Regression Calculator
Unweighted ordinary least-squares line with intercept, slope and R-squared. No causal or clinical inference.
In short
Unweighted ordinary least-squares line with intercept, slope and R-squared. No causal or clinical inference.
Formula: OLS y = a + bx; b = Σ((xᵢ − x̄)(yᵢ − ȳ)) ÷ Σ(xᵢ − x̄)²; a = ȳ − bx̄.
What this calculator does
Unweighted ordinary least-squares line with intercept, slope and R-squared. No causal or clinical inference. Formula, worked example, sources, FAQs and limitations included.
Use it to turn Observations, Paired response values y into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this statistics calculation.
Inputs and what they mean
- Observations
- — text value.
- Paired response values y
- — text value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
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.
Worked example
OLS slope
- x̄ = 2; ȳ = 5; Sxy = 4; Sxx = 2.
- Slope = 2, intercept = 1; y = 1 + 2x; R² = 1.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
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.
Reference: NIST
Last reviewed:
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.
Sources
Method based on NIST.
Cite this page
Free Calculator. (2026, October 23). Regression Calculator. https://freecalculator.tech/tools/linear-regression-calculator
"Regression Calculator." Free Calculator, 23 Oct. 2026, https://freecalculator.tech/tools/linear-regression-calculator.
Regression Calculator — Free Calculator, https://freecalculator.tech/tools/linear-regression-calculator
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