a relationship in which a rise in the value of one variable is accompanied by a fall in the value of another.
Inverse Relationship Details
We represent inverse relationships by numbers known as correlation coefficients. A correlation coefficient is a statistical measure of the relationship between two variables, represented by any number between -1.0 and 1.0. In an inverse relationship, the variables have a negative correlation, where a coefficient of -1.0 indicates a perfect negative correlation.
However, it is important to note that correlation is not the same thing as causation. In an inverse relationship, the drop in variable B does not automatically cause the hike in variable A. For example, a website that derives random correlations shows that a yearly increase in the number of Internet users in Detroit came with an annual decrease in the city’s crime rate from 2001 to 2010.
We must remove the trend from the analysis to see if there is a causal relationship between the two variables. We can do this by analyzing the difference between two consecutive points for the two parameters: number of Internet users and crimes. If such differences are correlated, then there is likely a meaningful inverse relationship between the two variables. Otherwise, you can dismiss the correlation as coincidence.
Real-World Example of Inverse Relationship
We can find inverse relationships everywhere in day-to-day life. For example, let us consider the daily commute of one Mr. Vedder. The opposite dynamic between speed and time is why Mr. Vedder arrives to work earlier when he travels faster in his car. The greater his speed, the faster he reaches his office.
Such an inverse relationship between travel speed and travel time is also one example of an inverse relationship that is causal: the decrease in Mr. Vedder’s travel time directly results from the increase in his travel speed. Nonetheless, other causal inverse relationships can also exist in this scenario, such as that between travel speed and amount of traffic.
Perhaps the most common illustration of an inverse relationship is the Philips Curve. Created by economist A. W. Philips, the graph shows that inflation and unemployment have a constant negative correlation. Philips’ theory claims that inflation always accompanies economic growth, which, in turn, opens up more jobs and thus reduces unemployment.
Significance of Inverse Relationship
A good grasp of inverse relationships and correlation, in general, is important for various uses in different industries and fields. In education, for example, knowing the relationship between test scores and other performance metrics—whether correlations are positive or negative—helps teachers design the right teaching approach based on the learners’ capacity.
In the corporate world, psychological tests help human resource managers and employers understand workers’ behavior and performance. This increase in understanding, in turn, helps the company create more effective strategies that help it achieve its goals more efficiently.
In finance, understanding inverse relationships (and other meaningful relationships between specific parameters) is useful in managing risk and forecasting trends, and creating and pricing complex financial instruments, such as derivatives.