Explanation

The statement in Option A is actually false and represents the correct answer to this "EXCEPT" question.

Understanding Adjusted R²

Adjusted R² is a modified version of R² that accounts for the number of predictors in the model. The correct formula for adjusted R² is:

$\text{Adjusted } R^2 = 1 - (1 - R^2) \times \frac{n-1}{n-k-1}$

Where:

• $R^2$ is the coefficient of determination
• $n$ is the sample size
• $k$ is the number of independent variables

Why Option A is Incorrect

The formula given in Option A: $\text{Adjusted } R^2 = 1 - \frac{SSR}{TSS} \times \frac{n-1}{n-k-1}$

Is incorrect because:

1. $\frac{SSR}{TSS}$ represents $1 - R^2$ (not R² itself)
2. The correct adjustment should be applied to $1 - R^2$, not to $\frac{SSR}{TSS}$ directly

Key Properties of Adjusted R²

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

Since this is an "EXCEPT" question, we're looking for the false statement, which is Option A.