**Quartic regression** fits a quartic function (a polynomial function with degree 4) to a set of data. Quartic functions have the form:

**f(x) = ax ^{4} + bx^{3} + cx^{2} + dx + e.**

For example:

f(x) = -.1072x^{4} + 13.2x^{3} – 380.1x^{2} – 154.2x + 998

The quartic function takes on a variety of shapes, with different inflection points (places where the function changes shape) and zero to many roots (places where the graph crosses the axis). For a > 0, three basic shapes are formed (graphed with Desmos.com):

## Why Use Quartic Regression?

Quartic regression is another option for finding a line of best fit for data; It fits just as well as a cubic regression function and may even provide a better fit.

When modeling the data, the **coefficient of determination** (R^{2}) will guide you when comparing different regression models (Aufmann & Nation, 2013). R-squared gives you the percentage variation in y explained by x-variables. The range is 0 to 1 (i.e. 0% to 100% of the variation in y can be explained by the x-variables). So when comparing models, the model with the higher R^{2} is the “better” model because it explains more variation in the model.

## How to Perform Quartic Regression on the TI 83

On the **TI-83,** follow the instructions for quadratic regression in the TI83 / TI89. The steps are exactly the same, except you choose #7 from the menu, instead of #5.

Note though, that you need at least five data points to fit a model to a quartic function.

## References

Aufmann, R. & Nation, R. Algebra & Trigonometry. Cengage Learning.

Hungerford, T. & Shaw, D. (2008). Contemporary Precalculus: A Graphing Approach. Cengage Learning.