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Least-Squares Regression Line — result sheet
Slope, intercept, and fitted equation for paired data.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: b = Sxy/Sxx; a = ybar - b*xbar.
The line minimizing squared vertical residuals. Slope is rise per x-unit; intercept is the fitted value at x = 0. Constant x lists have no defined line and are rejected.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- x values — Same count as y, up to 1,000 pairs.
- y values — Same count as x, same order.
Worked example
| Input | Value |
|---|---|
| x values | 1, 2, 3, 4 |
| y values | 3, 5, 7, 9 |
y-hat = 1 + 2x.
Assumptions and limits
- Paired lists, matching order, at least 2 pairs.
- Linearity assumed, not checked; no causation implied.
- At most 1,000 finite pairs.
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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