CORREL Function (OpenOffice Calc)

• Introduced: First release not established. The OpenOffice.org 3.3 appendix documents CORREL; that is historical presence evidence.
• Supported in: Apache OpenOffice 4.1.16; no final supported release established.
• Scope: Desktop Calc. Formulas below use English names and semicolon argument separators, with complete numeric example ranges.
• Checked: October 14, 2026. The eight reference formulas were recalculated in Apache OpenOffice 4.1.16 on Linux x86-64, Build 9816, using XLSX import and hard recalculation. Source and independent arithmetic were also checked.

CORREL measures the direction and strength of linear association between paired observations. Its mathematical range is −1 through 1. Positive values describe an increasing linear association, negative values a decreasing one, and values near zero weak linear association. Function entry.

=CORREL(Data1; Data2)

Exactly two arrays are required, with identical row and column dimensions. A row vector and a column vector of the same length are still different shapes. Keep paired observations aligned; dropping a value from only one side changes the relationship being analyzed. The release calculation logic is the authority for these contracts.

Enter this compact set of numeric observations starting in row 4. Column D is Y shifted by 10; C and E are exact straight-line transformations of X. Keep these labels outside the formula ranges.

These eight formulas were recalculated in Apache OpenOffice 4.1.16 on Linux x86-64, Build 9816, after XLSX import. Saved ODS values match independent arithmetic; results below are rounded to twelve decimal places.

For X in A4:A8 and Y in B4:B8, means are 3 and 4. The centered cross-product sum is 6, and the individual centered sums of squares are 10 and 6. Therefore r=6/SQRT(10×6), approximately 0.774596669241.

Put =CORREL(A4:A8;B4:B8) in a clearly labeled result cell. A scatter plot of these five pairs is a useful companion because the coefficient cannot reveal every pattern, individual outlier or separate cluster. Keep each X/Y pair on the same row.

Shifting Y by 10 leaves r unchanged, as columns B and D demonstrate. Multiplying one variable by a positive constant preserves r; a negative multiplier reverses its sign. Columns C and E show perfect negative and positive lines, returning −1 and 1.

Zero correlation does not imply independence. In a separate example X=−2,−1,0,1,2 and Y=X², the centered cross-product sum is 0 even though Y is completely determined by X. A straight-line summary misses that nonlinear relation. Correlation also does not by itself establish causality or a direction of prediction.

The source rejects a zero centered sum of squares in either variable with a division-by-zero error. One usable pair is therefore insufficient, and an all-constant variable has no defined Pearson coefficient. Shape mismatch is a separate invalid-argument condition. A numerical zero coefficient is not the same as an error.

The shared implementation calculates means first and then centered cross-products, avoiding the simplest raw-sum cancellation formula. That does not eliminate all floating-point limits for very large offsets or nearly constant data.

Selected boundary cases were checked in that same native session. Error displays are retained as errors, not interpreted as numeric zero.

• Function-specific 4.1.16 entry
• Shared evaluator and argument handling

The saved ODS retained the tested formulas and numeric inputs. A deliberately stale SUM result and an uncached SUM formula confirmed recalculation. Native evidence covers the eight reference formulas and listed boundary cases in the stated 4.1.16 build; other explanatory calculations are independent references. Other releases, locales and import formats were not tested.