Answer: 0.78

## Explanation To calculate the adjusted R², we first need to find the regular R² and then apply the adjustment formula. ### Step 1: Calculate R² $$R^2 = 1 - \frac{SSR}{TSS} = 1 - \frac{100}{500} = 1 - 0.2 = 0.8$$ Where: - SSR (Sum of Squared Residuals) = 100 - TSS (Total Sum of Squares) = 500 ### Step 2: Calculate Adjusted R² $$\bar{R}^2 = 1 - \left(\frac{n - 1}{n - k - 1}\right)(1 - R^2)$$ Where: - n = number of observations = 50 - k = number of independent variables = 4 - R² = 0.8 $$\bar{R}^2 = 1 - \left(\frac{50 - 1}{50 - 4 - 1}\right)(1 - 0.8) = 1 - \left(\frac{49}{45}\right)(0.2) = 1 - (1.0889 \times 0.2) = 1 - 0.2178 = 0.7822 \approx 0.78$$ ### Why Adjusted R² is Lower - The adjusted R² penalizes for adding more independent variables - With 4 predictors and only 50 observations, there's a penalty for model complexity - The regular R² of 0.8 is adjusted downward to 0.78 to account for the number of predictors **Therefore, the correct answer is B: 0.78**

Author: Tanishq Prabhu