Forty-five records where one variable — a unit cost pegged at almost exactly 1000 — varies by less than a tenth of a percent. Every variance inflation factor is between 1.0043 and 1.0518, which passes every rule of thumb there is. The condition number of the scaled design is 3180.34, and the variance-decomposition proportions put 1.000 of the intercept’s variance and 1.000 of that variable’s on a single direction: the near-dependency is with the constant term. VIF is computed from auxiliary regressions that each contain their own intercept, so it cannot see this one by construction, and a near-constant predictor is an easy thing to end up with.
45 rows · 3 predictors · condition number 3,180.34
Every VIF is below 10 and the condition number is 3,180.34
The variance inflation factors report nothing — the largest is 1.0518 — and the scaled design is badly conditioned anyway. Each VIF comes from an auxiliary regression that contains its own intercept, so a predictor that is nearly a multiple of the constant term is invisible to all of them. The decomposition below shows where the dependency actually is.
Largest VIF
1.0518
order size
Condition number
3,180.34
severe
Named dependencies
1
index past 30, two coefficients loaded
VIF misses it
yes
all VIFs quiet, design ill-conditioned
Variance inflation
Each predictor’s variance inflation factor, tolerance and auxiliary R-squared
Predictor
VIF
Tolerance
R² on the others
SE inflated by
unit cost
1.0043
0.99571
0.00429
1.002×
order size
1.0518
0.95075
0.04925
1.026×
lead time
1.0517
0.95087
0.04913
1.026×
The last column is the useful reading: a VIF of 25 means that coefficient’s standard error is five times what it would be with uncorrelated predictors, because the inflation is on the variance and the standard error is its square root. Thresholds of 5 and 10 correspond to 2.24 and 3.16 times.
Where the variance sits
Condition indices with the share of each coefficient’s variance on that direction
Direction
Condition index
intercept
unit cost
order size
lead time
1
1.000
5.062e-8
5.058e-8
0.003
0.006
2
6.410
0.000
0.000
0.176
0.630
3
11.982
0.000
0.000
0.818
0.362
4
3,180.339
1.000
1.000
0.002
0.002
Each column sums to 1 down the table: that coefficient’s variance is split across the directions. A row with a large condition index and two or more entries above 0.5 is a near-dependency, and the coefficients it loads are the variables involved in it. That is the question a VIF cannot answer.
The intercept is a column here on purpose. A predictor with a small coefficient of variation is nearly a multiple of the constant term, and every variance inflation factor is blind to that because the auxiliary regressions behind them each fit their own intercept.
Collinearity is a property of the predictors alone, so no outcome column is needed and this can be run on a planned design before any response is measured. Rescaling a predictor leaves its VIF unchanged, which the verification suite asserts on sixty generated sets.
Names the variables Condition indices No outcome needed Harms inference, not prediction
What this tool shows
On the shipped preset every variance inflation factor is between 1.0043 and 1.0518 — a clean result by every rule of thumb — and the condition number of the design is 3180.34. One predictor barely varies, so it is nearly a multiple of the constant term, and the variance-decomposition proportions put 1.000 of the intercept’s variance and 1.000 of that predictor’s on one direction. Every VIF is computed from an auxiliary regression that fits its own intercept, so none of them can see it.
Variance inflation and tolerance for every predictor, with the auxiliary R² each comes from
How much each coefficient’s standard error is inflated — the square root, which is the readable number
Belsley-Kuh-Welsch condition indices with variance-decomposition proportions, naming the variables in each dependency
A preset where every VIF is near 1 and the design is still badly conditioned
A preset where no pairwise correlation exceeds 0.74 and three variables are jointly dependent
Why no outcome column is needed, and why that means this can run before data collection
Names the variables Condition indices No outcome needed Variance proportions
Collinearity harms interpretation, not prediction.
Updated 13 September 2026 · Works in any browser, no installation
A variance inflation factor says how much a predictor’s coefficient variance is enlarged by its overlap with the other predictors: VIF = 1/(1 − R²) from regressing it on the rest. It detects entanglement and cannot say with which variables, cannot see a dependency involving the constant term, and is a variance rather than a standard error — a VIF of 25 means the standard error is five times larger, not twenty-five.
At a glance
Formula shown
VIFⱼ = 1/(1 − R²ⱼ), where R²ⱼ comes from regressing predictor j on all the others. Tolerance is its reciprocal. The standard error of that coefficient is √VIF times what it would be with orthogonal predictors, so 5 and 10 correspond to 2.24× and 3.16×. Condition indices are √(λ₁/λₖ) from the eigenvalues of the column-scaled XᵀX with the intercept included, and the variance-decomposition proportions split each coefficient’s variance across those directions.
Scenario support
Screening a predictor set before fitting anything, diagnosing a model whose F is significant while no coefficient is, deciding which of several overlapping variables to drop, and checking a planned design for collinearity before any outcome is collected.
Educational estimate
Planning support from the values you enter — not professional advice.
The dependency every VIF is blind to
The shipped preset produces a clean VIF table on a design that is close to singular, and the reason is structural rather than a matter of degree.
Every VIF is between 1.0043 and 1.0518. Nothing near 5, let alone 10.
The condition number is 3180.34. One predictor sits at almost exactly 1000 and varies by less than a tenth of a percent, so it is nearly a constant.
The decomposition names it. One direction carries 1.000 of the intercept’s variance and 1.000 of that predictor’s — the dependency is between the two of them.
VIF cannot see this by construction. Each auxiliary regression fits its own intercept, so the constant is removed before the R² is computed and a near-constant predictor looks perfectly independent of the rest.
A VIF says something is wrong, not what
This is the limitation that matters most in practice, because it turns a diagnostic into a puzzle.
