A student wants to create a multiple regression model to predict the height of a child with the $x$ variables age, length of foot, and shoe size. Using logic, are any of the variables irrelevant, and, if so, which one(s)?

• A. All variables are relevant.
• B. Length of foot and shoe size.
• C. Shoe size.
• D. All variables are irrelevant.

Answer: (C)

Verified step by step guidance

1. Understand the goal: The student wants to predict a child's height using multiple regression with three predictor variables: age, length of foot, and shoe size.
2. Consider the relationship between each predictor and the response variable (height). Age is generally strongly related to height because children grow as they get older.
3. Length of foot is also logically related to height since taller children tend to have longer feet, making it a relevant predictor.
4. Shoe size, however, is closely related to length of foot and may not add unique information beyond what length of foot provides. This suggests shoe size could be redundant or irrelevant in the presence of length of foot.
5. Therefore, using logical reasoning, shoe size is likely the irrelevant variable because it does not provide additional predictive power beyond length of foot and age.