polynomial

(noun)

An expression consisting of a sum of a finite number of terms: each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

Related Terms

Examples of polynomial in the following topics:

  • Polynomial Regression

    • Polynomial regression is a higher order form of linear regression in which the relationship between the independent variable $x$ and the dependent variable $y$ is modeled as an $n$th order polynomial.
    • Polynomial regression models are usually fit using the method of least-squares.
    • More recently, the use of polynomial models has been complemented by other methods, with non-polynomial models having advantages for some classes of problems.
    • Although polynomial regression is technically a special case of multiple linear regression, the interpretation of a fitted polynomial regression model requires a somewhat different perspective.
    • Some of these methods make use of a localized form of classical polynomial regression.

  • Model Assumptions

    • This trick is used, for example, in polynomial regression, which uses linear regression to fit the response variable as an arbitrary polynomial function (up to a given rank) of a predictor variable.
    • In fact, models such as polynomial regression are often "too powerful" in that they tend to overfit the data.

  • Plotting Lines

    • Best-fit curves may vary from simple linear equations to more complex quadratic, polynomial, exponential, and periodic curves.

  • Box-Cox Transformations

    • This gives a rigorous explanation for Tukey's suggestion that the log transformation (which is not an example of a polynomial transformation) may be inserted at the value λ = 0.

  • Line of Best Fit

    • Trend lines typically are straight lines, although some variations use higher degree polynomials depending on the degree of curvature desired in the line.

  • Summation Notation

    • Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group.

  • Counting Rules and Techniques

    • Generating functions can be thought of as polynomials with infinitely many terms whose coefficients correspond to the terms of a sequence.

  • Tukey Ladder of Powers

    • You may be familiar with polynomial regression (a form of multiple regression) in which the simple linear model y = b0 + b1X is extended with terms such as b2x2 + b3x3 + b4x4.

  • Glossary

    • Polynomial regression is a form of multiple regression in which powers of a predictor variable instead of other predictor variables are used.