SLOPE in Excel: Regression Rate of Change and Paired-Data Checks

• Introduced: first introduction version is not established by the reviewed official history; the current product list is not a launch record.
• Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
• Checked: October 14, 2026; official SLOPE reference. Documentation and independent models; no native Excel execution or wider platform certification.

=SLOPE(known_ys,known_xs)

Both series are required. Microsoft says text, logical values and empty cells in arrays or references are ignored, while numeric zeros are included. The examples use complete paired numeric rows so that mismatched missing positions do not introduce an unverified inclusion policy.

Empty series or differing data-point counts produce documented #N/A. Microsoft also shows that constant X=1 paired with Y=0 produces #DIV/0!, and warns that LINEST can behave differently on underdetermined data. A similar goal does not make those algorithms interchangeable in every case.

Enter this table in A1:B5:

=SLOPE(B2:B5,A2:A5)

Expected result: 1.8. X has mean 2.5 and Y has mean 4. The paired products of deviations are 3,1,0.5,4.5, totaling 9. Squared X deviations total 5. The documented slope equation gives 9/5=1.8.

This fitted slope is not the endpoint slope (7-2)/(4-1)=5/3. Regression uses all four pairs, so reducing the dataset to its first and last points answers a different question.

INTERCEPT gives -0.5 for these data. The line is therefore Y=-0.5+1.8*X.

Put =INTERCEPT($B$2:$B$5,$A$2:$A$5)+SLOPE($B$2:$B$5,$A$2:$A$5)*A2 in C2 and fill through C5. Expected fitted values are 1.3,3.1,4.9,6.7.

The line need not pass through every observed point. Its residuals, observed minus fitted, are 0.7,-1.1,0.1,0.3. A regression slope summarizes a fitted relationship rather than a rule that every adjacent pair must satisfy.

=SLOPE(A2:A5,B2:B5)

Expected result: 0.5. The centered-product total is still 9, but the denominator is now the Y squared-deviation total 18.

The reciprocal of the original slope is 1/1.8=5/9, approximately 0.555556, not 0.5. Fitting X from Y and fitting Y from X minimize different residual directions. Do not reverse a predictive model merely by swapping the function arguments and assuming an inverse.

Multiply every Y by ten, producing 20,20,50,70. Expected slope becomes 18. Multiply every X by ten instead, producing 10,20,30,40, and the slope becomes 0.18.

Adding 100 to every Y leaves the slope at 1.8, because deviations from the Y mean are unchanged. Negating Y gives slope -1.8. A unit change can alter the slope even when the dimensionless linear correlation magnitude is unchanged.

Reverse both columns together and the slope stays 1.8. Sorting only one column may create different pairs; preserve an observation identifier and sort complete records.

For a perfect line with Y 5,8,11,14 at X 1,2,3,4, the slope is 3. This is an arithmetic control, not proof that future observations will follow the same line.

The dedicated reference’s array/reference type rules do not settle every mixed-error or nonaligned-missingness case. Direct argument coercion and extreme-magnitude numerical stability remain outside these controls. RSQ and STEYX describe different aspects of fit; none by itself proves a causal relationship.

• Microsoft SLOPE reference.
• Editorial testing standards.

Expected outputs are independent mathematical calculations or explicitly documented rules, not captured native Excel results. Examples use fictional data, English function names and comma separators. Native floating-point boundaries remain untested.