Which two model selection criteria are commonly used for regressions?

Which two model selection criteria are commonly used for regressions?

• A. Adjusted R^2 and AIC/BIC
• B. p-values and confidence intervals
• C. F-statistic and t-statistics
• D. RMSE and MAE

Answer: (A)

Model selection in regression focuses on picking a model that explains the data well without being more complex than necessary. Adjusted R^2 improves on plain R^2 by penalizing adding predictors that don’t meaningfully boost fit, so it helps compare models with different numbers of variables. Information criteria like AIC and BIC combine a measure of fit with a penalty for model complexity; lower values indicate a better balance between accuracy and parsimony, with BIC applying a heavier penalty as sample size grows. These criteria are widely used to choose among candidate regression models. In contrast, p-values and confidence intervals concern the significance and uncertainty of individual coefficients, not overall model quality; the F-statistic and t-statistics are hypothesis tests on coefficients rather than global model selection; and RMSE/MAE measure predictive error but are not formal selection criteria on their own.

Model selection in regression focuses on picking a model that explains the data well without being more complex than necessary. Adjusted R^2 improves on plain R^2 by penalizing adding predictors that don’t meaningfully boost fit, so it helps compare models with different numbers of variables. Information criteria like AIC and BIC combine a measure of fit with a penalty for model complexity; lower values indicate a better balance between accuracy and parsimony, with BIC applying a heavier penalty as sample size grows. These criteria are widely used to choose among candidate regression models. In contrast, p-values and confidence intervals concern the significance and uncertainty of individual coefficients, not overall model quality; the F-statistic and t-statistics are hypothesis tests on coefficients rather than global model selection; and RMSE/MAE measure predictive error but are not formal selection criteria on their own.