STEYX Function (Gnumeric)

STEYX returns the standard error of the predicted Y value in a simple linear regression. More concretely, it estimates the residual spread of observations around the least-squares straight line. Its unit is the same as Y: if Y measures assessment points, a value of 0.80 means residual scale of roughly 0.80 points, not 80% and not the uncertainty of a single slope estimate. It is useful for comparing how closely two similarly measured datasets follow a straight line, but it is not by itself a confidence interval for a future prediction. Gnumeric’s Statistics manual documents the function and required argument order. [S1]

=STEYX(known_ys,known_xs)

Two aligned lists are required. Put Y first. There is no documented optional confidence_level or Boolean argument, and STEYX does not predict Y at a new X; the latter requires a model or a prediction function. [S1]

Enter the values below as numbers, not text. Row 1 consists of labels; exclude row 1 from every formula. Each row is one observation, so a sort must move its X and Y cells together. Column C is an ideal straight line; column D is reverse-ranked X for additional comparisons.

Use the ranges A2:A6 for X, B2:B6 for observed Y, C2:C6 for a perfect linear Y of 2X+1, and D2:D6 for a perfect negative linear relationship with X. The entries in C and D are fixed input numbers for this reproducible table; they are not outputs from an application session. This is a small instructional dataset, not an empirical or predictive validation study.

For independent checking, the five observations have n = 5, mean(X) = 3, mean(Y) = 4, Σ(X−3)² = 10, Σ(Y−4)² = 10, and Σ(X−3)(Y−4) = 9. Consequently the best-fit line is Ŷ = 1.3 + 0.9X, the Pearson correlation is 0.9, and its square is 0.81. The residual sum of squares is 1.9. All example outputs below were independently calculated in Python and cross-checked algebraically, not observed in Gnumeric.

Calculate the first result independently:

Slope m = 0.9; intercept b = 1.3
X:                1     2     3     4     5
Observed Y:       2     3     5     4     6
Fitted Ŷ:        2.2   3.1   4.0   4.9   5.8
Residual Y−Ŷ:   −0.2  −0.1   1.0  −0.9   0.2
Residual²:       0.04  0.01  1.00  0.81  0.04
Residual sum of squares (SSE) = 1.90
n = 5 numeric pairs; fitted parameters = 2 (slope + intercept)
Residual degrees of freedom = n − 2 = 3
Residual standard error = √(SSE/(n−2))
                        = √(1.9/3)
                        ≈ 0.7958224257542215

The conventional degrees-of-freedom correction n−2 is important: dividing by n or n−1 would compute a different measure. A high RSQ does not guarantee tiny STEYX: residual scale depends on the measurement units and magnitude of Y.

Put =SLOPE($B$2:$B$6,$A$2:$A$6) into H2 (expected 0.9) and =INTERCEPT($B$2:$B$6,$A$2:$A$6) into H3 (expected 1.3). In E2, enter the fitted value and fill through E6:

=$H$2*A2+$H$3

In F2, enter the error (=B2-E2), then fill F2:F6. Use a separate audit cell:

=SQRT(SUMSQ(F2:F6)/(COUNT(A2:A6)-2))

Expected: approximately 0.7958224258, matching =STEYX(B2:B6,A2:A6) for the clean numeric dataset. This comparison uses a conventional residual-error formula and Gnumeric-documented building blocks; we did not execute either formula in Gnumeric. A common spreadsheet mistake is forgetting to use $ in the fixed training ranges when copying formulas; do not let the H2/H3 references shift.

To compare two groups with different score scales, do not automatically conclude that the group with lower STEYX has the better model. Compare like measurement units, similar targets, number of observations, and the pattern of residuals. To estimate an individual student’s future score, build a prediction interval rather than treating ±1×STEYX as a guaranteed bound.

Exact-release source note: The official 1.12.62 source archive was checksum-verified. In src/collect.c, these paired-range functions receive GNM_ERROR_VALUE as the fallback: no accepted pairs, unequal collected lengths and failed numeric callbacks therefore follow a #VALUE! source path. Some manual entries instead name #N/A or #DIV/0 for empty/mismatched/constant inputs. Those manual tokens below are documentation claims, not confirmed runtime outcomes; the actual installed build was not executed.

