The formulas
- Slope b = sum((x - mean x)(y - mean y)) / sum((x - mean x)^2); intercept a = mean y - b x mean x
- Expected = a + b x current driver
- Standard error s = sqrt(SSE / (n - 2)), n = 6
- Interval = expected +/- t x s x sqrt(1 + 1/n + (x0 - mean x)^2 / Sxx), t with 4 degrees of freedom: 2.132 (90%) or 2.776 (95%)
How it works
Regression turns past periods into an expectation with a measurable precision. The prediction interval is the range a new observation falls in at the chosen confidence if the relationship holds. A recorded balance outside the interval is a difference the model cannot explain.
Six points is a small base, which widens the interval. Use periods from before the period under audit, check the R squared, and look at the residuals for a trend. A driver that management controls, or that is itself unaudited, weakens the evidence.
Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
Can I use monthly data?
Yes. Six recent months against a seventh is a common setup, and monthly data usually gives a more precise expectation than annual data.
What R squared is good enough?
There is no fixed cutoff. A low R squared shows up as a wide interval, which is the number that matters.
Why is the interval wider than the standard error?
It covers both the scatter of a single observation and the uncertainty in the fitted line, which grows as the current driver moves away from the past average.
Formulas on this page are the standard definitions.
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