How are individual coefficients in logistic regression typically evaluated for significance?

How are individual coefficients in logistic regression typically evaluated for significance?

• A. Use p-values and a hypothesis test.
• B. Use adjusted R-squared.
• C. Use mean squared error.
• D. Use cross-validated accuracy.

Answer: (A)

Assessing whether an individual coefficient in logistic regression is meaningful relies on hypothesis testing that yields a p-value. The typical null hypothesis is that the coefficient equals zero, meaning the predictor has no effect on the log-odds of the outcome. Because logistic regression is estimated by maximum likelihood, we obtain standard errors for each coefficient and use a test statistic (often a Wald test: coefficient divided by its standard error, approximating a normal distribution in large samples) to determine how compatible the observed value is with zero. A small p-value indicates evidence that the predictor influences the log-odds, and therefore the outcome, after accounting for other variables. Sometimes a likelihood ratio test is used, comparing the model with the predictor to a model without it, which serves the same goal in a slightly different framework. Other options aren’t about testing a single coefficient. Adjusted R-squared summarizes explained variance in linear models and isn’t a standard measure for significance of individual predictors in logistic regression. Mean squared error is a prediction error metric used for regression tasks, not for testing coefficient significance in classification. Cross-validated accuracy assesses overall predictive performance of the model, not whether a particular coefficient differs from zero.

Assessing whether an individual coefficient in logistic regression is meaningful relies on hypothesis testing that yields a p-value. The typical null hypothesis is that the coefficient equals zero, meaning the predictor has no effect on the log-odds of the outcome. Because logistic regression is estimated by maximum likelihood, we obtain standard errors for each coefficient and use a test statistic (often a Wald test: coefficient divided by its standard error, approximating a normal distribution in large samples) to determine how compatible the observed value is with zero. A small p-value indicates evidence that the predictor influences the log-odds, and therefore the outcome, after accounting for other variables. Sometimes a likelihood ratio test is used, comparing the model with the predictor to a model without it, which serves the same goal in a slightly different framework.

Other options aren’t about testing a single coefficient. Adjusted R-squared summarizes explained variance in linear models and isn’t a standard measure for significance of individual predictors in logistic regression. Mean squared error is a prediction error metric used for regression tasks, not for testing coefficient significance in classification. Cross-validated accuracy assesses overall predictive performance of the model, not whether a particular coefficient differs from zero.