An analytics team is evaluating three nested multiple linear regression models to predict annual energy consumption (kWh) for office buildings. The validation-set summary is:
Hardware constraints limit the production model to the smallest set of predictors that still yields clear performance gains. Which single performance metric from the table gives the most defensible basis for deciding which model best achieves this balance?
Adjusted R² modifies the ordinary R² by incorporating both sample size and the number of predictors, so it rises only when additional variables reduce the residual variance more than would be expected by chance. It therefore rewards genuine improvement while penalizing unnecessary complexity. In the table, Model 2 attains the highest adjusted R², indicating the best trade-off between parsimony and predictive power. Plain R² and RMSE both improve (or stay nearly the same) as more predictors are added, so they cannot flag overfitting. The F-statistic p-value only tests whether each model outperforms an intercept-only model; because all three p-values are identical, it offers no guidance for choosing among the competing models.
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Why is adjusted R² preferred over plain R² in model comparison?
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What is the role of RMSE in evaluating regression models?
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Why can't the F-statistic p-value guide model selection in this case?