How do I interpret a simple linear regression output for CFA Level I?

Simple linear regression models the relationship between one dependent variable (Y) and one independent variable (X). The CFA exam expects you to interpret every component of a regression output.

The Model:

Y = b₀ + b₁X + ε

• b₀ (intercept): The predicted value of Y when X = 0
• b₁ (slope): The change in Y for a one-unit increase in X
• ε (error): The unexplained variation

Example Regression Output:

An analyst at Summit Research regresses monthly stock returns (Y) on monthly market returns (X) using 60 months of data:

R² = 0.454, F-statistic = 48.2

Interpreting each piece:

Intercept (0.30%): When the market return is 0%, this stock is expected to return 0.30% — this is the stock's alpha (excess return independent of the market).

Slope (1.25): For every 1% increase in market return, the stock return increases by 1.25%. In CAPM terms, this is the stock's beta — it's more volatile than the market.

t-Statistics and p-values:

• b₁ t-stat = 6.94 (p = 0.000): The market return is a highly significant predictor. We strongly reject H₀: b₁ = 0.
• b₀ t-stat = 2.00 (p = 0.050): The alpha is marginally significant at the 5% level.

R² (0.454): 45.4% of the variation in stock returns is explained by market returns. The remaining 54.6% is firm-specific (unsystematic) risk.

F-statistic (48.2): Tests overall model significance. For simple regression, F = t² of the slope coefficient (6.94² ≈ 48.2). Highly significant.

Prediction:

If the market returns 3% next month:

Ŷ = 0.30% + 1.25 x 3% = 0.30% + 3.75% = 4.05%

Exam tip: The exam will give you an output table and ask what happens to Y for a given change in X, whether the coefficients are significant, and what R² means. Always check the t-statistic against 2.0 (approximate critical value for large samples at 5%).

Master regression analysis in our CFA Level I Quantitative Methods course.