Paste two columns of paired data to instantly calculate Pearson's correlation coefficient (r) — with a live scatter plot, regression line, R-squared, and a plain-English interpretation of strength and direction.
Enter your values on the left, then press Calculate.
Eight days of temperature vs defect rate data. Enter the lab and find out whether the relationship is real — and how strong it is.
Use the calculator above to paste two columns of paired data and instantly calculate Pearson’s correlation coefficient (r), with a live scatter plot, regression line, R-squared and a plain-English interpretation of strength and direction. Correlation is the starting point for any data-driven hypothesis about cause and effect.
Correlation measures the strength and direction of a linear relationship between two variables. Pearson’s r ranges from −1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive). It does not prove causation — only that the two variables move together in a predictable way.
Pearson’s r = Σ((x−x̄)(y−ȳ)) ÷ √(Σ(x−x̄)² × Σ(y−ȳ)²). The calculator standardises both variables, then computes the average product of their deviations from the mean. R-squared (r²) is the proportion of variation in one variable explained by the other.
A QA team plots oven temperature against defect rate across 30 batches. Pearson’s r comes back at −0.78 — a strong negative correlation. R² = 0.61, meaning 61% of the variation in defects is associated with temperature variation.
The team has a credible hypothesis: holding temperature tighter should reduce defects. They follow up with a designed experiment to confirm causation. Correlation pointed them at the right variable; the DOE proved the relationship was causal, not coincidental.
Correlation tells improvement teams which variables to investigate further. A strong r between a process input and an output justifies a designed experiment; a weak r saves effort that would have been wasted.
Use correlation in DMAIC Analyse to screen candidate root causes before launching a full Designed Experiment. It is also the first tool in Measurement System Analysis and regression studies.
Correlation, regression, hypothesis testing and DOE form the analytical core of Six Sigma. Correlation screens; regression quantifies; hypothesis testing validates; DOE optimises.
When r is strong, follow up with a Designed Experiment to confirm causation. When r is weak, save the effort and screen other variables. Always plot the scatter — the number can lie, the picture rarely does.
Combine correlation with regression, hypothesis testing and DOE. The resources below help turn an exploratory r into a defensible improvement action.
It measures the strength and direction of a linear relationship between two variables. Values range from −1 (perfect negative) through 0 (no linear relationship) to +1 (perfect positive).
A common rule of thumb: |r| above 0.7 is strong, 0.4-0.7 is moderate, below 0.4 is weak. Context matters — in physics 0.95 is weak; in social science 0.4 is notable.
No. Correlation only tells you two variables move together. Causation requires further evidence — typically a designed experiment that manipulates one variable and measures the effect on the other.
R² is the square of the correlation coefficient. It represents the proportion of variation in one variable that is explained by the other. R² = 0.61 means 61% of the variation is shared.
When the relationship is non-linear (use Spearman’s rank or transform the data), when the data is ordinal or categorical (use chi-square or rank methods), or when the sample is too small (n < 20).
Want to know how correlation analysis fits into root cause identification? The Green Belt covers this in full.
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