Assumptions and method
An association is not proof of causation. This tool does not adjust for confounders or calculate a prediction interval.
Test a scenario
Use the result in a decision
Understand the sampling design, units and distribution assumptions.
An association is not proof of causation. This tool does not adjust for confounders or calculate a prediction interval.
Set a baseline and change one assumption to compare outcomes.
A worked example
Follow the fixed teaching example
- The means of x and y are 2.5 and 5. Cross-deviations sum to 7; squared x deviations sum to 5.
- Slope = 7/5 = 1.4; intercept = 5 − 1.4×2.5 = 1.5. The fitted line describes association, not causation.
These illustrative inputs describe a project scenario, not a published benchmark. All monetary inputs use the same currency and price basis.
- One observation per row: x, y
- 1, 3 2, 4 3, 6 4, 7
- Pearson correlation
- 0.9899
- OLS slope
- 1.4
- Intercept
- 1.5
- R²
- 0.98
Interpret the output only within the assumptions above. Changing the inputs changes the result; it does not validate the inputs.
Source & credit
Standard mathematical statistics; the handbook is an authoritative technical reference, not a claim of sole origin.
NIST/SEMATECH: statistical methods
This is independently written code and explanation of the underlying method. The linked publication, its diagrams and its trademarks remain its owner’s material; no permission to reuse them is implied.