# What Is Correlation? (With Definition and Examples)

Updated March 10, 2023

Understanding and analyzing various correlations can be beneficial across different industries. For example, if you own a bakery, you might decide you'll make more coconut maple donuts on Fridays based on the correlation between coconut maple donut demand and the day of the week. Though there was a causal relationship in this circumstance, it's important to note that won't always be the case. All in all, knowing the correlation between two variables can help you make decisions that could positively impact your business. Calculating correlation is especially helpful if you're an investment manager or analyst.

In this article, we define the various types of correlation and explain how to calculate it.

Related: Your Guide to Careers in Finance

## What is correlation?

Correlation refers to the statistical relationship between two entities. In other words, it's how two variables move in relation to one another. Correlation can be used for various data sets, as well. In some cases, you might have predicted how things will correlate, while in others, the relationship will be a surprise to you. It's important to understand that correlation does not mean the relationship is causal.

To understand how correlation works, it's important to understand the following terms:

• Positive correlation: A positive correlation would be 1. This means the two variables moved either up or down in the same direction together.

• Negative correlation: A negative correlation is -1. This means the two variables moved in opposite directions.

• Zero or no correlation: A correlation of zero means there is no relationship between the two variables. In other words, as one variable moves one way, the other moved in another unrelated direction.

Related: A Guide to Scatter Plots

## Types of correlation coefficients

While correlation studies how two entities relate to one another, a correlation coefficient measures the strength of the relationship between the two variables. In statistics, there are three types of correlation coefficients. They are as follows:

• Pearson correlation: The Pearson correlation is the most commonly used measurement for a linear relationship between two variables. The stronger the correlation between these two datasets, the closer it'll be to +1 or -1.

• Spearman correlation: This type of correlation is used to determine the monotonic relationship or association between two datasets. Unlike the Pearson correlation coefficient, it's based on the ranked values for each dataset and uses skewed or ordinal variables rather than normally distributed ones.

• Kendall correlation: This type of correlation measures the strength of dependence between two datasets.

Knowing your variables is helpful in determining which correlation coefficient type you will use. Using the right correlation equation will help you to better understand the relationship between the datasets you're analyzing.

Related: Types of Graphs and Charts

## How to calculate the correlation coefficient

You can use the following equation to calculate correlation:

∑ (x(i) - x̅)(y(i) - ȳ) / √ ∑(x(i) - x̅) ^2 ∑(y(i) - ȳ)^2

When calculating a correlation, keep in mind the following representations:

x(i) = the value of x

y(i) = the value of y

x̅ = the mean of the x-value

ȳ = the mean of the y-value

Follow these steps to calculate the correlation coefficient:

### 1. Determine your data sets

In the beginning of your calculation, determine what your variables will be. You can organize them in a chart if it helps you to better visualize them. Separate them by x and y variables. For instance:

x: (1, 2, 3, 4) and y: (2, 3, 4, 5)

### 2. Calculate the mean of the x and y variables

To calculate the mean, also known as the average, add the values of each variable together and divide by the number of values in that dataset. Using the example, if you were to calculate the mean of x, you'd add 1, 2, 3 and 4 together and divide by 4 because you have four values for x. Do the same for the y variables. Using the example above, you'd add together 2, 3, 4 and 5 and divide by 4 because you have four values for y.

### 3. Subtract the mean

For the x-variable, subtract the mean from each value of x-variable and call it "a." For the y-variable, subtract the mean from each value of the y-variable and call it "b."

### 4. Multiply and find the sum

Multiply each a-value by the corresponding b-value. After you've done this, find the sum, which will end up being the formula's numerator.

### 5. Take the square root

At this point, you can square every a-value and determine the sum of the result. After you've done this, calculate the square root of the value you just determined. This will be the formula's denominator.

### 6. Divide

Divide the numerator (the value you determined in step 4) by the denominator (the value you determined in step 5). This will result in the correlation coefficient.

If you prefer to calculate digitally, there are correlation calculators online. This method is more efficient when you have larger datasets.

## Examples of correlation

Use the following correlation examples to help you better analyze the correlation results from your own datasets.

### Positive correlations

Here are some examples of positive correlations:

1. The more time you spend on a project, the more effort you'll have put in.

2. The more money you make, the more taxes you will owe.

3. The nicer you are to employees, the more they'll respect you.

4. The more education you receive, the smarter you'll be.

5. The more overtime you work, the more money you'll earn.

### Negative correlations

Here are some examples of negative correlations:

1. The more payments you make on a loan, the less money you'll owe.

2. As the number of your employees decreases, the more job positions you'll have open.

3. The more you work in the office, the less time you'll spend at home.

4. The more employees you hire, the fewer funds you'll have.

5. The more time you spend on a project, the less time you'll have.

### No correlation

Here are some examples of entities with zero correlation:

1. The nicer you treat your employees, the higher their pay will be.

2. The smarter you are, the later you'll arrive at work.

3. The wealthier you are, the happier you'll be.

4. The earlier you arrive at work, your need for more supplies increases.

5. The more funds you invest in your business, the more employees will leave work early.

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