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Quadratic Regression Calculator — result sheet
Fit a least-squares quadratic y=a+bx+cx² to paired data and evaluate the fitted equation at a target x.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Choose a,b,c to minimize Σ[yᵢ−(a+bxᵢ+cxᵢ²)]²; R²=1−SSE/SST.
The fit is quadratic in x but linear in its coefficients, so the normal equations can be solved directly from the entered pairs.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- X values — Comma-separated numeric values.
- Y values — Comma-separated numeric values matching X.
- Target x — minimum -1000000; maximum 1000000
Worked example
| Input | Value |
|---|---|
| X values | 0, 1, 2, 3, 4 |
| Y values | 1, 3, 7, 13, 21 |
| Target x | 5 |
Fit is y=1+1x+1x²; predicted y at x=5 is 31; R² = 1.
Assumptions and limits
- X and Y contain the same number of finite values and at least three independent design points.
- Least squares is sensitive to outliers and extrapolation beyond the observed X range.
- Residual independence, constant variance, and inferential intervals are not established by the fit alone.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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