Read VIF
VIF = 1 indicates no variance inflation from linear association with the other modeled predictors. Larger values indicate greater inflation. The number does not say which predictor to delete, whether a coefficient is biased, or whether prediction is poor.
VIF has a formal definition and a layer of practice around it. If R²ⱼ is obtained by regressing predictor j on the other predictors, then VIF = 1/(1 − R²ⱼ).3 The cutoff layer is contextual:
| Value or rule | Source/context | Category |
|---|---|---|
| VIF = 1 | Minimum: no variance inflation from the other modeled predictors3 | FORMAL |
| Exceeds 5 or 10 | One range of practice, explicitly called a rule of thumb in ISL3 | RULE OF THUMB |
| VIF below 3 | Stricter working guideline used in an ecological data-exploration protocol4 | DISCIPLINE CONVENTION |
| No universal cutoff | Design, signal strength, uncertainty, and model purpose can change what matters4 | NO UNIVERSAL THRESHOLD |
Values 5 and 10 occur in one source sentence as a range of commonly used practice, not as two independently authoritative thresholds. Zuur and colleagues used the stricter value 3 in an ecological context and noted that even VIF 2 can matter when signals are weak.4 That observation is context, not a fifth cutoff. A university reference likewise documents that applied guidance varies across 10, 3, and 2.5
The frequently repeated value 2.5 could not be supported above a practitioner source, so it is not printed as an authoritative cutoff. The defensible conclusion is no universal VIF cutoff: inspect design, coefficient intervals, condition structure, and sensitivity.
Why can one cutoff mislead? The practical effect of variance inflation depends on the uninflated precision, sample size, predictor role, and question. A high VIF for a lower-order term required by an interaction can be less concerning than unstable estimates for the predictors central to the claim. Conversely, VIF below a familiar rule cannot certify good design or precise coefficients.
Centering can reduce nonessential collinearity in polynomial or interaction terms without changing the underlying fitted surface. Removing a variable can create omitted-variable problems. Use residual and influence diagnostics, variance diagnostics, and the regression output guide as connected evidence. Provenance rules explain why floating cutoffs are omitted.
Read Durbin–Watson
The statistic is approximately 2 when successive residuals have little first-order autocorrelation, below 2 for positive autocorrelation, and above 2 for negative autocorrelation.2
Formal Durbin–Watson decisions use lower and upper bounds that depend on n, predictor count, and significance level. Values in an inconclusive region stay inconclusive; a generic “between 1.5 and 2.5 is fine” slogan is not the original bounds test.
Read the bounds table for the exact design. Depending on the statistic and bounds, the result can support positive autocorrelation, support no positive autocorrelation, or remain inconclusive. Then inspect residuals against time and an autocorrelation function. Durbin–Watson focuses on an ordered first-lag pattern; seasonal or higher-order dependence can remain.
Time ordering, lag structure, seasonality, and model specification matter. A statistic near 2 does not prove independent errors of every kind.
A defensible reporting sentence
“The largest VIF was 6.2, indicating substantial variance inflation but not an automatic deletion rule. Durbin–Watson was 1.31; the design-specific bounds and residual autocorrelation plot were examined before interpretation.”