STEYX in Calligra Sheets: Regression Standard Error Tutorial

STEYX calculates the standard error of the predicted y values for a straight-line regression, commonly called the residual standard error of the fitted line. It summarizes the typical vertical size of residuals in the units of y. Smaller values mean the observed y values lie closer to their fitted line for these sample data; zero means a perfect straight line in exact arithmetic. It is not the standard error of the slope and not, by itself, a forecast prediction interval.

=STEYX(B2:B6;A2:A6)

With the exact five-pair worksheet below, the independently calculated expected result is 0.948683298051. The computation was made independently, not by running Calligra Sheets. The function name and argument count are supported by the pinned Calligra 26.08.2 source; KDE’s XML defines the correct syntax even though its rendered handbook currently contains a separate display mistake.

=STEYX(y;x)

• y — required first argument: dependent numeric data points (a numeric range/array) in observation order.
• x — required second argument: corresponding independent numeric data points, paired row by row with y.
• Count: exactly two arguments in KDE’s 26.08.2 registration, accepting arrays; no optional arguments or defaults are registered.
• Expected output: a nonnegative numeric result where a straight-line regression is defined for sufficiently many valid points. It has the same physical unit as y, not x; multiplying y by 2 doubles the expected standard error.
• Statistical denominator: n−2 because an ordinary least-squares line with an intercept estimates two parameters (slope and intercept). At least three nondegenerate pairs are mathematically required to estimate residual standard error.

Documentation discrepancy: The rendered KDE handbook section titled STEYX currently prints SLOPE(y;x) in its syntax field. This is a documentation display defect, not evidence that the correct function is called SLOPE. The pinned KDE 26.08.2 XML explicitly names STEYX and gives STEYX(y;x); KDE’s registration and implementation also name STEYX. Use the XML/registration-supported name.

KDE’s formula-entry instructions show starting formulas with = and separating arguments using ;. A localized installation may use different numeric punctuation; locale-specific behavior was not executed here.

In a new sheet enter these exact numeric values. Row 1 is headings, and rows 2–6 contain five paired observations. The first series (column A) represents x, and column B represents y. Comparison columns are deliberate transformations that let you verify how regression scatter should change.

Steps: (1) type each heading and number into its specified cell; (2) choose a blank result cell such as K2; (3) enter the formula shown below, including = and the semicolon; (4) press Enter; (5) increase numeric decimal places if a rounded display hides differences; (6) repeat in a fresh result cell for each example. Do not put formula results within A2:I6 because that would overwrite input data. Do not sort only one column and lose the x/y pairing.

The values below were calculated from the mathematical regression definition and compared with the pinned C++ operation sequence. They are not native Calligra screenshots or execution results.

These examples intentionally avoid uncertain text and blank coercion. In a localized installation, the decimal literal 14.8 and argument separator may need local syntax. The source-level registration alone does not prove how a particular localized binary will parse them.

For the five original pairs, x̄ = 3, ȳ = 4.2, Sxx = Σ(x−x̄)² = 10, Sxy = Σ(x−x̄)(y−ȳ) = 11, and Syy = Σ(y−ȳ)² = 14.8. The least-squares slope is 1.1, and the intercept is 0.9. Fitted y values for x = 1,2,3,4,5 are 2, 3.1, 4.2, 5.3, 6.4.

Residuals (observed y minus fitted y) are 0, −0.1, 0.8, −1.3, 0.6. Their squared sum (SSE) is 2.7. With n = 5, two estimated line parameters mean n−2 = 3 remaining residual degrees of freedom:

SSE = 14.8 − 11²/10 = 2.7
STEYX expectation = SQRT(SSE/(5−2))
                  = SQRT(2.7/3)
                  = SQRT(0.9)
                  = 0.948683298051...

The pinned C++ func_steyx uses averages, a centered covariance-product sum, sums of squared deviations, and a denominator of n−2. That source structure supports the arithmetic for ordinary numeric inputs but is not proof of runtime errors or heterogeneous input rules.

Suppose A2:A6 are weeks 1–5 and B2:B6 are weekly sales. After reproducing the base data, place the following in unused cells (example location K2:K5):

K2: =SLOPE(B2:B6;A2:A6)
K3: =INTERCEPT(B2:B6;A2:A6)
K4: =STEYX(B2:B6;A2:A6)
K5: =RSQ(B2:B6;A2:A6)

The independent expectations are 1.1 (sales per week), 0.9 (intercept in sales units), 0.948683298051 (residual standard error in sales units) and 0.817567567568 (dimensionless r²).

