Consider the following model:

True or false: this model is additive in the predictors.

Question

Consider the following model:

True or false:  this model is additive in the predictors.

BlackTom AI · Accepted Answer

The question asks us to evaluate whether a given model is additive in the predictors and to decide True or False.
Option 1: True. If a model were additive in the predictors, it would imply that the overall effect is a simple sum of the individual predictor effects, with no interactions or nonlinear cross-terms between predictors. This would mean altering one predictor changes the outcome by a constant amount, regardless of the values of other predictors. However, without seeing the specific model form or terms, assuming additivity may overlook possible interaction terms or nonlinear relationships that violate additivity.
Option 2: False. If the model is not additive in the predictors, then there are either interaction effects (where the effect of one predictor depends on the level of another) or nonlinear transformations of predictors that lead to a combined effect that is not simply the sum of individual effects. In many practical models, especially in education, economics, or biology, interactions are common, and thus non-additivity is a plausible characteristic.
To evaluate which option is correct, one would look for evidence of interactions or nonlinear terms in the model specification. If interaction terms like X1*X2, or nonlinear terms such as X1 squared, are present and contribute significantly, that indicates non-additivity, supporting the claim that the model is not additive. Conversely, a model that includes only main effects with no interaction or nonlinear terms would be additive.
If the model in question indeed contains interaction effects or nonlinear components, the statement that the model is additive would be incorrect. If, on the other hand, the model contains solely main effects and no interactions or nonlinearities, the statement would be correct. Since the provided answer indicates False, the expectation is that the model includes non-additive components such as interactions or nonlinearities.
Note: When evaluating such statements, it helps to examine the formal specification (the equation or terms) and, if available, tests for interactions (significant interaction terms) or assessments of model fit with and without interaction terms to determine additivity.

QBUS6810 (ND) Week 3 Quiz

Consider the following model: True or false: this model is additive in the predictors.

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