Quadratic Regression Calculator
Fit a quadratic to observed X/Y pairs with a stable normalized least-squares calculation, residual table and fitted-value query.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Center and scale X, form a quadratic design and solve by twice-orthogonalized QR without normal equations.
Y ≈ aX²+bX+c; minimize Σ(observed Y−fitted Y)²
Worked example
Points (−2,9),(−1,2),(0,1),(1,6),(2,17) lie on Y=3X²+2X+1. The fitted value at X=3 is 34, with zero residual apart from floating-point rounding.
Assumptions and input details
4–500 complete pairs with coordinates up to 1e9 in magnitude. Need at least three independent X basis values and positive residual degrees of freedom. Coefficients are displayed in original units, while queries use the normalized basis. R² is undefined for constant Y. Fit quality is in-sample; no coefficient inference, prediction interval, causal interpretation or future validation is supplied.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Fit y=a+bx to 2–100 entered coordinate pairs. Inspect the regression equation, correlation, R², predictions, residuals and a scatter plot.
Fit positive y data to y=A exp(Bx) or y=A x^B by least squares after a logarithmic transformation. Inspect predictions and residuals on the original scale.
Fit an intercept and two to five numeric predictors, inspect original-unit coefficients and evaluate a predictor query.
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