Map observations and variables on principal component axes. Tune scaling, inspect loadings, and compare dispersion. Create clear biplots for reporting, validation, and teaching workflows.
These sample values match the prefilled inputs and demonstrate a typical two-component PCA output for engagement analysis.
| Observation | PC1 Score | PC2 Score |
|---|---|---|
| Segment A | 1.35 | 0.42 |
| Segment B | 0.55 | -0.88 |
| Segment C | -1.10 | 0.65 |
| Segment D | -0.80 | -0.45 |
| Segment E | 0.20 | 1.10 |
| Variable | PC1 Loading | PC2 Loading |
|---|---|---|
| Retention | 0.78 | 0.22 |
| Engagement | 0.83 | -0.18 |
| Conversion | 0.61 | 0.56 |
| Support Tickets | -0.48 | 0.51 |
| Revenue | 0.72 | -0.36 |
For a Gabriel-style biplot, the tool rescales observation scores and variable loadings with eigenvalues and a scaling factor α.
| Observation coordinates | x_i = s_{i1} \times \lambda_1^{\alpha/2}, y_i = s_{i2} \times \lambda_2^{\alpha/2} |
|---|---|
| Variable vector coordinates | v_{j1} = l_{j1} \times \lambda_1^{(1-\alpha)/2}, v_{j2} = l_{j2} \times \lambda_2^{(1-\alpha)/2} |
| Point distance / vector length | r = \sqrt{x^2 + y^2} |
| Plane variance coverage | (\lambda_1 + \lambda_2) / \text{Total Variance} \times 100 |
| Variable cos² (PC1-PC2) | \text{cos}^2 = l_{j1}^2 + l_{j2}^2 (assuming standardized loading output) |
Use α = 0 for variable-focused interpretation, α = 1 for observation-focused interpretation, and α = 0.5 for balanced scaling.
label,pc1,pc2 format.Reliable biplots begin with consistent preprocessing. Standardize variables when units differ, then generate observation scores and variable loadings from one PCA run. This calculator assumes both input tables share the same records, scaling rules, and component order. Mixing outputs from different extracts distorts point positions and vector directions. Document sample size, missing value treatment, and normalization choices so exported results stay auditable during model review and reporting cycles for every production refresh.
PC1 and PC2 variance percentages determine how much structure the biplot can represent. The calculator also reports plane coverage, the combined share of total variance explained by both displayed components. Higher coverage generally makes distances and vector angles more informative. Lower coverage can still support exploration, but important behavior may remain in later components. Compare variance coverage across model versions before making operational decisions, alerts, or stakeholder summaries and audit signoff packs.
Scaling alpha changes visual emphasis without changing the PCA model itself. With alpha near zero, variable vectors preserve correlation style interpretation more strongly. With alpha near one, observation distances become easier to compare. The midpoint balances both views for practical reporting. This calculator applies eigenvalue based scaling on each axis and returns adjusted coordinates, lengths, and angles, helping teams compare perspectives while keeping one consistent export workflow for repeated analyst comparisons.
Interpretation should combine geometry with table metrics. Observation distance from the origin indicates how strongly a row is represented in the PC1 PC2 plane. Variable vector length shows directional strength on the same plane, while cos2 estimates representation quality. Angle patterns help identify aligned or opposing behaviors. Contribution percentages add prioritization by showing which observations and variables dominate the displayed structure and deserve closer review during segmentation workshops and root cause discussion.
A strong reporting process pairs this calculator with versioned PCA outputs. Paste scores and loadings, validate variance inputs, render the biplot, and export CSV or PDF documentation. Teams can compare monthly snapshots to track segment movement, feature drift, or changing relationships between variables. Because the tool exposes coordinates, magnitudes, and contributions, it supports reproducible review conversations and governance notes instead of screenshot only analysis in business and research settings across analytics teams globally.
Enter PC1 and PC2 eigenvalues, total variance, then paste two CSV tables: observation scores and variable loadings. Both tables must use the same PCA model and component order.
No. It visualizes and rescales existing PCA outputs. Run PCA in your statistical workflow first, then paste the first two component scores and matching loadings here.
Start with alpha = 0.50 for a balanced view. Use alpha near 0 when variable relationships matter most, and alpha near 1 when comparing observation distances.
Short vectors usually mean the variable has weaker representation in the PC1-PC2 plane. Check its loading values and cos2 to confirm whether later components carry more information.
Be careful when plane coverage is low, inputs come from mismatched PCA runs, or variables were not standardized consistently. In those cases, distances and angles can mislead decisions.
Exports include variance metrics, scaled coordinates, magnitudes, angles, and contribution percentages for observations and variables. They are useful for reporting, review notes, and audit trails.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.