Which of the following statements is correct?

Question

BlackTom AI · Accepted Answer

The question asks which statement among the options is correct, so I will examine each choice in turn before drawing any overall conclusion.
Option a: 'The score in the linear discriminant model can lie outside the zero-one interval.' In linear discriminant analysis, the discriminant scores are real-valued linear combinations of the input features. These scores are not constrained to the [0, 1] interval because they are not probabilities themselves; they are inputs to a thresholding rule or probability mapping. Therefore, it is indeed possible for a discriminant score to take values outside the zero-one interval. This makes the statement plausible and consistent with how LDA scoring works.
Option b: 'According to the Altman linear discriminant model, an increase in the retained earnings leads to an increase in the default probability.' In Altman’s framework, retained earnings (typically reflected in a component like retained earnings/total assets) contribute positively to the Z-score, which is interpreted as a lower default probability when the Z-score is higher. Thus, an increase in retained earnings would generally decrease default probability, not increase it. This makes the statement incorrect.
Option c: 'The sign of the 'Working capital/Total assets ratio' on the z-score in the Altman linear discriminant model is negative.' In the classic Altman Z-score (and its linear discriminant formulations used in credit risk), the working capital to total assets ratio (X1) carries a positive coefficient (e.g., around +1.2). A positive coefficient means the sign on this ratio is positive in contributing to the score. Therefore, stating that the sign is negative contradicts the model’s typical specification and is incorrect.
Option d: 'None of the other statements is correct.' Since the analysis above indicates that option a is consistent with LDA scoring behavior, this option would be incorrect if a is indeed correct.
Overall, evaluating the statements shows that option a aligns with the nature of discriminant scores being real-valued and not bound to [0, 1], while options b and c conflict with the established interpretations of the Altman Z-score components, and option d claims nothing else is correct which would be false if a is correct.

Which of the following statements is correct?

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