Accuracy of Quadratic Regression

[Albert Chan]

(08-20-2023 05:07 PM)bernhardSA Wrote:  I am not sure if this is related to floating point accuracy

Yes, it is due to floating point precision. (HOME have only 12 decimals)



To solve for quadratic best fit, we need upto Σx²y (top-right, m=2)
Update: Worse, for quadratic fit, we need Σx⁴ (top-left, m=2)

Generalized mean, M4 ≥ M1

OP example, Σx⁴ ≥ ((2003+2012)/2)^4 * 10 ≈ 1.624E14      // 15 digits!

To get best fit coefficients, it may be better to reduce both x and y from its mean.

We can simply knock down year 2000, (2003 .. 2012) --> (3 .. 12)
APPS quadratic fits get Y = -5.4696969697*X^2+131.5*X+472.545454545

CAS> symb2poly(-5.4696969697*X^2+131.5*X+472.545454545 | X=x-2000

[−5.4696969697, 22010.2878788, −22141315.3333]

This matched Excel results, y = -5.46969697 x^2 + 22010.28788 x -22141315.33