What is a forecast model in the form of a quadratic equation called?

A forecast model in the form of a quadratic equation is referred to as a quadratic trend equation. This type of model captures relationships between a dependent variable and an independent variable based on a quadratic function, which is characterized by its parabolic shape. Quadratic equations typically take the form of (y = ax^2 + bx + c), where (a), (b), and (c) are constants.

Using a quadratic trend equation is particularly useful when the data exhibits a non-linear pattern, such as acceleration or deceleration in trends, which can’t be effectively modeled by linear equations. This approach allows forecasters to incorporate curvature into their predictions, thus providing a better fit for data that increases or decreases at varying rates over time.

The other options might refer to different types of models but do not apply specifically to a quadratic form. For example, an exponential trend equation models growth or decay in terms of a constant percentage change. A simple trend equation typically refers to a linear form, and a polynomial trend equation could encompass cubic or other higher-degree polynomials but does not specify that the model must be quadratic. Hence, the quadratic trend equation is the appropriate designation for a model expressed as a quadratic equation.