Statistics

Quadratic Regression Calculator

Fit a parabola y = ax^2 + bx + c to data points.

Calculated Output

a (x^2) 1

b (x) 0

c (constant) 1

Formula: Least squares fit of y = ax^2 + bx + c

Step-by-Step Breakdown

1. Values used:

2. x1 = 1

3. y1 = 2

4. x2 = 2

5. y2 = 5

6. x3 = 3

7. y3 = 10

8. x4 = 4

9. y4 = 17

10. x5 = 5

11. y5 = 26

12.

13. x1 x y1 = 1 x 2 = 2

14. a (x^2) = (x1 x y1) / x2 = 2 / 2 = 1

15. b (x) = 0

16. x1 x y1 = 1 x 2 = 2

17. c (constant) = (x1 x y1) / x2 = 2 / 2 = 1

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The math behind it

It solves the least-squares normal equations for a, b and c in y = ax^2 + bx + c. Leave a point at (0, 0) to ignore it.

Points on y = x^2 + 1 recover a = 1, b = 0, c = 1.

How many points do I need?

At least three; more points improve the fit.