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# Polynomial Trending Definition

## What Is Polynomial Trending?

Polynomial trending describes a pattern in data that is curved or breaks from a straight linear trend. It often occurs in a large set of data that contains many fluctuations. As more data becomes available, the trends often become less linear, and a polynomial trend takes its place. Graphs with curved trend lines are generally used to show a polynomial trend.

Data that is polynomial in nature is described generally by:

﻿ \begin{aligned} &y = a + x^n \\ &\textbf{where:}\\ &a = \text{the intercept}\\ &x = \text{the explanatory variable}\\ &n = \text{the nature of the polynomial (e.g. squared, cubed, etc.)}\\ \end{aligned}﻿

## Understanding Polynomial Trending

Big data and statistical analytics are becoming more commonplace and easy to use; many statistical packages now regularly include polynomial trend lines as part of their analysis. When graphing variables, analysts these days generally use one of six common trend lines or regressions to describe their data. These graphs include:

Each of these parameters has different benefits based on the properties of the underlying data. In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences. They are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science.

They are also used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra and algebraic geometry.

## Real-World Example of Polynomial Trending Data

For example, polynomial trending would be apparent on the graph that shows the relationship between the profit of a new product and the number of years the product has been available. The trend would likely rise near the beginning of the graph, peak in the middle and then trend downward near the end. If the company revamps the product late in its life cycle, we'd expect to see this trend repeat itself.

This type of chart, which would have several waves on the graph, would be deemed to be a polynomial trend. An example of such polynomial trending can be seen in the example chart below:

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