In the field of public health, an example of a dependent variable could be diarrheal disease incidence among children under five years old, while the predictor variables could include access to clean water, nutritional status, breastfeeding practices, and sanitation facilities.
Relationship between predictors: Yes, these predictor variables are likely related to each other. For example, access to clean water is often linked to better sanitation facilities, and both can impact a child's nutritional status. Additionally, breastfeeding practices may be influenced by access to health education, which also ties into sanitation and water access.
Linear relationship: It is unlikely that the relationship between all pairs of predictors is purely linear. For example, the effect of sanitation on diarrheal disease incidence might follow a threshold, where improvements in sanitation beyond a certain point have diminishing returns. Similarly, the relationship between breastfeeding and health outcomes may be non-linear, where the first few months of exclusive breastfeeding have a significant impact, but the effect plateaus over time.
Disadvantages of ignoring other predictors: Examining each predictor variable in isolation could lead to misleading conclusions. For example, focusing solely on access to clean water while ignoring sanitation and nutrition could underestimate the complexity of factors contributing to diarrheal disease incidence. Interactions between predictors can provide a more holistic understanding of the problem and help design more effective interventions.