What are the two main methods of cross-validation in regression?

What are the two main methods of cross-validation in regression?

• A. Data smoothing
• B. Adjusted R2 or data splitting
• C. Bootstrap resampling
• D. Split-half reliability

Answer: (B)

Assessing how well a regression model will predict new data is the goal of cross-validation. One way to do this is by holding out part of the data to train the model on the rest and then test its predictive accuracy on the held-out portion. This data-splitting approach gives a direct estimate of how the model is likely to perform on unseen data, especially when you use a separate test set or apply methods like k-fold cross-validation to average results across multiple splits. The other approach here uses adjusted R-squared. As you add predictors, the regular R-squared value tends to rise even if those predictors don’t truly help, which can mislead about generalizability. Adjusted R-squared corrects for the number of predictors, so it provides a more honest comparison of models with different complexities. A higher adjusted R-squared suggests the model generalizes better to new data, serving as a way to compare models without relying on a separate validation set in some contexts. Data smoothing, bootstrap resampling, and split-half reliability aren’t cross-validation methods in this regression sense: smoothing is about reducing noise, bootstrap is a resampling method for estimating accuracy (not the same as validating predictive performance on unseen data), and split-half reliability relates to the consistency of measurement, not model prediction.

Assessing how well a regression model will predict new data is the goal of cross-validation. One way to do this is by holding out part of the data to train the model on the rest and then test its predictive accuracy on the held-out portion. This data-splitting approach gives a direct estimate of how the model is likely to perform on unseen data, especially when you use a separate test set or apply methods like k-fold cross-validation to average results across multiple splits.

The other approach here uses adjusted R-squared. As you add predictors, the regular R-squared value tends to rise even if those predictors don’t truly help, which can mislead about generalizability. Adjusted R-squared corrects for the number of predictors, so it provides a more honest comparison of models with different complexities. A higher adjusted R-squared suggests the model generalizes better to new data, serving as a way to compare models without relying on a separate validation set in some contexts.

Data smoothing, bootstrap resampling, and split-half reliability aren’t cross-validation methods in this regression sense: smoothing is about reducing noise, bootstrap is a resampling method for estimating accuracy (not the same as validating predictive performance on unseen data), and split-half reliability relates to the consistency of measurement, not model prediction.