What is an example of a negative relationship between two variables?

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In layperson’s terms, a negative correlation is a relationship between two variables. They are part of a function in which dependent and independent variables move in different directions regarding value. For example, if the independent variableIndependent variable is an object or a time period or a input value, changes to which are used to assess the impact on an output value (i.e. the end objective) that is measured in mathematical or statistical or financial modeling.read more increases, the dependent variable decreases, and vice versa.

Negative correlation can be described by the correlation coefficientCorrelation Coefficient, sometimes known as cross-correlation coefficient, is a statistical measure used to evaluate the strength of a relationship between 2 variables. Its values range from -1.0 (negative correlation) to +1.0 (positive correlation). read more when the value of this correlation is between 0 and -1. The amount of a perfect negative correlation is -1. The strength of the correlation between the variables can vary. For example, suppose two variables, x and y, correlate -0.8. It means as x increases by 1 unit, y will decrease by 0.8. Now, consider that the negative correlation between these variables is -0.1. In this case, every unit change in the value of the x variable will result in a difference of 0.1 unit only in the cost of variable y.

Understanding Negative Correlation

To understand the negative correlation better, we need to have a basic understanding of correlation. CorrelationCORREL function is a statistical function in Excel. The CORREL formula finds out the coefficient between two variables and returns the coefficient of array1 and array2. The correlation coefficient determines the relationship between the two properties.read more is a statistical tool that is a measure of the degree of relation between two different functions. For example, the weight and height of a person. Generally, as the height increases, the person’s value also increases. Therefore, it indicates a positive correlation between height and weight because as one variable increases, other variables also increase. But, the correlation is negative if the two variables move in opposite directions—for example, height from the seal level and temperature. As the height increases, the temperature decreases.

The formula gives correlation:

Here,

• r = correlation coefficient;
• = Mean of variable X;
•  = Mean of variable Y

Rearranging gives us this formula:

Correlation can take any value between -1 to 1. The negative sign indicates a negative correlation, while the positive sign indicates a positive correlation. Zero correlation means that there is no relationship between the two variables.

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Why Negative Correlation Matters?

• Portfolio Management: Correlation is widely used in the management of portfolios. Often, it is said that portfolios should be diverse. It should consist of multiple investments involving different risks and returns. If we have the same type of securities in our portfolio, any major event will impact not just one security but the whole portfolio. For that purpose, we find a correlation between the returns of securities. One should not purchase deposits with perfectly positive correlationsPositive Correlation occurs when two variables display mirror movements, fluctuating in the same direction, and are positively related. In layman's terms, if one variable increases by 10%, the other variable grows by 10% as well, and vice versa.read more together. Often, the stakes with negative correlations add to diversify the portfolio. Consider the above-discussed example of airline stocks and oil prices. If a portfolio has energy stocks, the management can consider buying airline stocks to hedge against the decline in oil prices.
• Economics: Many trends associated with economics involve negative correlation. This relationship between the movements can be helpful for matters relating to economic policies. For example, unemployment and consumer spending. As spending increases, unemployment decreases (generally).

Real-Life Examples of Negative Correlation

Practical Example of Negative Correlation

Suppose two stocks have provided the following returns annually in the period 2011-16:

Considering the stock returns of the first stock as variable ‘x’ and that of second stock as ‘y.’

Calculation of variable xy

Calculation of variable X2

Calculation of variable Y2

Sum

Calculation of Correlation coefficientCorrelation Coefficient, sometimes known as cross-correlation coefficient, is a statistical measure used to evaluate the strength of a relationship between 2 variables. Its values range from -1.0 (negative correlation) to +1.0 (positive correlation). read more (r)

• =((6*14311)-(247*376))/(((6*11409)-(247^2))^0.5*((6*247160-(376^2))^0.5)
• =Correlation Coefficient (r) = -0.97608

Refer to the Excel sheet given above for detailed calculations.

The negative value of the correlation coefficient shows that the variables are negatively correlated.

Conclusion

At times, other factors may cause the variables to behave in a particular manner. In the example discussed above, one can deduce that when x increases, y decreases. But it would be wrong to suppose that the rise in ‘x’ is causing the ‘y’ to decrease because both companies may be involved in entirely different businesses and impacted by different economic conditions.

Thus, one should use the correlations only to determine a cause. The executives can use it to understand the relationship between variables, such as market demand and consumer spending, that already exists as part of the analysis. But one should not use it to investigate the change in one variable due to other variables because multiple factors will always impact that relationship. For example, consumer spending in the market and the revenue of an FMCGFast-moving consumer goods (FMCG) are non-durable consumer goods that sell like hotcakes as they usually come with a low price and high usability. Their examples include toothpaste, ready-to-make food, soap, cookie, notebook, chocolate, etc.read more company. They may show a positive correlation, but that company’s revenue may increase because of some other reason, like the launch of a new product or expansion into an emerging economy.

Recommended Articles

This article is a guide to Negative Correlation and its definition. Here, we discuss how to interpret negative correlation, practical examples, and its usage in real life. You can learn more from the following statistics articles: –