How this calculator works
The ordinary least-squares line is ŷ=a+bx, with slope based on paired deviations.
Formula
ŷ=a+bx; b=Σ((x−x̄)(y−ȳ))/Σ((x−x̄)²); a=ȳ−bx̄Fits the ordinary least-squares line of y on x.
Worked example
Line through doubled values is a verified test case used by the calculation engine.
Assumptions and limitations
- Datasets are paired and equal length.
- At least two observations are required.
- X cannot be constant.
- Regression describes the supplied data and does not establish causation.
Methodology & sources
This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.
- CalcuMint deterministic statistics engine
Frequently asked questions
What does R² represent?
R² is the squared Pearson correlation for this simple linear regression and summarizes the proportion of linear variation explained by the fitted line.
Can regression prove causation?
No. A fitted relationship does not by itself establish a causal relationship.