Discussion
The adjusted R2 is an adjustment in R for :
Answer: B
Adjusted R2 corrects for increasing regressors.
Ordinary \(R^{2}\) can only rise when a predictor is added, even a useless one, because each new variable soaks up some chance variance. The adjusted value penalises every added predictor:
\[ R^{2}_{adj} = 1 - (1 - R^{2}) \frac{n - 1}{n - k - 1} \]
It rises only if a new predictor improves the fit by more than chance would. Sample size enters the formula, but only through its ratio to the number of predictors; the adjustment exists because predictors are added. It has nothing to do with the scale of measurement, and Spearman's rank correlation is unrelated.
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