Answer-first summary for fast verification
Answer: Coefficient of Determination = 0.80, Standard Error of the Estimate = 0.50
**Step-by-step calculation:** 1. **Calculate Total Sum of Squares (TSS):** TSS = ESS + SSR = 60 + 15 = 75 2. **Calculate Coefficient of Determination (R²):** R² = ESS / TSS = 60 / 75 = 0.80 3. **Calculate Standard Error of the Estimate (SEE):** SEE = √[SSR / (n - 2)] = √[15 / (62 - 2)] = √[15 / 60] = √0.25 = 0.50 **Key formulas:** - TSS = Σ(Y - Ȳ)² (Total variation) - ESS = Σ(Ŷ - Ȳ)² (Explained variation) - SSR = Σ(Y - Ŷ)² = Σ(ê)² (Unexplained variation/residuals) - R² = ESS / TSS = 1 - (SSR / TSS) - SEE = √[SSR / (n - k - 1)] where k = number of independent variables (here k = 1, so denominator = n - 2) **Verification:** - Option C matches our calculations: R² = 0.80 and SEE = 0.50 - The sample size of 62 observations gives us 60 degrees of freedom (n - 2 = 62 - 2 = 60) for the SEE calculation.
Author: Nikitesh Somanthe
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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.
If we're dealing with a sample size of 62 observations, determine the coefficient of determination and the standard error of the estimate, respectively.
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