INTERCEPT Function (OpenOffice Calc)

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

INTERCEPT returns a in the fitted least-squares line y=a+b×x. It estimates the line’s response at x=0. Whether that point has a useful real-world interpretation depends on the predictor’s scale and whether zero is near the observed data. Function entry.

=INTERCEPT(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 slope is 0.6 and the means are 3 and 4. =INTERCEPT(B4:B8;A4:A8) gives 4−0.6×3=2.2.

Use it with =SLOPE(B4:B8;A4:A8) to reconstruct y=2.2+0.6×x. At the mean predictor value x=3, the fitted response is 4, equal to the mean response. This is an ordinary intercept-fitted least-squares property, not proof that the model is suitable.

Column D equals Y+10, so =INTERCEPT(D4:D8;A4:A8) is 12.2. The slope stays 0.6. If instead you center X by subtracting its mean 3 in a helper column, the intercept becomes 4, the mean response, while the fitted values remain unchanged.

Reversing response and predictor gives =INTERCEPT(A4:A8;B4:B8), which is −1. This is a different fitted regression, not merely an alternative arrangement of the same equation. Forcing the intercept to zero is also a different model and is not an option of this function.

A constant predictor has zero centered sum of squares, so the evaluator reports division by zero. A constant response with varying predictor is different: slope is 0 and intercept is the response constant. Empty data and mismatched shapes have separate checks. Do not replace a failed fit with a zero coefficient.

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.