Skip to content
Part BCSIR NET June 2025the-adjustment-divides-by-n-minus-k-minus-1-and-with-8-predictors-on-29-points-it-bites

The adjustment divides by n minus k minus 1 and with 8 predictors on 29 points it bites

Consider the multiple linear regression model yi=β0+β1x1i+⋯+β8x8i+εi,i=1,2,…,29y_{i} = \beta_{0} + \beta_{1}x_{1i} + \dots + \beta_{8}x_{8i} + \varepsilon_{i}, i = 1, 2, \dots, 29, where ε1,ε2,…,ε29\varepsilon_{1}, \varepsilon_{2}, \dots, \varepsilon_{29} are independent and identically normal distributed with mean 0 and variance σ2\sigma^{2}. Suppose the model is fitted using the method of least squares. If the calculated value of the F-statistic for testing the significance of regression is 2.50, then the possible values of R2R^{2} and Adjusted R2R^{2} are respectively

  1. A.0.30 and 0.10
  2. B.0.50 and 0.30✓ Correct
  3. C.0.50 and 0.16
  4. D.0.30 and −0.10

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 execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

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

Last revised . Found a mistake? Tell us — corrections are the fastest thing we act on.

ShareWhatsAppTelegram