Inverse Relationship

What is Inverse Relationship?

Definition: An inverse relationship is identified between two variables, which are interrelated but the change of one causes the opposite change to the other.

What is the definition of inverse relationship? The inverse relationship is also known as negative correlation in regression analysis; this means that when one variable increases, the other variable decreases, and vice versa. A typical example of this type of relationship is between interest rates and consumer spending.

When the interest rates increase, consumers are less willing to spend and more willing to save. Also, when unemployment increases, consumer spending decreases because people have less disposable income.

Inverse Relationship Graph

Two sets of data points can be plotted on a graph on an x and y-axis to check for correlation. This is called a scatter diagram, and it represents a visual way to check for a positive or negative correlation. The graph below illustrates a strong negative correlation between two sets of data points plotted on the graph.

Inverse Relationship Graph
Inverse Relationship Graph

Inverse Relationship Definition | Example

There are many real-life examples of inverse relationships. The speed of travel relative to travel time (the faster one travels from point to point B, the less travel time is required to arrive at point B from point A); current and resistance (the higher the resistance, the lower the current); savings and disposable income (the less the disposable income, the more the savings); government spending and unemployment rate (the higher the government spending, the lower the unemployment rate); unemployment rate and inflation (known as the Phillips Curve).

The Philips Curve is the most common example of a negative relationship. In fact, when the government spending increases, the unemployment rate decreases because more jobs are created. Following the higher government spending, employees are better compensated, which means that they have more money to spend. On the other hand, firms face higher compensation costs, which are passed to consumers through inflation. Hence, the lower the unemployment rate, the higher the inflation.

The negative relationship is portrayed as a downward sloping curve. The mathematical explanation is that if f(x) = x + 2 and y (x) = x -2, the relationship is inverse.

Also, f(x) = -x and f(x) = 1/x to eliminate a zero value.

Inverse Relationship
Inverse Relationship

What Is An Inverse Relationship

What Is an Inverse Correlation? An inverse correlation, also known as negative correlation, is a contrary relationship between two variables such that they move in opposite directions. For example, with variables A and B, as A increases, B decreases, and as A decreases, B increases. In statistical terminology, an inverse correlation is denoted by the correlation coefficient “r” having a value between -1 and 0, with r = -1 indicating perfect inverse correlation.

Direct Vs Inverse Relationship

Question from allison, a student:

A piece of string is cut into n pieces of equal lengths L
(1) does n vary directly or inversely with L


The relationship between two variables is a direct relationship if when one increases so does the other or as one decreases so does the other. The radius of a circle and its area are in a direct relationship since if I increase the radius the area increases also and if I decrease the radius the area decreases.

The relationship between two variables is an inverse relationship if when one increases the other decreases or as one decreases the other increases. A unit fraction is a fraction with 1 as the numerator and a positive integer as the denominator. The denominator of a unit fraction and the value of the fraction are in an inverse relationship. The larger the denominator the smaller fraction and the smaller the denominator the smaller the fraction.

Suppose you cut a piece of string into n pieces of equal length L. As n increases does L increase or decrease?

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