Which of the following statements regarding qualitative predictors is false?

The assertion that categorical variables can take an unlimited number of different values is indeed misleading, which makes it the false statement in the context of qualitative predictors. Categorical variables are defined as those that can take on a limited number of values, representing distinct categories or groups. For instance, a variable that indicates the type of fruit (such as apple, banana, or cherry) can only take these defined values, and thus they are limited.

In contrast, qualitative predictors, or categorical variables, can be further divided into nominal and ordinal types depending on whether the categories have a natural order. Therefore, the core classification of categorical variables fundamentally supports the notion that they do not span an infinite spectrum of values, affirming the truth of the correct answer being false as presented. This understanding is crucial for statistical modeling, where categorization plays a significant role in how data is analyzed and interpreted.