Which one of the following is NOT one of the 4 specification criteria for determining whether a given variable belongs in a regression equation?

Question

BlackTom AI · Accepted Answer

To tackle this question, I’ll examine each proposed criterion for including a variable in a regression equation and determine whether it is a valid, or commonly used, specification criterion.
Option A: Is the variable's place in the equation theoretically sound?
This is a foundational criterion. If a variable has theoretical justification for its inclusion, it supports model specification and interpretability. Accepting this criterion aligns with sound regression practice, as theory guides which predictors belong in the model.
Option B: Is the variable's estimated coefficient significant in the expected direction?
Statistical significance and the direction of the effect are standard criteria for including variables. If a predictor’s coefficient is significant and aligns with theoretical expectations, it provides evidence that the variable meaningfully contributes to the model beyond random chance.
Option C: Does the overall fit of the equation (R^2) improve when the variable is added?
Model fit improvement is a common practical criterion. If adding the variable increases R^2 (or adjusted R^2 appropriately), it suggests the variable explains additional variance in the outcome beyond what the existing predictors capture, supporting its inclusion.
Option D: Do the coefficients of other variables change significantly when the variable is added?
This reflects a diagnostic concern: substantial changes in other coefficients may indicate issues like multicollinearity or model instability, which can influence whether a variable should be retained. While informative, this is more of a diagnostic side effect than a primary specification criterion, and some practitioners treat it as a supplementary check rather than a core criterion for inclusion.
Option E: Does the variable's inclusion reduce the total sum of squares (TSS)?
This statement is not a valid specification criterion. TSS is the total variability of the dependent variable around its mean and remains constant regardless of which predictors are included in the model. What changes with predictor inclusion is the regression (explained) sum of squares and the residual sum of squares; TSS itself does not get reduced by adding variables. Therefore, relying on TSS reduction as a decision rule for inclusion is incorrect.

Putting it together, Options A, B, C, and D describe reasonable (or at least informative) ways to assess whether a variable should be included in a regression model, whereas Option E describes a property (TSS) that does not change with predictor inclusion and is not used as a criterion for adding variables. Hence, the statement in Option E is not a valid specification criterion for inclusion.

Which one of the following is NOT one of the 4 specification criteria for determining whether a given variable belongs in a regression equation?Single choice

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