Examples of Negative Correlation and How to Calculate It

By Indeed Editorial Team

Updated November 6, 2022

Published September 29, 2021

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

A negative or inverse correlation is an inverse relationship between two variables. A negative correlation means that when the value of variable x is high, the value of variable y becomes low. The value of variable x consequently drops when variable y rises. Understanding how to identify and calculate a negative correlation can help you think more critically. In this article, we explore what negative correlation is, provide examples, define other types of correlations, and discuss their importance.

What is negative correlation?

When two variables correlate, they form a decipherable link between their values, which may either be coincidental or a result of an underlying cause. Correlation does not deliberately translate to causation. Statisticians use negative correlation to determine the strength of the relationship between two variables and how to predict profits and losses for planning.

Examples of negative correlation

The following examples represent situations where the correlation between the variables is negative:

  • The more you eat, the less you can work.

  • The longer you work, the shorter the free time you have.

  • The longer you sleep, the less tired you feel.

  • The colder the weather, the more clothes you have to wear.

  • The cheaper the meal, the more customers who buy it.

  • The more sales, the less stock remains.

Inverse correlation is highly effective in the investment industry. In a correlation between stocks and bonds, the coefficient is negative. When economies are performing strongly, stocks generally do better than bonds. Similarly, a rise in the prices of crude oil results in low airline stock prices, eventually impacting the earnings of airline businesses.

When the price of jet fuel goes down, it causes a positive impact on the earnings of airline companies. Investment portfolios can change drastically when a negative correlation between two variables breaks down. To avert a hedge when oil prices decline, airline companies must strategize how to invest part of their portfolio in airline stocks using smart asset allocation techniques.

Related: What is Quantitative Analysis?

Other types of correlations

There are several other types of correlations, such as:

Positive correlation

A positive correlation means two variables increase or decrease at the same time. Situational circumstances under which a correlation becomes positive include the following examples:

  • The more you eat, the more weight you gain.

  • The more you eat out, the more you spend.

  • The less you sleep, the less you become active.

  • The more you exercise, the more fit you become.

  • The less you market a business, the fewer conversions you make.

Read more: Example of Positive Correlation (And How to Calculate It)

Zero or no correlation

When there is no relation between two variables, the correlation becomes neutral or zero. This means that the rising or falling of one variable does not affect how the other variable behaves. Examples include:

  • The more you exercise, the more you travel.

  • The more you sleep, the less soda you drink.

  • The more you travel, the fewer people eat chicken.

  • The taller you grow, the smarter you become.

Related: Top 10 Data Analyst Interview Questions (With Example Answers)

Correlation coefficient

The degree to which a variable moves in a correlation is a correlation coefficient. It's represented numerically, ranging from -1 to +1. A coefficient of 0 means there is no linear correlation between the two variables. Instead, the connection is zero. When the correlation is negative, the coefficient is represented as -1. A positive coefficient is denoted as +1. When the positive correlation is perfect, it's represented as 1.0 and when it's a perfect negative correlation, the coefficient is -1.0.

How to calculate negative correlation coefficient

There are various methods of calculating correlation, including the following:

1. Use a formula

You can use this formula to determine correlation coefficient:

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

The figures represent the following:

x = value of variable X

y = value of variable Y

x̅ = mean value of X

ȳ = mean value of Y

Related: Financial Analyst Interview Questions (With Sample Answers)

2. Use a correlation coefficient calculator

You can determine the strength and direction of the negative correlation between variables by using a coefficient calculator, which you can find available online. A correlation coefficient calculator allows you to list the values of your variables in their respective columns and run a calculation. Within a moment, it can determine your coefficient and you can use your result to plan and organize your business.

3. Create a scatter chart

A scatter chart, scattergram, or scatter plot is a visual representation of correlation on a graph. It indicates the strength and direction of the relationship that links two related variables. In a scattergram, one variable aligns on the x-axis and the other on the y-axis. Then, you mark the points where your values coincide and draw a straight line across them. The gradient of the line determines whether the correlation is positive or negative.

If the gradient is negative, the correlation is negative too. If the values do not form a regular pattern and thus the line cannot be straight, it means the correlation coefficient is zero.

4. Determine the strength of correlation

Depending on the value found after calculating the coefficient of your variables, the correlation may either be weak or strong. Coefficient values below -0.2 are considered weak negative correlations, and those above -0.8 are strong. A strong negative correlation forms a downward sloping gradient in a scatter chart while a weak correlation creates a sharper downhill sloping gradient.

Importance of negative correlation

The following situations show the importance of negative correlation:

Managing a portfolio

The Modern Portfolio Theory is a strategy that looks over the risk and return of portfolio assets. Operating under the belief that you can minimize the potential for risk by having diversified financial assets, the Modern Portfolio Theory reduces the risk of volatility of a portfolio. It facilitates a smooth flow of returns in the long run. Having a diverse portfolio doesn't rule out all risks, but becomes valuable when financial changes occur in the market. A negative correlation helps managers to determine precisely where to allocate assets in a business.

Essentially, negative correlation allows researchers to study variables that come about naturally and are precarious or unethical to test experimentally. For example, it may be impractical to explore whether certain roads cause accidents or if smoking leads to cancer of the lungs.

Economics

In economics, a negative correlation is important in determining trends associated with inversely related variables. For instance, consumption rates and unemployment rates can be used as variables to study economies and develop economic strategies. In a correlation between debts and growth/development, economists use the coefficient data to determine the limits to which governments and corporations can borrow money.

Related: Understanding How To Complete a Risk Analysis

Disadvantages of negative correlation

The following situations show the shortcomings of negative correlation:

Correlation does not imply causation

Even if the connection between two variables is strong, it's not enough to assume that one causes the other. For instance, if you find a negative correlation between watching football and performing better at it, you can't presume that they correlate. It may be the result of a peripheral variable such as practise. Likewise, a company that sells fast-moving consumer goods cannot totally point out consumer spending as the reason behind the change in its revenue earnings. Despite having shown a correlation, the company might have gathered more sales from newer products or expansion of its markets.

Correlation does not permit us to exceed specified data

Correlation is significant only with the values you have. For example, if using a phone for 25 minutes consumes 10% of its charge, it doesn't necessarily imply that it takes 250 minutes to drain the phone's battery. It's important to note that correlation only explores the two variations you have.

Correlation vs causation

Causation implies that one variable causes the other. The causing variable is an independent variable, while the result or the outcome is a dependent variable. When conducting experiments to determine causations, the independent variables are set aside and manipulated, and the changes in the outcome variables are observed. A correlation between variables does not automatically signify that the change in one variable causes the values of the other variable to change. Correlation does not equal causation but can identify the relationship between variables.

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