INTERCEPT: Fit the Y-Axis Crossing in WPS Spreadsheet
Calculate a regression intercept with y-first argument order, complete paired inputs, exact and nonperfect fits, residual checks and extrapolation cautions.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
INTERCEPT returns the y-intercept of a fitted straight line from paired x and y observations. It estimates the line’s y value at x=0. It does not simply return the first y observation, and the order of its arguments matters.
Syntax and orientation
=INTERCEPT(known_y_values, known_x_values)
The dependent y values come first and the independent x values second. Keep each y paired with its corresponding x. The official formula image gives slope b as the centered cross-product sum divided by the x centered sum of squares, then intercept a as mean(y)−b×mean(x).
This fitted intercept is a property of the chosen straight-line model. When zero lies outside the observed x range, interpreting it as a real-world prediction requires an additional assumption that the linear relationship extends there.
Enter an exact-line example
Put x values 1,2,3 in A2:A4 and y values 3,5,7 in B2:B4. Enter =INTERCEPT(B2:B4,A2:A4). The means are 2 and 5, the centered cross-product sum is 4, and the x centered squared sum is 2. Thus b=4/2=2 and a=5−2×2=1.
The corresponding line is y=1+2x. Substituting x=1,2,3 reproduces 3,5,7, so all three independent residuals are zero. The intercept is 1 even though the first observed y is 3.
A nonperfect fit
Now replace the y values with 1,2,2, keeping x=1,2,3. The centered cross-product sum is 1 and the x squared sum is 2, giving slope 1/2. Mean y is 5/3, so the intercept is 5/3−(1/2)×2 = 2/3, approximately 0.666666666667.
Predicted y values are 7/6, 5/3 and 13/6. Observed-minus-predicted residuals are −1/6, 1/3 and −1/6; they sum to zero. Their squared sum is 1/6. These are independent checks of the ordinary least-squares arithmetic, not additional WPS executions.
Additional controls
For each replacement dataset, use the same formula with B as y and A as x.
| x values | y values | Expected intercept |
|---|---|---|
| 1, 2, 3 | 3, 5, 7 | 1 |
| 1, 2, 3 | 7, 5, 3 | 9 |
| 1, 2, 3 | 1, 2, 2 | 2/3 |
| −1, 0, 1 | 1, 0, 1 | 2/3 |
| 0, 1, 2 | 2, 4, 6 | 2 |
The nonlinear x² control has a horizontal fitted line at 2/3. That does not make the underlying relation linear. An intercept is not a complete description of model quality; inspect residuals and the data pattern.
Practical use and interpretation
For a hypothetical calibration where x is an applied setting and y is a response, the intercept describes the fitted baseline at setting zero. If all measurements were made at positive settings, the baseline is extrapolated. It is not automatically a measured offset or proof of a physical mechanism. Keep the units of y when reporting the intercept.
Errors and data quality
The lesson specifies #N/A when the two sets have unequal counts or contain no data points. It describes ignoring text, logical values and blanks in referenced arrays while including zero. The worked examples avoid incomplete pairs and do not establish every coercion or missing-value alignment rule.
A constant x set makes the slope denominator zero mathematically. The cited lesson does not establish the exact runtime error for every such case, so no additional error token is invented. Swapping the arguments fits x on y instead of y on x and should not be treated as a harmless reordering. Numeric stability for ill-scaled or extreme inputs remains unverified.
Availability and evidence
The official WPS lesson is dated 2019-06-10 and explicitly labels its applicability WPS Office for Windows Personal. It does not identify a numeric release. This establishes documentation by that date, not the function’s original introduction or its last working version. Current build limits and equivalence across WPS clients remain unverified. The available evidence does not establish retirement or formal deprecation.
Checked October 18, 2026. The examples in this guide are original, independently calculated controls based on the lesson. They have not been run in WPS or another spreadsheet application. No screenshot or execution result is claimed.