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Correlation vs Regression: Top Difference Between Correlation and Regression

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31st Aug, 2022
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Correlation vs Regression: Top Difference Between Correlation and Regression

The basic need for the difference between both terms is connected to the statistical analytical approach it offers to find the mutual connections between two variables. The measure of each of those connections and the impact of those predictions are used to identify those analytical patterns in our day to day lives.

It is quite easy to get confused between the two terms. Here’s how their difference would be highlighted with a key note. The main difference in correlation vs regression is that the measures of the degree of a relationship between two variables; let them be x and y. Here, correlation is for the measurement of degree, whereas regression is a parameter to determine how one variable affects another.

In this article, I have explored the differences between regression and correlation along with explaining how they are similar.

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Correlation Coefficient

A correlation coefficient is applied to measure a degree of association in variables and is usually called Pearson’s correlation coefficient, which derives from its origination source. This method is used for linear association problems. Think of it as a combination of words meaning, a connection between two variables, i.e., correlation.

When a variable tends to change from one to another, whether direct or indirect, it is considered correlated. It is labeled such as there is no effect of one variable on the other. To create a better representation of this quality, let us assume such variables and name them x and y.

The correlation coefficient is measured on a scale with values from +1 through 0 and -1. When both variables increase, the correlation is positive, and if one variable increases, and the other decreases, the correlation is negative.

To measure the changes in each of these two units, they are considered positive and negative.

Positive change implies that the variables x and y have movement in the same direction.

The correlation coefficient “1” shows that the two variables x and y have a positive linear correlation. If the x variable’s value changes, the y variable’s value changes equivalently (in the same direction).

Negative change implies that the variables x and y are moving in opposite directions.

If there is a positive or negative effect on the variables, it creates an opportunity to understand the nature of trends in the future and predict it for the best of needs. This hypothesis would be completely based on the nature of variables and would define the nature of any physical or digital events.

The correlation coefficient “-1” shows that the two variables x and y have a negative linear correlation. If the x variable’s value changes, the y variable’s value changes equivalently (in the same direction).

If the correlation coefficient is “0”, it means there is no linear correlation between the two variables x and y.

The main beneficial source of correlation is that the rate of concise and clear summary defining the two variables’ nature is quite high compared to the regression method.

Example of Correlation

When you go through the examples of correlation and regression, you can better understand how they are useful in real-life scenarios.

Let’s first understand an example of correlation. A correlation chart (also called a scatter diagram) makes it simpler to analyze the correlation between two variables visually. A single point represents data in a correlation chart.

Now let’s think of correlation from a marketing perspective to observe the relationship strength between the two variables. For example, it can benefit your company if a predictable relationship is carried out between the sale of a product and certain factors like advertising, weather, and consumer income. Here are a few more real-life examples of correlation:

  • Weight and height:

There is a positive linear correlation between an individual’s weight and height.

  • Exam marks and time wasted in unnecessary activities:

A negative linear correlation exists between the student’s exam scores and the time spent watching TV, playing, gossiping, etc.

  • Body Fat and Exercise:

If you exercise more, you will burn fat more. So, a negative correlation exists between them.

  • Tea consumption and Intelligence:

Zero linear correlation exists between tea consumption and intelligence quotient.

  • Marketing in business:

A business can entice more customers if it spends more time on marketing.

  • Clothing size:

The clothing size increases with your age. So, it is an example of a positive linear correlation.

  • Summer season and ice cream sales:

During summer, the sales of ice cream increase, so there exists a positive correlation between them.

Regression

Regression can be defined as the parameter to explain the relationship between two separate variables. It is more of a dependent feature where the action of one variable affects the outcome of the other variable. To put in the simplest terms, regression helps identify how variables affect each other.

The regression-based analysis helps to figure out the relationship status between two variables, suppose x and y. That helps create estimation on events and structures to make future projections more relatable.

