Choose variables based on VIFj values. For a dataset with 4 independent variable, VIF1=1.54, VIF2=5.54, VIF3=7.89, VIF4=6.90, we should

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Choose variables based on VIFj values. For a dataset with 4 independent variable, VIF1=1.54, VIF2=5.54, VIF3=7.89, VIF4=6.90, we should

BlackTom AI · Accepted Answer

The question asks us to select variables based on VIFj values for a dataset with 4 independent variables, given VIFs: VIF1 = 1.54, VIF2 = 5.54, VIF3 = 7.89, VIF4 = 6.90.

First, recall the guiding rule of thumb for VIF in regression: a high VIF indicates multicollinearity, and variables with VIFs above a certain threshold warrant consideration for removal or further investigation. Common thresholds are VIF > 5 or VIF > 10, depending on the strictness of the analysis.

Looking at the values provided:
- X1 has VIF 1.54, which is well below typical concern levels, so it is generally considered safe from multicollinearity issues on its own.
- X2 has VIF 5.54, which exceeds 5 and thus signals potential collinearity with other predictors. It is a candidate for removal or transformation.
- X3 has VIF 7.89, clearly above 5 (and even above 7 in this case), indicating strong multicollinearity concerns. It should be a primary candidate for removal or adjustment.
- X4 has VIF 6.90, also above 5, suggesting multicollinearity problems as well. It is another strong candidate for action.

At this point, a typical approach would be to consider removing the predictor(s) with the highest VIFs first, often in an iterative fashion: remove one variable, refit the model, recompute VIFs, and repeat until all VIFs fall below the chosen threshold (commonly 5, or 10 if a more lenient criterion is used). In this scenario, X3 and X4 have the two highest VIFs and are both above 6–8, so they are prime targets. Depending on the research goal and theoretical considerations, one might remove X3 or X4 first (or possibly both), but removing at least X3 and/or X4 would typically be the course of action preceding any model kept with all four variables.

Regarding the specific answer given: delete X3. This option would reduce multicollinearity by removing one of the high-VIF predictors, but it does not address X2 and X4, which still have VIFs above 5. If the instruction is to reduce multicollinearity to acceptable levels with a minimal set of deletions, you would likely need to remove more than just X3 (for example, consider removing X3 and X4, or X2 and X3, and then reassessing the VIFs). If the options were to choose which single variable to delete to immediately lower multicollinearity, X3 is indeed a strong candidate due to its highest VIF, but the broader goal typically requires a more comprehensive removal plan.

An important caveat: the provided data shows an answer option but the list of possible choices is empty in the prompt. This means the question sheet is missing the full set of multiple-choice options. In practice, one would compare all listed options against the VIF analysis above and select the combination that achieves acceptable multicollinearity levels, using an iterative VIF-check approach.

In summary, based on the VIF values, X2, X3, and X4 are all flagged for multicollinearity (exceeding the common threshold of 5), with X3 and X4 being the strongest offenders. The recommended action is to iteratively remove high-VIF predictors and re-evaluate, rather than keeping all four variables unmodified. The single-option suggestion to delete only X3 is a partial step toward reducing multicollinearity but would not fully address the issue unless followed by further simplification or model adjustments.

Choose variables based on VIFj values. For a dataset with 4 independent variable, VIF1=1.54, VIF2=5.54, VIF3=7.89, VIF4=6.90, we should

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