Quadratic Regression Calculator

Your details

Enter the x (independent) values separated by commas or spaces. You need at least 3 points.
Enter the y (dependent) values in the same order as the x values.
Number of decimal places shown in the coefficients and statistics.
Regression equationExcellent fit
y = 0.9714x² - 0.8371x + 1.8800

The best-fit quadratic equation y = ax^2 + bx + c

Coefficient a0.9714
Coefficient b-0.8371
Coefficient c1.88
R-squared0.9999
Vertex x0.4309
Vertex y1.6996
Data points used6
0.9999 R²
Poor fit<0.6Moderate fit0.6-0.8Good fit0.8-0.95Excellent fit0.95+

Best-fit equation: y = y = 0.9714x² - 0.8371x + 1.8800

  • The parabola opens upward (concave up), so it has a minimum at x = 0.4309, y = 1.6996.
  • R-squared is 0.9999, meaning the quadratic explains 100.0% of the variation in y - an excellent fit.
  • The quadratic term a = 0.9714 controls the curvature. Larger |a| means a sharper parabola.

Next stepUse the equation to predict y for a new x by substituting it in: y = ax^2 + bx + c. Verify the model by checking whether residuals are randomly scattered.

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