Forecasting techniques

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 $X$:

$$Y = a + bX$$

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:

$$Y = a + b_1 X_1 + b_2 X_2 + \ldots + b_n X_n$$

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.

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 $Y = a + bX$ by least squares (a is fixed cost, b is variable cost per driver unit); multiple regression fits $Y = a + b_1X_1 + b_2X_2 + \ldots + b_nX_n$
• 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 $\bar{T}_N = T_1 \cdot N^{\log_2 L}$.

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

• 1B3

Browse all free CMA Part 1 lessons or jump into free CMA Part 1 practice questions.