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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 R2R^{2} and Rˉ2{\bar{R}}^{2}, respectively, denote the coefficient of determination and adjusted coefficient of determination. Which of the following statements are true?

  1. A.Rˉ2<R2{\bar{R}}^{2} < R^{2}✓ Correct
  2. B.R2R^{2} increases as the number of independent variables increase✓ Correct
  3. C.Rˉ2{\bar{R}}^{2} decreases as the number of independent variables increase
  4. D.Rˉ2>0{\bar{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, and why this one tests what the inference means.

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50 are analysed free — try those first.

The trap it tests

What the inference means

p-values, size, power and error types say specific things. This was not one of them.

Drill statements like this

Related counterexample: OLS is the BLUE in every linear model

More on this topic

The chapter behind this: Linear models, Gauss–Markov and ANOVA — free to read

From Linear Models and Multivariate › Gauss–Markov, regression, ANOVA basics

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