Part CCSIR NET June 2024adjusted-r-squared-can-rise-and-can-go-negative

Adjusted r squared can rise and can go negative

In a standard linear regression model, let $R^{2}$ and $\overset{ˉ}{R}^{2}$ , respectively, denote the coefficient of determination and adjusted coefficient of determination. Which of the following statements are true?

A. $\overset{ˉ}{R}^{2} < R^{2}$ ✓
B. $R^{2}$ increases as the number of independent variables increase✓
C. $\overset{ˉ}{R}^{2}$ decreases as the number of independent variables increase
D. $\overset{ˉ}{R}^{2} > 0$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward.

See pricing

50 are analysed free — try those first.

Related counterexample: OLS is the BLUE in every linear model

Adjusted r squared can rise and can go negative

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