I have a data set where one independent variable perfectly predicts the outcome. Specifically, age will perfectly predict if the user will buy the product.
However, I also have a number of other variables such as income, marital status, and gender.
When creating a model using a decision tree, it only uses the age variable and has 100% accuracy on the testing data.
I also tried logistic regression, which incorporates more variables. Though its accuracy is about 94%.
My question is how I should approach this issue? Should I just not use all of the other variables and only use age? Or should I use a seemingly less accurate model that uses more variables but is more flexible?
Update - some more information about data set.
My data is fictional with a size of 2,000. 950 people bought the product (represented as 1) and 1050 did not buy (represented as 0). My concern is that this problem seems too easy, the objective is to determine which variables should be looked at to determine if someone will buy a product. Seems suspiciously easy that it would only be one (age).