Fit non-linear curves to your data to capture complex trends.
Data Submission
Matrix Math
(XᵀX)β = Xᵀy
Using the normal equations to solve for the coefficients of the polynomial that minimizes the sum of squared residuals.
Regression Analysis
Goodness of Fit (R²)0.997499.7% of variance explained
Model Equation
y = 4.400 - 3.386x + 1.214x^2
Model ProfileQuadratic
Sample Volume5Pairs
Least Squares Optimization Active
About this calculator
Overview
Polynomial regression fits a non-linear relationship between the value of x and the corresponding conditional mean of y. It is useful when the data shows curved trends that simple linear regression cannot capture.
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Pro Tips
Start with a low order (1 or 2). Only increase it if the trend is clearly more complex.
Beware of 'Runge's Phenomenon'—high-order polynomials can oscillate wildly at the edges of your data.
Check the R² value: it tells you what percentage of the data's variance is explained by the model.
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Fun Facts
"A polynomial of order 1 is exactly the same as simple linear regression."
"As the order increases, the model can fit more complex shapes, but risk of 'overfitting' increases."
"Least squares optimization is used to find the coefficients that minimize the distance from every point to the curve."
