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?
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TTanishq
A
Coefficient of Determination = 0.50, Standard Error of the Estimate = 0.50
B
Coefficient of Determination = 0.80, Standard Error of the Estimate = 0.80
C
Coefficient of Determination = 0.80, Standard Error of the Estimate = 0.50
D
Coefficient of Determination = 0.25, Standard Error of the Estimate = 0.25
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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