Put =$K$2*A2+$K$3 in L2, copy it through L6, and put =B2-L2 in M2, copying it through M6. The resulting fitted values should mathematically be 2, 3.1, 4.2, 5.3, 6.4 and the residuals 0, −0.1, 0.8, −1.3, 0.6. The independent check =SUMSQ(M2:M6) should be 2.7 if the relevant Calligra functions behave as documented.

A forecast from the fitted equation at week 6 is 7.5 sales units, but STEYX = 0.9487 is not an automatic ±0.9487 prediction interval. Prediction intervals must also account for where the new x lies relative to the observed x values, parameter uncertainty, chosen confidence level and model assumptions. Correlation and a narrow-looking residual error do not show that a time-series trend will persist.

1. n fewer than 3: The standard formula divides SSE by n−2 and therefore is not defined as a regression residual standard error at n=2 (and inadequate at n<2). Notably, the inspected func_steyx C++ only has an explicit number < 1 guard, not a direct number < 3 guard. Do not infer the visible error string at two or one observations: downstream math can produce an internal arithmetic error, and native execution is required.
2. Unequal counted numeric observations: The pinned implementation checks whether calc->count(args[0]) equals calc->count(args[1]) and returns an internal Value::errorVALUE() if not. The GUI text and exact count/coercion behavior were not observed. For reliable teaching, use equal-length, fully numeric, row-aligned ranges.
3. Same count, different shape: A separate centered covariance helper checks array row/column dimensions. Do not assume differently shaped arrays work just because their scalar counts happen to match.
4. Constant x (H2:H6): A line slope cannot be estimated when every x is identical; Sxx=0. The inspected func_steyx has no explicit dedicated constant-x check in its own wrapper and performs division by its x-deviation term. Native error handling is unverified. Avoid relying on a display-specific code.
5. Perfect line or constant y: The residual standard error is mathematically zero when x varies and the response lies perfectly on an intercept-fitted line. Displayed tiny nonzero roundoff is possible; no native precision testing was done.
6. Text, logical values and blanks: A range containing them may change the count or calculation; the full installed evaluator’s coercion path was not exercised. Excel’s documented treatment cannot stand in for Calligra evidence.
7. Unexpectedly large result: Examine the underlying y unit (dollars versus thousands of dollars), pairing, outliers, and whether the relationship is curved. STEYX’s unit is the y unit.
8. Sample size and inferential claims: Only three pairs give one residual degree of freedom, making an uncertain estimate. This summary is in-sample and does not validate linearity, independent errors or stable future performance.

Troubleshooting checklist

First verify =STEYX(, not the wrongly printed SLOPE( in the handbook’s STEYX syntax display. Check two arguments in y-first, x-second order; ensure no range was sorted independently; ensure numeric cells with at least three valid paired observations and nonconstant x; confirm the semicolon convention supported by the active locale; and increase decimal display precision. If an error appears, recreate the explicit five-row all-numeric worksheet, compare to the independent arithmetic, and add actual data back gradually. Do not label an untested error #N/A, #DIV/0! or #VALUE! solely because Excel uses such errors.

KDE’s 26.08.2 release is dated October 8, 2026. KDE’s Calligra app listing includes Linux install avenues. The STEYX signature was checked in KDE’s version-pinned function XML and statistical C++ source, accessed 2026-10-13; it was not tested on Linux, Windows, macOS, a specific distribution package, or any particular locale. Source registration ≠ observed calculation in a running binary.

Microsoft Excel’s STEYX reference covers the same statistic with comma-separated English Excel arguments, and gives Excel-specific input and error behavior. That is a comparison only. No Microsoft behavior is presented as native Calligra evidence; no XLSX exchange, app-to-app formula import, text/blank handling parity, GUI error mapping or older-version compatibility was tested.

• KDE STEYX documentation, pinned statistical.xml and pinned statistical.cpp func_steyx.
• KDE SLOPE, INTERCEPT, RSQ, DEVSQ, COUNT, and SUMSQ explain related regression pieces.
• KDE formula-entry conventions; KDE Gear 26.08.2 release announcement; Microsoft Excel STEYX reference for comparison only.

October 13, 2026: KDE function help, Calligra 26.08.2 XML and registration/implementation, release and formula-entry documentation checked; arithmetic calculated independently. NOT EXECUTED: native Calligra application; locale variants; mixed-type/edge-case error displays; XLSX import/export.