Covariance vs Correlation: What Is the Difference?

Written by Coursera Staff • Updated on

Data science has taken the global economy by storm recently and is projected to keep growing quickly.

Coworkers are analysing data on holograms during a business meeting at the office.

According to Analytics Insight, India is one of the top global markets for data professionals and is expected to contribute nearly 32 percent of the worldwide big data market by 2026 [1]. 

With data science emerging as such a hot field, many professionals wonder what skills are needed to keep up in this industry. Data science skills are used in several professional sectors, including data science, business, finance, and computer programming. 

While necessary knowledge will vary depending on job responsibilities, most professionals who work with data benefit from having strong statistical skills. These skills help data professionals organise, store, analyse, and interpret data. Finding relationships between variables within data sets can help businesses and organisations make informed decisions and maximise returns. Understanding the difference between covariance and correlation is essential for making unbiased interpretations of random variables within a data set. 

Covariance vs Correlation

Both covariance and correlation measure the relationship between two variables. Covariance measures how variables depend on one another and how a change in one variable may lead to another. Correlation shows how they relate and how one variable may impact the other. While these terms may sound similar, they have distinct differences that are important in statistical analysis.

Both covariance and correlation measure the relationship between variables and can help data-driven professionals decide which variables to include in models and how to interpret the trends in big data sets. 

A few of the key differences are summarised in the following table:

Measures solely the linear relationship between variablesMeasures both the direction and strength of the linear relationship between the variables
Takes the units of the variables it is measuringUnit-free measurement
Will be affected by changes in scaleWill not be affected by changes in scale
Limited to two variablesAble to be used for several sets of numbers

Because of the independence of scaling and the ability to measure several variables, correlation is often chosen over covariance when looking at the relationship between variables. Let’s take a closer look at each type of measurement.

What is covariance?

Covariance refers to the movement of two random variables with one another. Essentially, covariance assesses how the movement of each variable affects the other. This value can range from negative to positive infinity, meaning there are no bounds to this value. 

When there is a higher covariance value, the variables are more connected. This can be positive or negative. For example, if an increase in one variable leads to a significant increase in the other, these two terms would have a high positive covariance value. If an increase in one variable leads to a substantial decrease in the other, this would lead to a significant negative covariance. 

Equation for covariance

Covariance can be calculated in a population using the following formula:

[Feature image] Equation for covariance

In this formula, Σ(X) and Σ(Y) are expected variable values. Furthermore, xi is the data value of x, yi is the data value of x, x̄ is the mean of x, ȳ is the mean of y, and N is the number of values.

How is covariance used?

Covariance is used in several industries. Covariance is a statistical tool that can show the relationship between the movement of two random variables. This can be useful in several businesses that use statistical analysis, such as investing. When stocks move together, they are considered to have a positive covariance. This can help investors choose which stocks to invest in simultaneously. Covariance is also used when building portfolios and can inform decisions to reduce risk when pairing assets.

Another common use of covariance is in machine learning. You can use covariance to measure the direction of a linear relationship between two random variables, which can inform machine learning models. Data science professionals can use this tool to better understand how one variable in the model may affect another. Covariance is also important in several statistical methods, such as principal component analysis and Cholesky decomposition.

What is correlation?

Correlation is the measure of how closely two random variables move in sequence. If one variable moves in one direction, does the other variable follow? If the answer is yes, these variables are correlated. 

The correlation value can range from -1 to 1, with -1 and 1 representing entirely dependent relationships between variables. Positive correlation is when both variables move in the same direction, while negative correlation is when they move in opposite directions. If the correlation value is 0, the variables are independent. 

You can work with three main types of correlation:

  • Simple: A single number represents the correlation value between two variables.

  • Partial: A partial correlation must have more than two variables. This correlation occurs when several variables are studied, but only two are considered to influence one another when the other variables are held constant.

  • Multiple: At least three variables are studied simultaneously and affect each other. Often, two or more variables are used to predict the value of a separate variable. 

Equation for correlation

The equation for correlation is as follows:

[Feature image] Equation for correlation

The term ‘n’ is the number of data points in the data set, i.e., (x,y) pairs. Sqrt(Var(X)) represents the standard deviation of X, and Sqrt(var(Y)) represents the standard deviation of Y. Cov(X,Y) represents the covariance of X and Y. As you can see from this equation, covariance and correlation are closely related.

How is correlation used?

Many industries use correlation values to make informed decisions. For example, businesses and financial analysts often use correlation values to forecast sales, market trends, and business outcomes. If one variable is highly correlated with another, and the business expects a change in one variable, it can anticipate changes in the other. 

Data scientists often use correlation values to find patterns in big data sets. Correlation matrices can also be used to look for patterns and find highly correlated variables. These variables can often be grouped, which helps reduce the data set and make associations more straightforward. 

Correlation is also used in several statistical analyses, such as factor analysis, structural equation models, and linear regression. When performing linear regression, data analysts and scientists often use correlation values to indicate whether the linear regression produced reliable values.

Next steps

Are you interested in expanding your statistical knowledge? Several courses on Coursera are suited for learners of all levels interested in building their data skills and opening their career opportunities.

Consider a beginner's Introduction to Statistics course offered by Stanford University to get started. For more advanced learners, try the Data Science Specialisation by Johns Hopkins to expand your skill set.

Article sources

  1. Analytics Insight. “Big Data Analysts and Data Scientists Recruitment Landscape in India,” Accessed May 28, 2024.

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