Financial Risk Manager Part 1

Financial Risk Manager Part 1

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Tom Well, FRM, works for a trading company. Using historical data, he has computed the following variables considering one independent and one dependent variable.

  • Explained Sum of Squares (ESS) = 60
  • Sum of Squared Residuals (SSR) = 15

If we are dealing with a sample size of 62 observations, what is the coefficient of determination and the standard error of the estimate, respectively?

TTanishq

Explanation:

Calculation Explanation

Step 1: Calculate Total Sum of Squares (TSS)

Total variation (TSS) = Explained variation (ESS) + Unexplained variation (SSR)
TSS = 60 + 15 = 75

Step 2: Calculate Coefficient of Determination (R²)

R² = ESS / TSS = 60 / 75 = 0.80

Step 3: Calculate Standard Error of the Estimate (SEE)

SEE = √(Unexplained variation / (n - 2)) = √(15 / (62 - 2)) = √(15 / 60) = √0.25 = 0.50

Final Answer

  • Coefficient of Determination = 0.80
  • Standard Error of the Estimate = 0.50

Key Formulas:

  • Total Sum of Squares (TSS) = Σ(Y – Ŷ)²
  • Explained Sum of Squares (ESS) = Σ(Ŷ – Ȳ)²
  • Sum of Squared Residuals (SSR) = Σ(Y – Ŷ)² = Σ(ε)²
  • R² = ESS / TSS
  • SEE = √[Σ(Y – Ŷ)² / (n – 2)] = √[SSR / (n – 2)]

Therefore, the correct combination is Coefficient of Determination = 0.80 and Standard Error of the Estimate = 0.50.

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