STEYX Function (OpenOffice Calc)

• Introduced: First release not established. The OpenOffice.org 3.3 appendix documents STEYX; 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.

STEYX estimates residual standard deviation around a simple least-squares regression line with an intercept. It uses the response values first, predictors second, and divides residual sum of squares by n−2 before taking the square root. Its units are response units. Function entry.

=STEYX(KnownY; KnownX)

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 first range is KnownY and the second KnownX; swapping them changes the fitted problem. 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, the fitted line is y=2.2+0.6×x. The five residuals are −0.8,0.6,1,−0.6,−0.2 and their squared sum is 2.4. With n=5, =STEYX(B4:B8;A4:A8) gives SQRT(2.4/3), approximately 0.894427191000.

This is not Y’s ordinary sample SD, approximately 1.224744871392, because the fitted line has removed its explained linear component. The regression estimates two coefficients, which is why the residual denominator is n−2 rather than n−1.

STEYX is not automatically the standard error of the fitted mean at any chosen x, nor a full prediction interval. Under the usual independent, equal-variance linear-error model, mean-response SE at x₀ is s×SQRT(1/n+(x₀−meanX)²/Sxx); a new-observation prediction SE adds 1 inside the square root.

At the sample mean x₀=3, this example has mean-response SE 0.4 and new-observation prediction SE approximately 0.979795897113. Constructing an interval additionally requires the chosen coverage and an appropriate t critical value with n−2 degrees of freedom. Diagnose the residual model rather than interpreting s alone as a 95% margin.

At least three usable pairs are required because two coefficients are fitted. A constant predictor causes division by zero. A constant response with varying predictor, or a perfect fitted line, can legitimately have zero residual spread. Extreme roundoff or ill-scaled data is not covered by the ordinary examples.

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.