Question

If our model of a dummy dependent variable produces a proportionate reduction of error equal to 0.75, which of the following is true?

a) The model is 75% accurate.
b) The model explains 75% of the variation in the dependent variable.
c) The model reduces the error by 75% compared to a baseline model.
d) The model has a 75% probability of prediction success.

Answer 1

A model with a proportionate reduction of error of 0.75 reduces the error by 75% compared to a baseline model, which is option (c) in the provided choices.

Step-by-step explanation:

If our model of a dummy dependent variable produces a proportionate reduction of error equal to 0.75, it means that the model reduces the error by 75% compared to a baseline model. To clarify, option (c) 'The model reduces the error by 75% compared to a baseline model.' is the correct interpretation of proportionate reduction of error. This measure is also known by its acronym, PRE, and is a way of comparing the accuracy of a model against a simple baseline or null model.

The other options listed do not accurately describe the meaning of a proportionate reduction of error of 0.75. For example, 75% accuracy (option a) implies the correctness of direct predictions, which is not directly indicated by PRE. Option (b) would relate to a coefficient of determination (R-squared value) rather than PRE. The probability of prediction success (option d) cannot be inferred solely from PRE since it does not convey predictive certainty on individual outcomes.