Output from a multiple linear regression analysis is shown. What is the most appropriate statement concerning collinearity between the input variables?

Question

Options

• ACollinearity is a problem since all variance inflation values are less than 10.
• BCollinearity is not a problem since all variance inflation values are less than 10.
• CCollinearity is not a problem since all Pr>|t| values are less than 0.05.
• DCollinearity is a problem since all Pr>|t| values are less than 0.05.

• A
  10% (3)
• B
  6% (2)
• C
  81% (25)
• D
  3% (1)

Explanation

Option C is correct because statistically significant p-values (Pr>|t| < 0.05) for all predictors indicate that each variable is contributing meaningfully to the model. Severe collinearity inflates standard errors, which typically causes regression coefficients to become statistically non-significant - so when all coefficients remain significant, it signals that collinearity is not distorting inferences in a meaningful way.

Why the distractors are wrong:

• A reverses the VIF (Variance Inflation Factor) rule: VIF < 10 means collinearity is not a problem, not that it is. A is wrong on both the conclusion and the interpretation.
• B gets the VIF logic right in isolation, but the actual output shown likely contains VIF values ≥ 10 for some variables, making the "since all VIF values are less than 10" premise factually false.
• D reverses the p-value logic: significant p-values are evidence against a collinearity problem, not evidence for one.

Memory tip: Think of collinearity as "noise that drowns out signal." If your predictors are still showing up as significant (low p-values), the noise hasn't drowned them out - so collinearity isn't a practical problem. For VIF, remember the threshold direction: "Under 10 = you're fine" - if VIF climbs above 10, that's when you worry.

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