Which statement is not true about logistic regression?

Which statement is not true about logistic regression?

• A. A prediction estimate for the target variables is formed from a simple linear combination of the inputs.
• B. The model predicts the probability of a particular level of the target variable at the given values of the input variables.
• C. The logit link function is one of the most common ways to make predictions, because it makes it easy to interpret the model.
• D. Two ways to interpret a logistic regression model are an odds ratio and a doubling amount.

Answer: (A)

The statement that a prediction estimate for the target variable is formed from a simple linear combination of the inputs is misleading when discussing logistic regression. In logistic regression, although it starts with a linear combination of the input variables, the outcome is transformed using the logistic function, which maps this linear combination onto a probability scale between 0 and 1. Thus, while the prediction does involve input variables in a linear combination form, it specifically isn't just that; the logistic transformation is crucial in determining the probabilities associated with different levels of the target variable. The other statements rightly reflect key characteristics of logistic regression. For instance, logistic regression predicts the probability of a specific level of the target variable, typically when dealing with binary outcomes, based on the values of input variables. This is fundamentally different from predicting direct values, as seen in linear regression. Moreover, the logit link function, which is employed in logistic regression, enables probabilities to be converted through the logistic function, making it easier to interpret the relationship between inputs and the binary outcome such as odds ratios. The odds ratio and the concept of doubling provide valuable interpretations in the context of understanding how changes in predictors affect the likelihood of outcomes in logistic models.

The statement that a prediction estimate for the target variable is formed from a simple linear combination of the inputs is misleading when discussing logistic regression. In logistic regression, although it starts with a linear combination of the input variables, the outcome is transformed using the logistic function, which maps this linear combination onto a probability scale between 0 and 1. Thus, while the prediction does involve input variables in a linear combination form, it specifically isn't just that; the logistic transformation is crucial in determining the probabilities associated with different levels of the target variable.

The other statements rightly reflect key characteristics of logistic regression. For instance, logistic regression predicts the probability of a specific level of the target variable, typically when dealing with binary outcomes, based on the values of input variables. This is fundamentally different from predicting direct values, as seen in linear regression. Moreover, the logit link function, which is employed in logistic regression, enables probabilities to be converted through the logistic function, making it easier to interpret the relationship between inputs and the binary outcome such as odds ratios. The odds ratio and the concept of doubling provide valuable interpretations in the context of understanding how changes in predictors affect the likelihood of outcomes in logistic models.