Key Differences Between Correlation and Regression

Regression and correlation are statistical tools that have repeatedly proven useful for businesses and research. However, it is fairly common to confuse the two.

Understanding the correlation between two variables is necessary to comprehend their relationship. Similarly, regression analysis helps us estimate one variable's value depending on the value of another variable. 

Read on to understand the difference between correlation and regression and how they are used in business and other circumstances.

What is correlation?

We can employ the correlation measure to assess if there is a connection between two variables in statistics. This connection is useful when it is necessary to know whether a particular parameter will positively or negatively impact the accomplishment of a specific target. Estimating the impact of a relationship requires first establishing the direction and strength of the correlation between two variables, and correlation analysis can help explain if such a relationship exists.

Types of correlation values

Measurement of correlation is on a scale ranging from +1 to -1. This can lead to various correlation values:

Positive correlation 

When two variables move in the same direction and one increases or decreases when the other does, the two variables have a positive correlation.

Negative correlation 

When two variables have a negative correlation, a rise in one is accompanied by a decrease in the other and vice versa. 

Zero correlation  

Zero correlation suggests that no relationship exists between the two variables. In this situation, modifying one variable will not impact the other.

What is regression?

Regression is the measurement used to explain the relationship between two distinct variables. It is a dependent characteristic in which a variable's action influences another variable's outcome. In simpler terms, regression analysis helps to understand how multiple factors influence each other.

Regression is a more detailed statistical tool frequently used to justify the correlation result. Regression estimates the effect of the change in quantitative terms. Regression-based analysis is a reliable tool for assessing the strength of a connection between two variables. It also helps to create estimates of future events and structures, allowing us to make more accurate predictions.

Types of regression

Using regression analysis, you can draw a line between two variables on an x-y graph to show their relationship. This is termed linear regression. Two types of linear regression exist: simple and multiple linear regression.

Simple linear regression

This tool allows you to summarise the relationship between a dependent variable (x) and an independent variable (y). It first establishes if there is a linear relationship between two variables and then allows you to quantify the relationship. An example would be the relationship between sales in Q1 and the revenue spent on advertising for that quarter. 

Multiple linear regression

With this tool, you can evaluate the relationship between a dependent variable and more than one independent variable. In other words, you assess how a dependent variable interacts with several independent variables by constructing a linear relationship between them. This type of regression can be used to make accurate predictions about the effects of multiple factors on the outcome. An example would be how the distance a car can drive on a gallon of gas (x) is affected by the car's weight, speed, number of cylinders, and displacement.

Difference between correlation and regression

Discerning the distinction between correlation and regression is essential. To better understand how they are used, let's look at some key differences in different aspects.

Relationship

Correlation indicates the possibility of a relationship or association between two variables. It only provides the relationship with strength and direction. 

On the other hand, regression is a tool to determine the strength of the correlation between dependent and independent variables. It gives you the ability to quantify this relationship with accuracy. This can give valuable insights into the correlation between them.

Coefficient 

In terms of coefficients, correlation and regression differ significantly from one another. Establishing the correlation between two variables is essential in understanding their relationship—how strongly correlated they are. This can be accomplished by examining the signed numerical value of the correlation. The correlation coefficients are between -1.00 and +1.00. 

Regression coefficients range from byx >1 to bxy<1, where b is the regression coefficient. Regression coefficients are typically absolute values, whereas correlation coefficients are relative. They must also have the same sign. If byx is positive, bxy must also be positive, for example.

Variables

Correlation and regression are two distinct concepts in which two variables interact. Correlation means that mutual dependence exists between them, while regression shows the impact of the independent variable on the dependent variable.

Cause and effect 

It is evident that there is a correlation between the two variables, yet it is not feasible to determine a cause-and-effect relationship. In contrast, regression is based on a cause-and-effect relationship because a change in the values of x (the cause) creates a change in y (effect) values.

Analysis

Correlation analysis is a useful tool for measuring the relationship between two variables; for example, salary levels and employee satisfaction. This helps you see if one is related to the other. 

Regression analysis allows you to see how the variables are related. Therefore, you can make predictions and optimise your efforts based on the data results. 

Advantages

Correlation analysis is an effective way to summarise the connection between two variables concisely and straightforwardly.

Regression analysis facilitates a detailed examination of the data and includes equations that aid in future prediction and optimisation of the data set.

Usage  

Correlation is useful when you need to make a quick judgment based on determining the influence of one variable on another.

Regression becomes necessary when there is a clear correlation between two variables. When a correlation is clear, you only attempt to quantify their connection. 

Objectives

Correlation is all about finding the most accurate numerical value to describe the connection between different values, while regression calculates quantitative measures of a random variable with fixed variables. Overall, these two methods help provide useful insights into data analysis.

Similarities between correlation and regression

After going through the main differences, let us now look at the similarities between the two.

• If the correlation between two variables is positive, then the regression slope will be positive.

• If two variables correlate negatively, their regression slope will be downward.

• Usage for both is the same as statistical measurements to fully comprehend the relationship between the variables.

How do businesses use correlation and regression?

Here are some uses for correlation and regression by organisations and businesses.

Predictive analytics

Business analysts and data scientists frequently use correlation and regression analysis to predict future business outcomes for companies. For example, a company may use regression analysis to predict how gross domestic product (GDP) fluctuations might affect its future sales revenue.

Improved operations

Business executives use correlation and regression to improve their operations. Data results can be used to explore new advertising options, customise products or services, and increase employee productivity.

Minimise errors and risk

Statistical tools like correlation and regression allow business owners to make decisions based on hard data instead of intuition or experience. Investors often use negative correlations, such as the prices of two investments moving in opposite directions, to minimise financial risk.

Reveal new business opportunities

Correlation and regression analysis help uncover new business prospects that might not otherwise be obvious by providing fresh insights that can be strategically applied. For example, data analysed with a test group could help a business decide whether to start a new sales promotion or opt for another.

Learn more with Coursera

When considering the differences between correlation and regression, regression is the method of choice for creating a strong model or predicting an outcome. The correlation route will be your best bet if you're looking for a quick solution to evaluate the connection between two variables. This can provide you with an immediate answer instead of compiling a summary. Correlation and regression are inseparable parts of data science. To learn more, turn to courses on Coursera. You may want to begin with the IBM Data Science Professional Certificate, which can provide you with data science skills and an advanced understanding of all its components.