On the second preset the VIFs are 166.41, 113.52 and 241.66. All three are alarming, and none of them says which variables are involved with which.
The largest pairwise correlation is 0.73418. A correlation matrix scan finds nothing worth reporting.
The worst direction, at a condition index of 259.77, loads all three at 0.997, 0.993 and 0.999. The third variable is the sum of the other two, and the decomposition says so.
The remedy depends entirely on that answer. One redundant pair is fixed by dropping a variable; three variables in a linear identity is fixed by dropping the derived one, and the two situations produce indistinguishable VIF tables.
It is a variance, and people read it as a standard error
The most common misreading of this number is a factor-of-the-square-root error, and it makes collinearity sound far worse than it is.
A VIF of 25 does not mean a standard error twenty-five times larger. It means the variance is twenty-five times larger, so the standard error is five.
The conventional thresholds read differently in that light. A VIF of 5 is a 2.24 times wider interval; 10 is 3.16 times.
The page prints the square root for that reason. “This coefficient’s interval is 3.2 times wider than it would be with independent predictors” is a statement anyone can act on.
And it puts the thresholds in perspective. 5 and 10 are conventions with no distributional basis; what matters is whether an interval that wide still answers the question, which depends on the question.
It damages interpretation, not prediction
Collinearity is often treated as a defect to be removed before anything else happens. What it actually breaks is narrower than that.
Predictions and their intervals are unaffected. A model with a VIF of 200 forecasts exactly as well as one without, as long as future predictors have the same relationship to each other.
R² and the overall F are unaffected too. The fit is the fit.
The individual coefficients are what suffer. Their standard errors inflate, their signs can flip on small changes to the data, and the classic symptom is a highly significant model in which no single predictor reaches significance.
So the question is what the model is for. Forecasting tolerates collinearity; anything where a coefficient will be read as an effect does not — the same distinction that separates a model’s R² from its per-predictor contributions.
No outcome is needed
Collinearity is a property of the predictor columns alone, and the consequences of that go beyond convenience.
Nothing on this page uses the response. The VIFs come from regressions among the predictors and the condition indices from the design matrix.
So a planned design can be checked before anything is measured, in the same way that leverage can — and for the same reason, since both are functions of X alone.
It also means collinearity cannot be fixed by collecting more of the same data. More rows with the same relationships among the predictors leave every VIF where it was.
The fixes are structural: drop a redundant variable, combine several into an index, collect observations that break the pattern, or accept wider intervals and say so.
What a high condition index does not prove
The fourth preset has a condition number of 25.42 and three completely unrelated variables, which is worth understanding before the index is used as a threshold.
The decomposition works on the uncentred design. That is deliberate — it is what lets it see dependencies involving the intercept.
It also means scale affects the index. A predictor with a small coefficient of variation raises it without being collinear with any other predictor.
The proportions are what disambiguate. A high index with only one coefficient loaded on that direction is a scaling artefact; two or more is a dependency.
Which is why the page counts dependencies rather than indices, and why the VIF table is still worth reading alongside — it is unaffected by scale entirely, which the verification suite asserts by rescaling every predictor by a random factor up to sixty and requiring every VIF to be unchanged.
Reporting collinearity
Four items, and the second is the one that turns a warning into something a reader can act on.
Give the VIFs and name the variables involved. “Maximum VIF 32” is not actionable; “list price and net price are nearly identical” is.
Give the standard-error inflation, not just the VIF. The square root is what the reader is actually affected by.
Say what the model is for. A high VIF is a serious problem for a model whose coefficients will be interpreted and close to irrelevant for one that only forecasts.
And say what you did. Dropping one of a redundant pair, combining variables, or keeping both and reporting wider intervals are all defensible — leaving it unaddressed after reporting a VIF of 200 is not.
Method. Each variance inflation factor is computed from its own auxiliary regression of that predictor on all the others, which is the definition rather than a matrix shortcut, and the verification suite recomputes every one of them independently and requires agreement to better than 1e-9. The condition indices and variance proportions follow Belsley, Kuh and Welsch: the design is scaled to unit column length with the intercept column included — uncentred deliberately, because a near-dependency with the constant is one of the cases a VIF cannot see — and decomposed by cyclic Jacobi rotations, which give the eigenvectors that the proportions need. The suite asserts the structural identities on 100 generated sets: every VIF is at least 1, the first condition index is exactly 1, the last equals the reported condition number, and each coefficient’s variance proportions sum to 1 down the table. It separately asserts scale invariance by rescaling every predictor by a random factor up to sixty and requiring every VIF to be unchanged. That engine is verified on every change against 103 assertions. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
Multiple CorrelationMultiple R with adjusted R-squared, an F test, and a per-predictor table of simple, partial and unique contributions beside the variance inflation factors.
Covariance MatrixSample covariance and correlation matrices with eigenvalues, determinant and condition number, so redundancy spread across several variables cannot hide from a pairwise scan.
Multiple RegressionFits several predictors with a VIF on every term, and names the configuration people misread: a model significant at p = 0.0103 where neither predictor reaches 0.05, at a VIF of only 7.11.
LeverageHat values for every observation with the 2p/n and 3p/n cutoffs, the studentised residuals alongside, and the Σh = p identity printed as a check.
Correlation CoefficientReports Pearson, Spearman and Kendall together with the scatter plot, and ships Anscombe's quartet built in — four datasets with an identical r of 0.816 that Spearman tells apart.
Partial CorrelationPartial and semi-partial correlation with any number of controls, computed from residuals, with the raw correlation and the share each control already explains.
An educational tool. A variance inflation factor detects entanglement without naming the variables involved, and is blind by construction to a near-dependency with the constant term, since each auxiliary regression fits its own intercept. The condition index is computed on the uncentred design, so it can be raised by scale alone — only the variance proportions distinguish that from a genuine dependency.