# Correlation vs. Regression: What's the Difference?

Edited by Aimie Carlson || By Harlon Moss || Published on November 19, 2023
Correlation measures the strength and direction of a linear relationship between two variables, while regression predicts the value of one variable based on another.

## Key Differences

Correlation is a statistical measure that describes the extent to which two variables change together. If one variable tends to go up when the other goes up, there is a positive correlation. Conversely, regression provides a mathematical equation that describes the relationship, allowing for predictions.
When discussing correlation, we refer to the strength and direction (positive or negative) of the linear relationship between two variables. However, no matter how strong the correlation, it doesn't imply causation. In contrast, regression specifically attempts to draw a line through data in a way that minimizes the distance between the line and the data points, and this line can then be used for prediction.
Another significant difference is the output. Correlation results in a coefficient (ranging from -1 to 1) that represents the strength and direction of the linear relationship. Regression results in an equation that can predict the outcome for the dependent variable based on the value of the independent variable.
Correlation is often the first step in understanding a relationship between two variables, giving a quick insight. Once a correlation is established, regression analysis can be conducted to delve deeper into the relationship and predict future values.
Both correlation and regression are tools in statistics that have different purposes. While correlation gauges the relationship, regression provides a means to make predictions.

## Comparison Chart

### Purpose

Measures strength/direction of relationship
Predicts value of one variable based on another

### Output

Coefficient (-1 to 1)
Equation

### Implies causation?

No
Can be used to understand potential causative relationships

### Variables

Both treated equally
Distinct dependent and independent variables

Descriptive
Predictive

## Correlation and Regression Definitions

#### Correlation

A method to understand the relationship between two sets of data.
The correlation between ice cream sales and temperature was evident.

#### Regression

An equation expressing the relationship between variables.
The regression equation helped us forecast monthly expenses.

#### Correlation

A value expressing the strength and direction of a linear relationship.
A correlation of -1 means a perfect negative linear relationship.

#### Regression

A statistical analysis used to predict the value of one variable based on another.
Using regression, we estimated future sales based on ad expenditure.

#### Correlation

A concept highlighting mutual change between entities.
There's a notable correlation between a country's education level and its economic development.

#### Regression

A method to determine the strength and character of the relationship between one dependent and one or more independent variables.
The regression showed that both diet and exercise affect weight loss.

#### Correlation

A statistical measure indicating the extent two variables fluctuate together.
There's a high correlation between smoking and lung diseases.

#### Regression

A tool for modeling the relationships between a dependent variable and one or more independent variables.
The regression model was accurate in predicting housing prices.

#### Correlation

A tool indicating whether variables have a positive or negative association.
The correlation between studying and grades was positive.

#### Regression

A technique that helps in understanding the cause-and-effect relationship among variables.
Regression analysis revealed the factors most impacting production downtime.

#### Correlation

A relationship or connection between two things based on co-occurrence or pattern of change
A correlation between drug abuse and crime.

#### Regression

The process or an instance of regressing, as to a less perfect or less developed state.

#### Correlation

(Statistics) The tendency for two values or variables to change together, in either the same or opposite way
As cigarette smoking increases, so does the incidence of lung cancer, indicating a positive correlation.

## FAQs

#### Can correlation establish causation?

No, correlation does not imply causation.

#### What is the output of a regression analysis?

The output of regression is an equation expressing the relationship between the variables.

#### Are there different types of correlation coefficients?

Yes, the Pearson (linear), Spearman (rank), and Kendall Tau are common correlation coefficients.

#### How is regression used in predictions?

Regression provides an equation that predicts the value of the dependent variable based on the independent variable(s).

#### What does correlation measure?

Correlation measures the strength and direction of a linear relationship between two variables.

#### Can regression handle multiple independent variables?

Yes, multiple linear regression can analyze the impact of multiple independent variables.

#### What are residuals in regression?

Residuals are the differences between the observed and predicted values in a regression analysis.

#### Can correlation be negative?

Yes, a negative correlation indicates that as one variable increases, the other decreases.

#### How do outliers affect regression?

Outliers can skew the regression line, making predictions less accurate.

#### What's the range of a correlation coefficient?

The correlation coefficient ranges from -1 to 1.

#### What is the significance of the slope in a regression line?

The slope indicates the rate of change in the dependent variable for a unit change in the independent variable.

#### Can two variables have a correlation of 1?

Yes, a correlation of 1 indicates a perfect positive linear relationship.

#### Can correlation be used for prediction?

Correlation gauges the relationship but doesn't directly provide a predictive equation like regression.

#### Are there different types of regression?

Yes, including linear, logistic, polynomial, and ridge regression, among others.

#### What assumptions are made in linear regression?

Assumptions include linearity, independence, homoscedasticity, and normality of residuals.

#### Is a correlation of -0.5 considered strong?

A correlation of -0.5 indicates a moderately strong negative linear relationship.

#### Is a correlation of 0.8 strong?

Yes, a correlation of 0.8 is considered a strong positive linear relationship.

#### Why is regression important?

Regression helps in understanding relationships between variables and making predictions.

#### Is correlation always linear?

No, correlation can be nonlinear; non-linear correlations might not be captured well by the Pearson coefficient.

#### When would one choose regression over correlation?

One would choose regression when interested in predicting outcomes or understanding the impact of variables, not just the relationship.