A model committee challenges an earnings forecast

Learning goals

• Use coefficients to produce a conditional forecast.
• Separate goodness of fit from valid statistical inference.

Draft · approximately 30 minutes, excluding further revision.

Case briefing

The fictional Lan River Research team models annual earnings growth in percentage points: ŷ = 1.5 + 0.8×sales growth − 0.3×financing cost. Both explanatory variables are also measured in percentage points. The sample contains 40 firms, includes an intercept, and reports R²=0.64. Forecast inputs are sales growth 5 and financing cost 2. Residual plots show a widening fan as firm size increases. The committee has not established causation or independence between firms.

The researcher proposes using ordinary homoskedastic standard errors, interpreting the sales coefficient as a guaranteed causal effect, and selecting a model solely because its in-sample R² exceeds a competitor’s. The committee asks for a conditional forecast, adjusted fit and a defensible next step. All figures are synthetic.

Analytical framework

Holding other regressors fixed is a model comparison, not evidence that the analyst can causally change one company’s outcome. Adjusted R² penalizes added regressors: 1−(1−R²)(n−1)/(n−k−1), with k excluding the intercept. A fan-shaped residual plot is consistent with heteroskedasticity; under suitable exogeneity assumptions OLS coefficients may remain unbiased while conventional standard errors become unreliable. Robust inference must still use an appropriate design; it does not cure omitted variables or dependence automatically.

Formula and assumptions

ŷ = b₀ + Σbⱼxⱼ; adjusted R² = 1−(1−R²)(n−1)/(n−k−1)

Build the committee response

1. Forecast = 1.5 + 0.8×5 − 0.3×2 = 4.9 percentage points. It is a conditional fitted value, not a prediction interval.
2. Adjusted R² = 1−0.36×39/37 = 0.62054. Compare models on the same dependent variable and sample; then test out of sample.
3. Investigate the variance pattern, exogeneity, dependence and economic specification before interpreting significance. Preserve the original data and record every model choice.

Errors to catch

• Treating conditional coefficients as proven causation.
• Using robust standard errors as a cure for every model problem.

Original knowledge check

Answer every question before checking. Review explanations after submitting; retry starts a new attempt.

Sources and coverage status

These original lessons are drafts. Public outlines are used to check scope; the official learning-outcome text and proprietary question banks are not reproduced here. Follow the source for exam-year requirements and updates.

• Reference · www.cfainstitute.org