Slope (Linear Regression)
Is the metric trending up or down over time?
Definition
Slope measures the average per-period change of a metric using ordinary least squares (OLS) linear regression. The X-axis is the array index (0, 1, 2, ...), treating each data point as an equally spaced time period.
Formula
Where
Interpretation
The slope is expressed in the same unit as the metric per year (%/yr for ratios, absolute/yr for amounts).
| Signal | Meaning |
|---|---|
| Slope > 0 | Metric is rising over time |
| Slope < 0 | Metric is declining over time |
| Slope ≈ 0 | No clear trend |
Caveats:
- Slope only captures linear trends — a parabolic trajectory (rise then fall) may have slope ≈ 0
- Small samples (3-5 years) make slopes unreliable — always check R² alongside
- Missing years in the data will shift indices and distort the slope
In Finsco
Used in all audit commands as part of the summary statistics table. The slope is always paired with R² to indicate trend reliability.
| Command | Metrics with Slope |
|---|---|
audit returns |
ROE, ROTE, ROA, ROIC |
audit moat |
Gross Margin, ROIC |
audit earning-quality |
Accruals, Cash Conv, FCF Conv |
audit debt-discipline |
D/E, D/EBITDA, Coverage, Net D/E |
audit capital-flow |
FCF Conv, CapEx Int, Payout/FCF |
Related Metrics
- R² — how reliable is this slope?
- Coefficient of Variation — stability metric (complementary to trend)