Explanation

The given formula for adjusted R² is incorrect.

Correct formula for adjusted R²: $\text{Adjusted } R^2 = 1 - \frac{SSR/(n-k-1)}{TSS/(n-1)}$

Where:

• SSR = Sum of Squared Residuals
• TSS = Total Sum of Squares
• n = number of observations
• k = number of independent variables

Alternative correct forms: $\text{Adjusted } R^2 = 1 - (1 - R^2) \times \frac{n-1}{n-k-1}$ $\text{Adjusted } R^2 = 1 - \frac{SSR}{TSS} \times \frac{n-1}{n-k-1}$

Why option A is false:

• The formula shows (SSR/TSS) multiplied by [(n-1)/(n-k-1)]
• But it should be 1 minus this product, not the product itself
• The correct form is: Adjusted R² = 1 - [(SSR/TSS) × (n-1)/(n-k-1)]

Key properties of adjusted R²:

• Penalizes for adding irrelevant variables
• Can be negative when model performs worse than the mean
• Always ≤ R²
• Increases only if new variable improves model more than expected by chance

Correct answer: A - This statement is false because the formula is incorrect.