Examples
Examples
Try the starting example
- Samples: x,y, one pair per line
- -1,1 0,0 1,1
- Polynomial degree, at most 8
- 2
- Positive weight for each sample
- 1,1,1
- Polynomial coefficients in ascending powers of x
- 0, 0, 1
- Fitted values at sample x coordinates
- 1, 0, 1
- Weighted residual sum of squares
- 0
- Condition estimate of scaled weighted design
- 3.225505
Try another scenario
- Samples: x,y, one pair per line
- -1,-1 0,1 1,3
- Polynomial degree, at most 8
- 1
- Positive weight for each sample
- 2,1,2
- Polynomial coefficients in ascending powers of x
- 1, 2
- Fitted values at sample x coordinates
- -1, 1, 3
- Weighted residual sum of squares
- 0
- Condition estimate of scaled weighted design
- 1.118034
Calculation method
Calculation method
Polynomial coefficients in ascending powers of x
Centre and scale x, solve weighted least squares by SVD, then convert coefficients back to ascending powers of original x.
Fitted values at sample x coordinates
Evaluate the stable centred/scaled fit at each sample.
Weighted residual sum of squares
Sum weight_i×(fit_i−observed_i)².
Condition estimate of scaled weighted design
Largest/smallest singular value of the weighted scaled Vandermonde design; reject relative rank below 1e-12.
Symbols and units
- a
- Samples: x,y, one pair per line
- b
- Polynomial degree, at most 8
- c
- Positive weight for each sample
Use the units shown. A list keeps the order in which you enter its values. The symbol ^ means “raised to the power of”.
Assumptions & limits
Assumptions & limits
- Weighted real least squares for degree 0–8 below the sample count, with positive matched weights. Large coordinate offsets can make the expanded x coefficients ill-conditioned even when the centred fit is stable. No statistical confidence interval is inferred. Double-precision results are approximate. Numeric tables use 12 significant digits and display components at roundoff scale (32 machine epsilons relative to their row or relevant calculation scale) as zero; scalar diagnostics retain full precision.
Are these inputs private?
These calculations run in your browser. A shared link contains the values you choose to share. Only questions submitted to the separate AI finder are sent to OpenAI.
Further reading
ml-matrix: numerical decompositions ↗
Background reading; this does not imply endorsement or independent review of SumFizz.