Negative Correlation: Definition and Examples (With Types)

Updated February 3, 2023

Correlation is a statistical term that describes the relationship between two variables or datasets. There are many types of correlations, and understanding how each one works can help statisticians, managers and other professionals discover the relationships between the variables they study.

In this article, we discuss negative correlation and its differences from other correlation types, and we offer steps for calculating negative correlation and examples of negatively correlated variables.

What is negative correlation?

Negative correlation, or inverse correlation, describes a situation where, with two variables, one variable increases in value while the other decreases. You might see negative correlation represented with a -1. This shows that while x, or the first variable, gains value, y, or the second variable, decreases in value. The reverse can also be true with a negative correlation. This is the opposite of positive correlation, where both variables increase or decrease at the same time.

Negative correlation examples

Consider the following variable examples that would produce negative correlations. It's important to note that in some circumstances, correlations might change. This is can be especially true with stocks and bonds. Even though two variables might have a negative correlation, things could change as time passes.

Here are some examples of negatively correlating variables:

The more it rains, the less you can water the garden
The more you cook at home, the less you might eat out.
The lower the temperature, the more clothes you may wear.
The more money you spend, the less you might have.
The more you sleep, the less tired you may feel.

Data correlation types

Negative correlation is just one statistical term used to identify data relationships between two variables. Here are other types of data correlation:

Positive correlation

Represented as 1, a positive correlation shows variables moving in the same direction. This means that both variables increase or decrease simultaneously. Here are some examples of positive correlations:

The more you eat, the more groceries you may buy.
The more money you make, the more you might pay in income taxes.
The more hair you have, the more conditioner you may use.
The more the temperature rises, the higher the lemonade sales rise.

Zero or no correlation

A correlation of zero means there's no relationship between the two variables. As one variable moves one way, the other moves in a different, or unrelated, direction. Here are some examples of zero or no correlations:

The more you exercise, the more you sing.
The more you cook, the smarter you may be.
The higher the room temperature, the lower the rabbit population
The more money you spend, the happier you can be.
The less you sleep, the more soda you might drink.

What is a correlation coefficient?

The correlation coefficient measures the strength of the relationship between two variables. A correlation coefficient of -1 represents a perfect negative correlation, +1 represents a perfect positive correlation and 0 represents no correlation. That said, if two datasets have a correlation coefficient of -0.8, they would have a strong negative correlation. If they had a correlation coefficient of -0.1, that would mean they had a weak negative correlation. The higher the negative correlation is, the closer you can expect the correlation coefficient to be to -1.

Why is negative correlation important to understand?

There are many reasons why knowing the correlation coefficient between variables is important. One reason is that it can help portfolio managers reduce risks within their asset holdings. Often, portfolio managers look at correlation to help them diversify their portfolios. Some believe that you can reduce risks in a portfolio by maintaining uniquely correlated financial assets. A portfolio of exclusively positive correlations could prove volatile, so it's important to maintain negative correlations in a portfolio, too.

How to determine negative correlation

If you want to determine the correlation of your negatively correlated variables, here are some steps you can take:

1. Determine your two variables

Your variables are the two things you want to measure the correlation or relationship between. If you're looking to determine a negative correlation, these two datasets are likely to move in opposite directions. Keep in mind that correlation doesn't always equal causation. Just because a negative correlation exists between variables, that doesn't always mean there's a causal relationship occurring.

2. Determine your method for finding the correlation

There are various methods you can employ when calculating a correlation. Here are some of them:

Use a formula

You can choose to calculate the correlation with this formula:

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

When calculating a correlation, consider 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

Use a correlation coefficient calculator

You can often find correlation coefficient calculators online. If you have a large dataset, using a calculator might save you a lot of time and it can also reduce the risk of error in your calculation. Be sure to double-check your inputs to ensure your results are accurate.

Make a scatter plot

You can also see correlation visually by mapping your data points on a graph. An effective graph to use for this is a scatter plot, where you can mark points along your x and y axis to see if there's a positive relationship, a negative relationship or no relationship. If you're using a scatter plot, a line that slants downward from left to right signifies a negative correlation.

Related: A Guide to Scatter Plots

3. Calculate the correlation

Once you've narrowed down which method to use, use your datasets to calculate their correlation. If you use the formula or calculator, you can expect to see a result between -1 and 1. On a scatter plot, your line can tell you what the correlation is. Remember that a negatively sloping line represents a negative correlation.

4. Determine the type of correlation

A correlation can be positive, negative or zero. Use the number to assess the type of correlation you have. The closer your result is to zero, the less likely it is that there's a correlation between your variables. As your numbers approach 1 and -1, the stronger the correlation is in one way or another.