Forecasting techniques | Free CMA Part 1 Lesson

A planner forecasting next quarter's overhead has three statistical tools on the shelf: regression, learning curves, and expected value. The exam tests which tool fits the data and what each result actually tells you.

Simple linear regression models a dependent variable $Y$ as a linear function of one driver $X$ :

$Y = a + b X$

In cost analysis, $Y$ is total cost, $X$ is the driver (machine hours, units), $a$ is fixed cost, and $b$ is variable cost per driver unit. Least squares finds $a$ and $b$ by minimizing squared deviations between actual and predicted $Y$ .

When several drivers influence cost, use multiple regression:

$Y = a + b_{1} X_{1} + b_{2} X_{2} + \dots + b_{n} X_{n}$

Each $b_{i}$ is the partial slope: the change in $Y$ per unit change in $X_{i}$ , holding others constant. This handles overhead that responds to both machine hours and setups.

KEY: Three statistics anchor regression interpretation: R², t-statistic, F-statistic.

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Common mistakes

Reading R² as a significance test. R² measures explanatory power, not coefficient significance. A high R² with a t-stat of 0.8 still means the slope is unreliable. Use t-stats for coefficients, F for the joint model.
Applying the cumulative average-time rate to the next unit. The 80% rate cuts the cumulative average, not the time for the next unit produced. Confusing this with the incremental unit-time model is the most-tested learning-curve trap.
Forgetting probabilities must sum to 1. A scenario list of 30% / 40% / 40% is internally inconsistent. Verify sum = 1.00 before computing EV.

Bottom line

Simple regression fits $Y = a + b X$ by least squares (a is fixed cost, b is variable cost per driver unit); multiple regression fits $Y = a + b_{1} X_{1} + b_{2} X_{2} + \dots + b_{n} X_{n}$
In multiple regression each coefficient is partial, measuring one driver's effect while holding the others constant
R² measures explanatory power (0 to 1); t-stat tests one coefficient; F-stat tests the joint model
Cumulative average-time learning curve: each doubling of cumulative units multiplies the cumulative average time per unit by the learning rate (80% curve cuts the average by 20% per doubling)

Exam shortcut

When a regression question gives R², slope, and intercept, apply the slope to the new X and add the intercept. R² is interpretive flavor; it rarely drives the numeric answer but often distinguishes the right interpretation from a distractor. When a learning-curve question lists cumulative units that double (1, 2, 4, 8, 16), multiply the cumulative average by the learning rate each doubling. For non-doubling units, use $T ˉ_{N} = T_{1} \cdot N^{l o g_{2} L}$ .

The full lesson (about 1,806 words, 12 min read) adds 2 worked examples, all 6 common mistakes, a self-check, free in the app.

Learning objectives

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