Regression input variables with missing values can cause problems such as biased predictions. Methods to _______________ these values include synthetic distributions, estimation, and tree algorithms.

The correct answer is "impute" because it specifically refers to the process of replacing missing values in a dataset with substituted values. In the context of regression analysis, having missing values can lead to biased predictions and can undermine the integrity of the model. Imputing missing values allows for a more complete dataset, enhancing the robustness of the analysis.

Common methods for imputation include synthetic distributions that generate plausible values based on existing data patterns, estimation techniques that predict missing values based on relationships within the dataset, and tree algorithms that can effectively handle missing data through their structure. By using imputation, one maintains as much of the dataset as possible while providing reasonable estimates for missing information, ultimately improving model performance.

Other methods listed, such as transforming or modifying data, do not specifically address missing values in the same way that imputation does. Eliminating missing values may seem intuitive, but it often leads to loss of valuable data that could inform the model, especially if the missingness is not random. Thus, imputation is the most appropriate term in this context.