# Quartic Regression Calculator

The quartic regression calculator applies a **4th-order polynomial model** to a set of x-y data. A higher-order polynomial is suitable when your data is more complicated than a cubic or quadratic equation can handle.

Read on to learn about:

- What is the quartic regression formula?
- How to use this quartic regression calculator.
- What is the difference between linear and polynomial regression?

## Quartic regression formula

The quartic regression formula is a 4th-order polynomial, similar to the standard quadratic equation, but the two additional terms: $x^3$ and $x^4$. Here is the general quartic formula:

Different complex lines with two turning points can be generated by changing the values $a_0$ through to $a_4$, an example of which is shown below.

To obtain the values of these coefficients, an algorithm **minimizes the difference** between each data point's y-value and the y-value given by the quartic formula.

How well a quartic model fits your data is determined by all the errors between the model and the data and is called R^{2}: For a perfect fit, R^{2} is equal to 1.

For more on the math behind quartic regression, please check out the polynomial regression calculator.

## How to use the quartic regression calculator

To get a quartic regression model for your dataset, type in the x and y coordinates of each point into the calculator. You will need to **enter at least 5 data points**, and the calculator can accept a maximum of 30 data points (x, y pairs).

The results section gives you all the coefficients of the quartic equation and how well the model fits the data.

You can use the `advanced mode`

of the calculator to change the precision of the coefficients.

## Other regression calculators

Here are some other polynomial-based regression calculators that you might find useful:

## FAQ

### What is a quartic function?

A quartic function is a **4th-order polynomial** consisting of five terms:

**y = a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀**

Such a function has three critical, or turning, points and four real roots (found at points where the function crosses the x-axis).

### What is the difference between linear and polynomial regression?

In linear regression, we assume that the data best fit a straight line. Polynomial regression uses higher-order x-axis terms so that we can model more complex data.

Generally, if you get a poor fit between data and model, try the next order of polynomial regression or another function (for example, the exponential function).

**y = a**

_{4}x^{4}+ a_{3}x^{3}+ a_{2}x^{2}+ a_{1}x + a_{0}