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 $y_{i} = β_{0} + β_{1} x_{1 i} + \dots + β_{8} x_{8 i} + ε_{i}, i = 1, 2, \dots, 29$ , where $ε_{1}, ε_{2}, \dots, ε_{29}$ are independent and identically normal distributed with mean 0 and variance $σ^{2}$ . 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 $R^{2}$ and Adjusted $R^{2}$ are respectively

A.0.30 and 0.10
B.0.50 and 0.30✓
C.0.50 and 0.16
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

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

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