Quadratic Regression Calculator
Fit y = ax^2 + bx + c to your data points.
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Enter X values and Y values separated by commas or spaces. You need at least 3 data points for a quadratic fit. The calculator solves the normal equations using Cramer's rule to find the coefficients a, b, and c that minimize the sum of squared residuals.
The R-squared value indicates how well the parabola fits your data compared to just using the mean.
About Quadratic Regression
Quadratic regression fits a second-degree polynomial (parabola) to data. It is useful when the relationship between variables is curved but not exponential. Common applications include projectile motion, revenue optimization, and any phenomenon with a turning point (maximum or minimum). The vertex of the parabola occurs at x = -b/(2a).
Frequently Asked Questions
When should I use quadratic instead of linear regression?
Use quadratic regression when your data shows a curved pattern or when the linear R-squared is poor. If adding the quadratic term significantly improves R-squared, the extra complexity is justified.
How many data points do I need?
You need at least 3 points (one more than the degree of the polynomial). However, more points give more reliable estimates. For meaningful results, use 10 or more data points.
What does the sign of coefficient a indicate?
If a is positive, the parabola opens upward (U-shape) with a minimum. If a is negative, it opens downward (inverted U) with a maximum. The magnitude of a determines how steep the curve is.