• #N/A: the official STEYX entry specifies this when Y and X are empty or have different numbers of data arguments. This is a documented rule, not a claimed observed outcome of our non-executed examples.
• Insufficient usable pairs (n ≤ 2): residual degrees of freedom n−2 is zero or negative, so a residual standard error cannot be estimated in the usual way. The official entry does not specify a particular cell error string for every such dataset. Confirm Gnumeric’s actual display during native validation before adding one.
• Zero variance in X: no unique regression slope exists. The precise Gnumeric STEYX error string in this special case was not verified; avoid inventing 0 or a particular code.
• A surprising zero: if at least three valid data points fit a straight line perfectly, the mathematical STEYX is zero; however it says nothing about the reliability of extrapolating outside the observed X values.

• Order and pairing: the first vector of known_ys is the dependent Y variable, followed by known_xs (independent X); RSQ accepts first and second arrays and is symmetric for valid aligned numeric inputs. Select matching cell ranges representing the same rows. Do not independently sort just one column or silently shift one range.
• Numbers versus text: enter actual numeric cells. Labels must remain outside formula ranges. The official Statistics documentation does not specify every detail of coercion and alignment for each regression function; if you have text such as '5, blanks, TRUE/FALSE, errors, or mismatched shapes, clean or pair-filter the data and test the result in your installed Gnumeric. Do not assume such entries become zeros or new pairs by row position.
• Missing values: rather than filling blanks with zero or relying on unverified pair-omission semantics, build a contiguous two-column table of complete observations. Preserve each record’s identity during filtering and sorting; the apparent fit can change dramatically if pairs are misaligned.
• Mathematically undefined regressions: a zero-variance X vector contains no information about slope; constant Y makes some correlation calculations undefined. One or two valid observations are also insufficient for meaningful regression uncertainty. The exact displayed Gnumeric error is not assumed unless its official reference explicitly specifies it.
• Error-valued cells: upstream #VALUE!, #N/A, etc. can invalidate calculations. Repair the referenced inputs instead of wrapping the entire calculation in a blanket error replacement that might hide a damaged dataset.
• Decimal display and separators: these examples use English function names, a comma between arguments, and a period for decimal numbers, as illustrated in Gnumeric’s manual. Its locale is derived from the operating system. If your installed configuration differs, use the formula syntax and number formats accepted there; no alternate-locale parser was executed in this review. [S3]
• Rounded results: the decimal outputs below are display approximations from exact input integers. Use additional displayed precision to compare calculations; a tiny floating-point difference alone is not proof of changed statistical logic.

SLOPE describes estimated Y change per one X-unit (0.9 here), while INTERCEPT gives the zero-X constant (1.3). RSQ measures squared correlation (0.81, unitless), unlike STEYX (≈0.7958, measured in Y-units). PEARSON measures signed correlation (0.9). LINEST can provide richer regression statistics when called with appropriate options; it is a distinct function, separate from STEYX. [S1], [S5]

The Gnumeric 1.12-series Statistics manual lists this function by name and explicitly labels it Microsoft Excel compatible. That statement supports broad function-level compatibility; it is not a substitute for checking edge cases, function-name translation, type coercion, or file interchange in Excel or another spreadsheet. The current official GNU/GNOME 1.12 release archive identifies 1.12.62 dated 2026-09-21 as the latest release in the reviewed source series. It does not prove that the website manual has been regenerated for that exact binary build. [S1], [S4]

Platform and availability: Gnumeric is a GNOME-family spreadsheet application currently released and packaged for Linux; do not assume an up-to-date maintained Windows build or that a plugin is available in every distribution package. The official public function catalogue lists this function as Complete / Basic (registration/implementation and an upstream test classification), not as a native run of the worked examples on this page. [S2], [S4]

Validation limits: Exact official 1.12.62 source was checksum-verified and inspected, and all displayed numbers independently recalculated. No native Gnumeric execution, screenshots, locale regression or workbook round-trip tests were performed.

• [S1] Gnumeric Statistics manual: STEYX. Supports standard-error purpose, exact known_ys,known_xs syntax, official #N/A note and compatibility label. The displayed numerical formula is independently derived statistical mathematics, not quoted as a manual worked example.
• [S2] Gnumeric’s official public function catalogue. STEYX Complete / Basic reflects upstream classification only.
• [S3] Cell reference and formula entry plus localization settings.
• [S4] Official GNOME Gnumeric 1.12 release index: source release 1.12.62 dated 2026-09-21.
• [S5] Gnumeric SLOPE, INTERCEPT, RSQ, and LINEST official entries for related analysis.