What is quadratic regression?
Quadratic regression is a statistical method that fits a second-degree polynomial curve (a parabola) to a set of data points. The resulting equation takes the form Y = ax² + bx + c, where a, b, and c are constants determined to minimize the sum of squared differences between the observed and predicted Y values. See also our Interpolation Calculator.
How does the quadratic regression calculator work?
The calculator uses the method of least squares to find the coefficients a, b, and c that best fit your data. It sets up a system of normal equations using sums of powers of X and solves a 3×3 linear system. The result is the parabola that minimizes total squared error across all your data points.
How do I use the quadratic regression calculator?
Enter your X values in the first field and your corresponding Y values in the second field, both separated by commas. Make sure the number of X and Y values match. The calculator will immediately display the equation coefficients a, b, c, the R² value, and a table of fitted vs. actual values.
When should quadratic regression be used?
Quadratic regression is best when your data follows a curved, parabolic trend rather than a straight line — for example, projectile motion, profit optimization, or any phenomenon that rises and then falls (or vice versa). If a scatter plot of your data looks like a U-shape or an inverted U, quadratic regression is a strong candidate. You might also find our calculate Quartic Regression R² (Goodness of Fit) useful.
What does R² mean in quadratic regression?
R² (the coefficient of determination) measures how well the fitted parabola explains the variability in your Y data. A value of 1.0 means a perfect fit, while 0.0 means the model explains none of the variance. Generally, R² above 0.9 indicates a strong fit for most practical applications.
What is the difference between linear and quadratic regression?
Linear regression fits a straight line (Y = mx + b) and assumes a constant rate of change. Quadratic regression fits a curved parabola (Y = ax² + bx + c) and captures non-linear relationships where the rate of change itself increases or decreases. If your data curves, quadratic regression will produce a much better fit than linear regression.
What are the advantages and disadvantages of quadratic regression?
Advantages include the ability to model curved, non-linear data that linear regression cannot capture, and relative simplicity compared to higher-degree polynomials. Disadvantages include potential overfitting with small datasets, sensitivity to outliers, and the risk of extrapolating wildly outside the range of your input data.
How many data points do I need for quadratic regression?
You need at least 3 data points to uniquely determine the three coefficients a, b, and c. However, for statistically meaningful results, using 6 or more data points is strongly recommended. More data points generally lead to a more reliable and stable regression equation. Check out our Predicted Y (Ŷ₀) — Prediction Interval as well.