The intention of regression-based analysis is to estimate the value of a random variable that is entirely based on the two variables, i.e., x and y. Linear regression analysis is the most aligned and suitable and fits almost all data points. The main advantage based on regression is the detailed analysis it creates, which is more sophisticated than correlation. This creates an equation that can be used for optimizing the data structures for future scenarios.

Read: 6 Types of Regression Models in ML

Example of regression

You can easily point out 10 difference between correlation and regression.However, you can better understand those differences by looking at the regression example.

Regression is used to predict trends like how a business’ traffic is anticipated to increase in the upcoming months. The ability to visualize data helps it to observe trends and predict what the data could appear in the future. Moreover, it helps to define team goals and comprehend how traffic will be in the next few months.

The predictions collected from the regression-based models help a business to define goals for metrics like keyword acquisition. Since predictions are dependent on historical data, the company gets enough insights into how it is presently trending compared to the historical growth trends.

Correlation vs Regression: Table of Comparison 

Here is a table highlighting difference between regression analysis and correlation analysis across five parameters: 

Parameter Correlation Regression 
Definition Measures the strength and direction of a linear relationship between two variables. Predicts the value of one variable based on the value of another. 
Purpose Describes the association between variables without implying causation. Establishes a predictive model and explores the cause-and-effect relationship. 
Range of Values -1 to 1, where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 indicates no correlation. No defined range; depends on the data and model. 
Causation Does not imply causation; correlation does not prove that changes in one variable cause changes in another. May imply a causal relationship, especially in experimental settings. 
Application Used to identify patterns, relationships, or trends in data. Applied for prediction, forecasting, and understanding the impact of one variable on another. 

Correlation vs Regression

To have a thorough comparison, you can go through 10 difference between correlation and regression. But before that, let’s understand the similarities between correlation and regression.

Similarities:

  • Both of them are used as statistical measurements to gain a decent understanding of the relationship between the variables.
  • If the correlation is negative, the regression slope (line in the graph) will be negative.
  • If the correlation is positive, the regression slope (line in the graph) will be positive.

Listed below are some key correlation vs regression examples that will help create a better perspective on differentiating and understanding between both of them.

  • The regression will give relation to understand the effects that x has on y to change and vice-versa. With proper correlation, x and y can be interchanged and obtained to get the same results.
  • Correlation is based on a single statistical format or a data point, whereas regression is an entirely different aspect with an equation and is represented with a line.
  • Correlation helps create and define a relationship between two variables, and regression, on the other hand, helps to find out how one variable affects another.
  • The data shown in regression establishes a cause and effect pattern when change occurs in variables. When changes are in the same direction or opposite for both variables, for correlation here, the variables have a singular movement in any direction.
  • In correlation, x and y can be interchanged; in regression, it won’t be applicable.
  • Prediction and optimization will only work with the regression method and would not be viable in the correlation analysis.
  • The cause and effect methodology would be attempted to establish by regression, whereas not it.

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When we discuss the difference between correlation and regression in statistics, there is a greater emphasis on the variables’ relationship. In statistics, a measure of multiple variables and therefore, it is also known as the multivariate distribution.

A prominent correlation and regression difference are from an analysis perspective. Correlation analysis helps you to know whether the relationship exists or not between the two variables like ‘x’ and ‘y’.  If you want to study the correlation regression difference from an analysis perspective, you must also know how regression analysis works. It helps you to predict the dependent variable’s value depending on the independent variable’s value. It does this after assuming the average mathematical relation between two or more variables.

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Class 12 students must note the difference between correlation and regression because these terms are important chapters in their syllabus.

Correlation specifies the degree to which both variables can move together.   Regression specifies the influence of the change in the unit on the evaluated variable (q) due to the known variable(p). Moreover, correlation helps to establish the connection between the two variables, whereas regression helps in predicting a variable’s value depending on another given value.

