STEYX in Google Sheets: Residual Scale and Transparent Regression Checks

• Introduced: first introduction date is not established by the reviewed official history; no desktop release number is inferred.
• Availability: documented in the rolling Google Sheets service; these examples use the web worksheet workflow.
• Checked: October 14, 2026; official STEYX reference. Documentation and independent models, with no native Sheets execution or wider client certification.

=STEYX(data_y,data_x)

Y comes first and X second. Both ranges are required. Google documents the statistical purpose and says text is ignored, but its compact page does not print the estimator equation or enumerate native errors.

The independent simple-regression model below is SQRT(residual_sum_of_squares/(n-2)), using a fitted slope and intercept and at least three complete numeric pairs. This labeled mathematical model is not a claim that an unobserved target-app calculation was executed.

Do not transfer Excel’s exact error labels or type matrix to Sheets. Missing observations in different rows require a deliberate pairing policy rather than separately compacting both columns.

Enter X 0,1,2,3,4 in A2:A6 and Y 1,2,4,4,4 in B2:B6:

=STEYX(B2:B6,A2:A6)

Expected result under the stated model: approximately 0.730296743. The means are X=2 and Y=3. Centered products total 8, and centered X squares total 10, so slope is 0.8 and intercept is 1.4.

The fitted line Y=1.4+0.8*X gives 1.4,2.2,3,3.8,4.6. Residuals are -0.4,-0.2,1,0.2,-0.6. Their squares 0.16,0.04,1,0.04,0.36 total 1.6.

With five pairs, the model divides by three and takes the square root: SQRT(1.6/3).

In C2 enter and fill through C6:

=INTERCEPT($B$2:$B$6,$A$2:$A$6)+SLOPE($B$2:$B$6,$A$2:$A$6)*A2

In D2 enter =B2-C2 and fill down. In E2 enter =D2^2 and fill down. =SUM(E2:E6) has expected value 1.6, and =SQRT(SUM(E2:E6)/3) reproduces the modeled standard error.

The fixed denominator three applies only to this five-pair fixture. A changed included count requires a fresh denominator and a review of the data policy.

Dividing the same squared-residual total by the number of pairs gives SQRT(1.6/5), approximately 0.565685425. That root-mean-square residual is different from the n-minus-two estimator used here.

The arithmetic difference is substantive, not a choice of cell formatting. Label the statistic and denominator when comparing two error summaries.

For a perfect line Y 2,5,8,11,14 at the same five X values, all residuals vanish and the independent model gives 0. An exact fit to these supplied points is not a promise of zero error on future measurements.

Add 100 to every original Y. The fitted intercept rises by 100, residuals stay the same, and expected error stays about 0.730296743.

Multiply original Y by ten instead. Residuals become -4,-2,10,2,-6, their squared total becomes 160, and expected error becomes approximately 7.302967433. Negating Y reverses residual signs while preserving their squared magnitude.

The error is measured in Y units, unlike a dimensionless correlation or percentage rank.

Repeat all five original paired records, giving ten rows. The fitted line stays unchanged; residual squared errors double to 3.2. The model denominator is now eight, giving SQRT(3.2/8), approximately 0.632455532.

The smaller number does not demonstrate improved measurement quality. The repeated records added no new independent information, yet the estimator sees a different row count.

STEYX takes no target-X argument, so it cannot by itself supply a different prediction interval for every future X. Such intervals require additional assumptions and calculations.

Constant X makes the fitted-slope denominator unavailable. Insufficient points, empty data, mixed errors, shape mismatches and extreme-magnitude stability remain native-test holds. SLOPE and INTERCEPT expose line coefficients, while RSQ describes a different normalized aspect of fit.

• Google STEYX reference.
• Editorial testing standards.

Examples use fictional data, English function names and comma separators. Expected outputs are independent mathematical calculations or explicitly documented rules, not native Sheets captures. Check the spreadsheet locale when reproducing punctuation-sensitive formulas.