# Regression Calculator

> Unweighted ordinary least-squares line with intercept, slope and R-squared. No causal or clinical inference.

Page: https://freecalculator.tech/tools/linear-regression-calculator
Last reviewed: 2026-10-23

## Formula

OLS y = a + bx; b = Σ((xᵢ − x̄)(yᵢ − ȳ)) ÷ Σ(xᵢ − x̄)²; a = ȳ − bx̄.

- Methodology type: scientific equation.
- Methodology: NIST straight-line least squares with an intercept, unweighted y-on-x fit.
- Descriptive line only. Inferential tests would require additional residual assumptions; x measurement error is not modeled.
- OLS y = a + bx; b = Σ((xᵢ − x̄)(yᵢ − ȳ)) ÷ Σ(xᵢ − x̄)²; a = ȳ − bx̄.
- Inputs used: Observations, Paired response values y.

## Inputs

- Observations
- Paired response values y

## Worked example: OLS slope

x̄ = 2; ȳ = 5; Sxy = 4; Sxx = 2. Slope = 2, intercept = 1; y = 1 + 2x; R² = 1.
1. x̄ = 2; ȳ = 5; Sxy = 4; Sxx = 2.
2. Slope = 2, intercept = 1; y = 1 + 2x; R² = 1.

## Common questions

### How are observations paired?

The first x is paired with the first y, and so on; the lists must have equal lengths. Check the formula, example, and limitations on this page before using the result for a real statistics decision.

### Does association prove causation?

No. Neither a regression line nor correlation establishes causation.

### Can I extrapolate?

The arithmetic can evaluate a line, but behavior outside the observed range is not validated by this tool. Check the formula, example, and limitations on this page before using the result for a real statistics decision.

### How do I use the Regression Calculator?

Enter the required values for Observations, Paired response values y. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.

### What formula does the Regression Calculator use?

OLS y = a + bx; b = Σ((xᵢ − x̄)(yᵢ − ȳ)) ÷ Σ(xᵢ − x̄)²; a = ȳ − bx̄. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.

### Can the Regression Calculator be used for exact decisions?

Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.

## Limitations and assumptions

- Unweighted simple linear regression with intercept only.
- No causal claim, multivariate fit, residual tests or prediction intervals.
- For education and operational analysis only. No diagnosis, treatment recommendations, prescribing, dosing instructions, or reimbursement entitlement. Scientific calculations require appropriate laboratory verification; operational estimates do not replace local clinical, safety or financial policies.
- The result depends on the values you enter for this regression calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- NIST — https://www.itl.nist.gov/div898/handbook/pmd/section1/pmd141.htm

## Cite this page

- APA: Free Calculator. (2026, October 23). Regression Calculator. https://freecalculator.tech/tools/linear-regression-calculator
- MLA: "Regression Calculator." Free Calculator, 23 Oct. 2026, https://freecalculator.tech/tools/linear-regression-calculator.
- Link: Regression Calculator — Free Calculator, https://freecalculator.tech/tools/linear-regression-calculator