Another important difference between correlation and regression in statistics is in terms of coefficients.  Correlation uses the signed numerical value to predict the relationship strength between the variables. Its coefficients range from -1.00 to +1.00. The regression coefficients range from byx > 1 to bxy < 1.

The difference between correlation and regression analysis is prominent in terms of their advantage. Correlation analysis allows students to get a brief and clear summary of the relation between two variables.  Regression analysis helps you to take an in-depth look at the data and also contains equations that help to predict and optimise the data set in the future. With this understanding of correlation and regression difference, you can now better know which one benefits you the most.

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What are the Similarities between Correlation and Regression? 

Let me take you through the main points of similarity between Correlation vs Regression:  

  • Relationship Analysis: Both correlation and regression are statistical tools used to unravel connections between two variables. 
  • Dual Variable Exploration: These methods are tailored for examining the dynamics between pairs of variables, providing insights into how they interact. 
  • Direction Identification: Both techniques offer clues about the direction of the relationship. They let you know if one variable tends to go up when the other does (positive correlation/regression) or if they move in opposite directions (negative correlation/regression). 
  • Strength Assessment: Whether it’s a casual wave or a firm handshake, correlation and regression measure the strength of the relationship. They assign a numerical value indicating how closely the variables are linked. 
  • Real-world Applicability: In practical terms, both correlation and regression find utility in diverse fields.   
  • Data Interpretation Tools: Correlation and regression act as interpreters for data relationships, helping to uncover patterns and trends that might not be immediately apparent.  

When to Use

After thoroughly understanding the difference between correlation and regression analysis, let’s know when they can be used.

  • Correlation – When there is an immediate requirement for a direction to understand, the relationship between two or more variables is involved.
  • Regression – When there is a requirement to optimize and explain the numerical response from y to x. To understand and create an approximation of how y an influence x.

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To summarize

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When looking for a solution to build a robust model, an equation, or for predicting response, regression is the best approach. If looking for a quick response over a summary to identify the strength of a relationship, the correlation would be the best alternative.

The above discussion infers that there is a huge difference between correlation and regression, though they are studied together. Correlation is used when researchers want to know whether the variables being studied are correlated or not. If they are correlated, they further want to know the strength of their relationship. Regression establishes a functional relationship between two variables to make predictions on events.

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Pavan Vadapalli

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Director of Engineering @ upGrad. Motivated to leverage technology to solve problems. Seasoned leader for startups and fast moving orgs. Working on solving problems of scale and long term technology strategy.
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Frequently Asked Questions (FAQs)

1What is the difference between regression and correlation analysis?

Correlation and regression are two types of analyses that are based on the distribution of several variables. They are useful for describing the type and degree of a connection between the two continuous quantitative variables. Although these two mathematical concepts are studied simultaneously, it is clear from the foregoing description that there is a significant distinction between correlation and regression. When a researcher wants to determine if the variables being investigated are associated, and if so, how strong their relationship is, correlation is used. Pearson's correlation coefficient is often regarded as the most accurate measure of correlation. In regression analysis, a functional relationship between two variables is formed in order to make future event estimates.

2When should I use regression analysis?

When you wish to estimate a continuous dependent value from a set of independent factors, you utilize regression analysis. Logistic regression should be used if the dependent variable is dichotomous. (Both logistic and linear regression will produce similar findings if the split here between two levels of the dependent variable is close to 50-50.) In regression, the independent variables could be either continuous or dichotomous. In regression analysis, independent variables with far more than two levels can be employed, but they must first be converted into variables with just two levels.

3What is the difference between correlation and regression slope?

The direction and strength of the association between two numeric variables, X and Y, is measured by correlation, which is always between -1.0 and 1.0. Y = a + bX is a simple linear regression equation that connects X with Y. Both measure the degree and direction of a link between two numeric variables. The regression slope (b) will be negative if the correlation (r) is negative. The regression slope will be positive if the correlation is positive.

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