Assumptions and method

When to be cautious

An association is not proof of causation. This tool does not adjust for confounders or calculate a prediction interval.

Slope = Σ(x−x̄)(y−ȳ)/Σ(x−x̄)²

Test a scenario

Use your own inputs

Inputs stay in your browser. Shared scenario links include your inputs.

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
  1. The means of x and y are 2.5 and 5. Cross-deviations sum to 7; squared x deviations sum to 5.
  2. 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.

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