A linear combination of inputs generates what score in predictive models?

In predictive modeling, a linear combination of inputs refers to a mathematical expression where different predictor variables (inputs) are multiplied by their corresponding coefficients and then summed to produce a single score. This approach is foundational in many statistical models, particularly in logistic regression and other classification algorithms.

The logit score specifically refers to the score computed from such a linear combination before it is transformed into a probability. In logistic regression, for example, the logit score is represented as the natural logarithm of the odds of the positive outcome. The formula can be expressed as:

[ \text{Logit Score} = \beta_0 + \beta_1 X_1 + \beta_2 X_2 + ... + \beta_n X_n ]

where (\beta_0) is the intercept and (\beta_1, \beta_2, ..., \beta_n) are the coefficients for each predictor variable (X_1, X_2, ..., X_n). This score is crucial as it allows the model to predict the probability of a particular class or outcome occurring based on the inputs provided.

This understanding is essential for constructing and interpreting predictive models in SAS Enterprise Miner, where these scores form the basis for making informed predictions