Answer: 0.78

## Explanation **Step 1: Calculate R²** R² (coefficient of determination) is calculated as: $$R^2 = 1 - \frac{SSR}{TSS}$$ Where: - SSR = Sum of Square Residuals (error) = 100 - TSS = Total Sum of Squares = 500 $$R^2 = 1 - \frac{100}{500} = 1 - 0.2 = 0.8$$ **Step 2: Calculate Adjusted R²** The adjusted R² (denoted as $\bar{R}^2$) accounts for the number of independent variables and sample size. The formula is: $$\bar{R}^2 = 1 - \left(\frac{n - 1}{n - k - 1}\right)(1 - R^2)$$ Where: - n = number of observations = 50 months - k = number of independent variables = 4 - R² = 0.8 **Step 3: Plug in the values** $$\bar{R}^2 = 1 - \left(\frac{50 - 1}{50 - 4 - 1}\right)(1 - 0.8)$$ $$\bar{R}^2 = 1 - \left(\frac{49}{45}\right)(0.2)$$ $$\bar{R}^2 = 1 - \frac{49}{45} \times 0.2$$ $$\bar{R}^2 = 1 - \frac{9.8}{45}$$ $$\bar{R}^2 = 1 - 0.2178$$ $$\bar{R}^2 = 0.7822 \approx 0.78$$ **Why Adjusted R² is lower than R²:** The adjusted R² penalizes the model for having additional independent variables that don't significantly improve the model's explanatory power. Since we have 4 independent variables and only 50 observations, the adjustment factor $\frac{n-1}{n-k-1} = \frac{49}{45} \approx 1.089$ reduces the R² value. **Key Formulas:** 1. $R^2 = 1 - \frac{SSR}{TSS}$ 2. $\bar{R}^2 = 1 - \left(\frac{n-1}{n-k-1}\right)(1-R^2)$ **Answer: B (0.78)**

Author: Nikitesh Somanthe