Quadratic Regression Calculator
Fit a quadratic curve to your data points using the least squares method. Enter summary statistics and get the equation y = ax² + bx + c, plus R-squared and predicted values.
Quadratic regression fits a second-degree polynomial to your data. It captures curved (parabolic) relationships that linear regression misses.
The Model: y = ax² + bx + c
The coefficients a, b, and c are found by solving the normal equations, which minimize the sum of squared residuals.
When to Use Quadratic Regression:
- Your scatter plot shows a curved pattern
- Linear regression gives a poor R² but the data clearly has a trend
- The relationship has a maximum or minimum (like projectile motion, revenue curves, or growth that levels off)
Interpreting the Coefficients:
- a > 0: Parabola opens upward (U-shaped)
- a < 0: Parabola opens downward (inverted U)
- b: Affects the tilt and position of the vertex
- c: The y-intercept (value of y when x = 0)
Required Summary Statistics: You need n, Σx, Σy, Σx², Σx³, Σx⁴, Σxy, Σx²y, and Σy². These can be computed from raw data in a spreadsheet.