Answer-first summary for fast verification
Answer: Coefficient of Determination = 0.80, Standard Error of the Estimate = 0.50
## 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.
Author: Tanishq Prabhu
Ultimate access to all questions.
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 are dealing with a sample size of 62 observations, what is 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
No comments yet.