How do I interpret regression output for CFA Level I? The R-squared, coefficients, and t-stats all blur together.

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AcadiFi · Accepted Answer

Regression analysis interpretation follows a logical sequence. Here is the framework I recommend for working through any regression output on the exam: ```mermaid graph TD A[Regression Output] --> B{Step 1: Check R-squared} B -->|High R2 > 0.7| C[Model explains most variation] B -->|Low R2 < 0.3| D[Model has weak explanatory power] A --> E{Step 2: F-test significant?} E -->|p < 0.05| F[Overall model is significant] E -->|p > 0.05| G[Model not significant - stop here] F --> H{Step 3: Check each coefficient} H --> I[t-stat > 2 or p < 0.05?] I -->|Yes| J[Coefficient is significant] I -->|No| K[Coefficient not significant] J --> L{Step 4: Interpret magnitude} L --> M[Slope = change in Y per unit change in X] ``` **Worked Example:** Mapleton Research runs a simple linear regression to predict quarterly revenue ($M) for Pinecrest Holdings based on advertising spend ($M): | Statistic | Value | |---|---| | Intercept (b0) | 12.40 | | Slope (b1) | 3.75 | | Std Error of b1 | 0.62 | | t-statistic for b1 | 6.05 | | R-squared | 0.72 | | F-statistic | 36.60 | | Observations | 16 | **Step-by-step interpretation:** **Step 1 — R-squared (0.72):** Advertising spend explains 72% of the variation in quarterly revenue. The remaining 28% is driven by other factors not in the model. **Step 2 — F-test (36.60):** With 1 and 14 degrees of freedom, the critical F-value at 5% is approximately 4.60. Since 36.60 >> 4.60, the overall model is statistically significant. **Step 3 — t-statistic for slope (6.05):** The critical t-value with 14 df at 5% (two-tailed) is approximately 2.145. Since 6.05 > 2.145, the slope coefficient is statistically significant — advertising spend has a real relationship with revenue. **Step 4 — Interpret the slope (3.75):** For every additional $1M spent on advertising, Pinecrest's quarterly revenue is predicted to increase by $3.75M, holding all else equal. **The regression equation:** Revenue = 12.40 + 3.75 x Advertising Spend **Prediction:** If Pinecrest spends $8M on advertising next quarter: Revenue = 12.40 + 3.75(8) = 12.40 + 30.00 = **$42.40M** **Key Concepts to Remember:** - **R-squared** measures goodness of fit (0 to 1). Higher is better but beware of overfitting. - **t-statistic** = coefficient / standard error. Tests whether the individual coefficient differs from zero. - **F-statistic** tests whether the model as a whole is significant (in simple regression, F = t-squared). - **Standard Error of Estimate (SEE)** measures the typical prediction error — lower is better. **Common Exam Traps:** 1. Confusing R-squared with correlation (r). In simple regression, R-squared = r-squared. If R-squared = 0.72, then r = sqrt(0.72) = 0.849. 2. Using regression outside the range of observed data (extrapolation) — the model may not hold. 3. Correlation does not imply causation — even if advertising and revenue are correlated, other factors may drive both. Practice interpreting regression tables in our CFA Level I Quantitative Methods question bank.

How do I interpret regression output for CFA Level I? The R-squared, coefficients, and t-stats all blur together.

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