Pearson correlation
The Pearson correlation coefficient measures how closely two variables move together in a linear relationship, as a single number between -1 and 1. This page shows the formula, what r² actually means, and why the tool refuses to return an r value when the data has no variation.
60% of y's variation is explained by the linear trend with x; the other 40% comes from scatter the line does not capture, like the point (4,4) that breaks the steady climb.
Flipping a rising trend into a falling one changes r's sign without changing its strength; covariance flips sign along with it because the product of deviations turns negative more often.
When y never varies (every point equals 5), the denominator in the r formula hits zero; the tool detects that division by zero and refuses to compute, instead of returning r=0.
Pearson's r measures the strength and direction of the linear relationship between two variables. It ranges from −1 to +1: values near ±1 indicate strong correlation; near 0 indicate weak or absent correlation.
It means there is no detectable linear relationship between them; two variables can have a strong but curved relationship (like y = x²) and still produce an r near zero, because the Pearson coefficient only picks up the linear component of the association.
Yes, and it is one of the most common risks: since r uses the sum of deviations from the mean, one point far removed from the rest can pull r from moderate to strong (or from weak to moderate) on its own, without the pattern in the rest of the data having changed.
Correlation measures statistical association, not mechanism; two variables can correlate by coincidence, through a third variable that influences both (a confounding variable), or through real causation, and the Pearson coefficient alone cannot tell these three possibilities apart.
With fewer than 2 points there is no way to compute a deviation from a statistically meaningful mean; the 200-point ceiling exists to keep manual entry practical, since the form accepts typed or pasted rows, not an external data file.
One x, y pair per line. Maximum 200 pairs.
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