PEARSON in Collabora Office: Centered Correlation and the Curve Counterexample

• Introduced: original Collabora release and launch date are not established by the reviewed sources.
• Availability: currently documented in Collabora Office 26.04 desktop help.
• Platform scope: online and mobile deployments are not inferred from this desktop-help release.
• Checked: October 14, 2026. Function-specific documentation and independent calculations; no native Collabora execution.

=PEARSON(data1;data2)

Both arguments are required arrays or ranges. The dedicated Collabora source explicitly names the Pearson coefficient but does not provide a complete missing-data or native error specification.

The independent numeric model divides the sum of centered cross-products by the square root of the two centered sums of squares multiplied together. The worked data are complete numeric pairs; no implicit text removal or mismatched-pair policy is assumed.

Enter A1:B5:

=PEARSON(A2:A5;B2:B5)

Expected result: 0.8. The means are 2.5 and 6. Centered X differences are -1.5,-0.5,0.5,1.5; centered Y differences are -3,1,-1,3.

Paired products 4.5,-0.5,-0.5,4.5 total 8. X squares total 5, and Y squares total 20. Their product’s square root is 10, giving 8/10.

The negative middle contributions are visible even though the aggregate association is positive. A coefficient summarizes the complete centered pattern rather than demanding that every adjacent Y change follow X.

Negate every original Y. The independent coefficient becomes -0.8, because the cross-product total changes sign while squared totals do not.

Multiply each original Y by five and add 2 instead, giving 17,37,27,47. Expected correlation remains 0.8. The positive multiplier cancels during normalization, and the additive shift disappears during centering.

A slope would respond differently to these unit changes. SLOPE reports a fitted change in Y per X unit, while PEARSON remains dimensionless.

Use X -2,-1,0,1,2 and Y 4,1,0,1,4 in D2:E6:

=PEARSON(D2:D6;E2:E6)

Expected result: 0. The means are 0 and 2, and centered products are -4,1,0,-1,4, totaling zero. Both centered square totals are positive.

Yet every Y equals X squared exactly. Zero linear correlation does not establish independence or the absence of every possible relationship. Plot the paired values and consider the meaning of the variables before interpreting the coefficient.

Return to the primary four observations. Reversing both X and Y together preserves the same pairs and coefficient 0.8.

Sort Y alone into 3,5,7,9, while X remains 1,2,3,4. The altered data now lie exactly on Y=2×X+1 and have coefficient 1. That improvement is artificial: the row matching was changed.

Keep identifiers attached to both measurements. A spreadsheet function cannot infer that a seemingly tidy table now connects measurements from different records.

The coefficient’s square is 0.64, a separate quantity returned by RSQ for this numeric model. Squaring loses the sign: coefficients 0.8 and -0.8 both square to 0.64.

Swapping the two entire numeric series also preserves 0.8 in the Pearson model because its numerator and denominator are symmetric. That symmetry does not imply that a regression predicting Y from X is the inverse of a regression predicting X from Y.

A constant series makes the mathematical denominator zero. The compact Collabora section does not name its native error code, so none is certified here. Empty datasets, unequal dimensions, Boolean/text conversion, source errors and numerical extremes remain unverified.

CORREL also has current linear-correlation documentation. Similar mathematical purposes are not a blanket claim of identical invalid-input behavior or retirement of either name. A correlation by itself supplies no causal conclusion, significance level or forecast interval.

• Collabora Office 26.04: PEARSON.
• Editorial testing standards.

Complete function-specific documentation reviewed. Worked outputs are independent statistical models or explicitly documented rules, not application screenshots or native test results. Unverified type, error and numerical boundaries retain their stated scope.