Polynomial Regression Calculator
Fit a polynomial of degree 1 through 10 to your data.
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Request a ToolHow to Use the Polynomial Regression Calculator
Enter X and Y values separated by commas or spaces, then select the polynomial degree (2 through 10). You need more data points than the degree. The calculator solves the normal equations using Gaussian elimination to find the best-fit polynomial coefficients.
Start with a low degree and increase only if R-squared improves meaningfully. Higher degrees can overfit the data.
About Polynomial Regression
Polynomial regression extends linear regression by fitting a curve of the form y = c0 + c1*x + c2*x^2 + ... + cn*x^n. It can model complex non-linear relationships while still using the least squares framework. The trade-off is that higher-degree polynomials are more flexible but risk overfitting, especially with limited data.
Frequently Asked Questions
What degree should I use?
Start with the lowest degree that gives a good fit. A degree-2 (quadratic) or degree-3 (cubic) model handles most curved data. Higher degrees risk overfitting and producing wild predictions outside the data range.
What is overfitting?
Overfitting occurs when the model fits the noise in the data rather than the underlying pattern. A polynomial with too many terms will pass through every data point (R-squared = 1) but make poor predictions for new data.
How many data points do I need?
You need at least one more data point than the polynomial degree (e.g., at least 4 points for a cubic). For reliable results, have at least 3 to 5 times more data points than the degree.