In logistic regression, the smaller the p-value for an independent variable, the more predictive power that variable has relative to the dependent variable.

• A. True
• B. False
• C. Not significant
• D. Unrelated

Answer: (A)

Statistical significance does not equal predictive power. In logistic regression, a small p-value for a coefficient means there is evidence the predictor is associated with the outcome (the coefficient is unlikely to be zero under the null). But this does not automatically translate into how much that predictor improves predictions on new data. Predictive power depends on effect size, variability, and how the predictor interacts with other variables, as well as sample size and multicollinearity. A variable can have a very small p-value yet add only a modest improvement to accuracy or AUC, especially if it’s highly correlated with others or its effect is small in practical terms. Conversely, a predictor with a less impressive p-value might still help the model’s predictive performance when combined with other features or through interactions. So the statement equating smaller p-values with greater predictive power is not always correct; p-values reflect significance, not direct predictive contribution.