How to Visualize Numerical Data with Histograms and Visualizing Data with Bar, Pie and Pareto Charts.*

## Key Differences Between Correlation and Regression

To sum up, there are four key aspects in which these terms differ.

- When it comes to
**correlation**, there is a relationship between the variables.**Regression**, on the other hand, puts emphasis on how one variable affects the other. **Correlation**does not capture causality, while**regression**is founded upon it.**Correlation**between x and y is the same as the one between y and x. Contrary, a**regression**of x and y, and y and x, yields completely different results.- Lastly, the graphical representation of a
**correlation**is a single point. Whereas, a**linear regression**is visualized by a line.

So, now that you have proof that **correlation** and **regression** are different, it is time for a new challenge. Find out how to decompose variability by diving into the linked tutorial.

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Sum of Squares Total, Sum of Squares Regression and Sum of Squares Error

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