Cubic
A third-degree polynomial. Use it as an empirical curve for smooth data with up to two turns, such as a calibration curve that a quadratic cannot follow.
Fit the example dataStart with your own data
Example: simulated thermocouple voltage from 0 to 400 °C, 21 points with x and y uncertainties, opened as a new copy you can edit.
Parameters
- Coefficient of x³.
- Coefficient of x².
- Coefficient of x.
- Value of y at x = 0.
Tips
- Use the lowest degree that leaves no pattern in the residuals. AIC in Fit Statistics penalizes each extra coefficient, and Previous compares fits of the same data.
- Polynomial coefficients are usually strongly correlated, so a coefficient can have a large uncertainty even when the curve itself is well determined. The model uncertainty band shows how well the curve is determined.
- Avoid extrapolating: a polynomial can turn sharply just outside the fitted range.
- With no uncertainties selected, the goodness of fit is R², because the model is linear in its parameters.