Across both linear and logistic regression, smaller p-values indicate greater predictive usefulness.

• A. True
• B. False
• C. Sometimes
• D. Not applicable

Answer: (A)

P-values in linear and logistic regression test whether a predictor’s coefficient is significantly different from zero, signaling an association with the outcome after accounting for other variables. A small p-value means there is evidence that the predictor matters to the model, but it does not directly measure how much it improves predictions on new data. Predictive usefulness depends on how much unique information the predictor adds beyond others and on how well the model performs when predicting unseen observations, which is best assessed with cross-validated performance metrics (like RMSE for regression or AUC for classification). P-values are influenced by sample size and can be affected by multicollinearity, so a predictor can have a small p-value yet contribute little to predictive accuracy, or vice versa. In practice, rely on predictive performance rather than p-values alone to judge usefulness.