Covariance vs Correlation

While working with data, one of the most important things that you should understand is how two variables relate to each other. This is where covariance and correlation come into play. Both of these are statistical tools that are used to measure relationships between variables, but they are not the same. Understanding the difference between covariance and correlation is very important for interpreting the relation between data, making accurate predictions, and applying the right statistical techniques. In this blog, we will discuss what covariance and correlation are, their differences, and when to use each.

Table of Contents

• What is Covariance?
• What is Correlation?
• Difference between Covariance and Correlation
• Covariance Formula
• Types of Covariance
• Correlation Formula
• Types of Correlation
• Applications of Covariance and Correlation
• Conclusion

What is Covariance?

Covariance is basically a way to measure how two variables move together. If one variable changes, it shows whether the other variable changes in the same or opposite direction. To find covariance, you have to compare how far each value is from its average and then check how these differences work together. The result gives you the direction of the relationship, but it does not give any idea about the strength. This is because the number depends on the units that are being used. In short, covariance lets you see whether two things are connected and if they move in the same or opposite direction.

Become a Data Science Professional

Transform raw data into actionable insights, master Python, Machine Learning, and AI, and build a successful data science career.

Explore Program

What is Correlation?

Correlation is basically a way to measure both the direction and strength of the relationship between two variables. Unlike covariance, it gives you a clear number between -1 and +1, which makes it easy for you to understand. A value which is close to +1 means that the two variables move in the same direction, while a value which is close to -1 means that the variables are moving in opposite directions. A value that is around 0 means that there is no clear relationship between the two. Correlation is easier to interpret because it removes the effect of units and shows how strongly two things are related to each other.

Difference between Covariance and Correlation

Covariance Formula

Covariance is all about how two variables move together. In order to calculate it, you need to have a look at how far each value is from its average (mean) and then multiply those differences together. At last, you have to take the average of those products. There are two main formulas in covariance.

1. Sample Covariance

You can use the Sample covariance formula while you are working with a sample, which is basically a part of the data, and not the whole population. The formula is given below:

Where,

• X_i, Y_i represent the individual values of the variables.
• X, Y denotes the mean (average) of the variables.
• n denotes the number of data points in the sample.

Here, you have to divide (n – 1) because you’re working with just a sample, and not the whole population. This small adjustment helps to make the result more accurate.

2. Population Covariance

You can use the Population covariance formula when you are working with the entire population. The formula is given below:

Where,

• X_i, Y_i= Denotes the individual values of the variables.
• μX​, μY​  = Mean (average) of the population for each variable.
• N = is the total number of data points in the population.

Here, you need to divide by N because you are using the entire population. Therefore, there is no need to make any adjustment like you do with a sample.

Types of Covariance

While studying covariance, you mainly look at two variables moving together. Based on that result, covariance can be divided into three main types:

1. Positive Covariance

Positive covariance occurs when the two variables move in the same direction. This means that if one variable increases, the other variable also increases, and vice versa. For example, the more you study, the higher marks you will get in the exams. This shows a positive relationship between the rise and fall of the two variables.

2. Negative Covariance

Negative covariance occurs when two variables are moving in opposite directions. If one variable goes up, then the other variable goes down, and vice versa. A good example of negative covariance is the time that you spend watching TV and your exam marks. As the number of hours spent on TV increases, your exam marks usually decrease. This shows an opposite relationship between the two.

3. Zero Covariance

Zero covariance occurs when there is no relationship between the two variables. In this case, any changes made in one variable do not affect the other variable in any way. For example, the number of books you read in a day has nothing to do with how much it rains in your city. Since the two variables are completely unrelated to each other, their covariance is close to zero.

Correlation Formula

Correlation is basically a way to measure both the direction and strength of the relationship between two variables. Unlike covariance, correlation provides you with a standardized value between -1 and +1. This makes it very easy to understand.

The most common type of correlation is Pearson’s Correlation Coefficient. The formula for this is given below:

Where,

• Cov(X, Y) = denotes the covariance between two variables.
• σ_X   = denotes the standard deviation of the variable X.
• σ_Y  = denotes the standard deviation of variable Y.

When you divide the covariance by the standard deviation of both variables, you can avoid the effect of different units or scales. That’s why correlation ends up as a value between -1 and +1.

Types of Correlation

Correlation basically tells you how strongly two variables are connected to each other and whether they move in the same direction or opposite direction. Given below are the three main types of correlation:

1. Positive Correlation

Positive correlation occurs when two variables move in the same direction. If one variable increases, the other variable also increases, and vice versa. For example, the more hours you study, the higher marks you get. This shows a positive relationship between the two.

2. Negative Correlation

Negative Correlation occurs when two variables move in opposite directions. If one variable goes up, the other goes down. A simple example of negative correlation would be the number of hours you exercise and your body weight. As the number of exercise hours increases, your body weight decreases. This shows a negative relationship.

3. Zero Correlation

Zero Correlation occurs when there is no relationship between the two variables. In this case, a change in one variable does not affect the other variable at all. For example, the number of movies that you have watched has nothing to do with the rainfall in your city. Since both of them are unrelated to each other, their correlation is close to zero.

Applications of Covariance and Correlation

In this section, we will discuss the applications of both Covariance and Correlation.

Applications of Covariance

1. Covariance is used in finance to show how stocks move together to help reduce the risk of investment.

2. It is also applicable in economics because it helps to study how factors like income and spending change together.

3. You can also use Covariance in Machine Learning to find the relationships between features to avoid any duplicate information.

4. Covariance can also be used for weather forecasting as it shows how temperature and humidity change together to get better predictions.

5. Covariance is also applicable in engineering, as it helps to analyze signals or images to detect patterns and improve the quality.

Applications of Correlation

1. Correlation can be used in finance as it shows how closely two stocks or assets move together.

2. It can also be used in healthcare because it helps to find the link between habits like exercise and health outcomes.

3. It can also be used for educational purposes, as it helps to check relationships between study time and performance in exams.

4. Correlation can also be used for marketing purposes, as it shows how the expenses made in advertisements relate to the sales growth.

5. You also use correlation in science as it helps to study connections, like between temperature and the growth of plants.

Conclusion

In conclusion, when you compare Covariance vs Correlation, both these tools help you to understand the relationship between two variables. But they work differently in how they measure and present relationships between variables.. Covariance specifies the direction of how two things move together. On the other hand, correlation shows both the direction and strength of that relationship in a range between -1 and +1. Having an idea of which tool to use when, you can analyze your data more effectively, whether it is finance, research, or regular problem-solving.

To enhance your skills and stay ahead in your career, enroll in our Data Science Course and gain practical, hands-on experience. Also, get interview-ready with our Data Science Interview Questions, prepared by industry experts.

Covariance vs Correlation – FAQs