Reduce a high-dimensional dataset to its most informative components and remove multicollinearity from your analysis.
Principal Component Analysis (PCA) is a dimensionality reduction technique that transforms a set of possibly correlated variables into a smaller set of uncorrelated linear combinations called principal components. The first component captures the greatest possible variance in the data; each subsequent component captures as much remaining variance as possible, subject to being orthogonal (uncorrelated) to all preceding components. PCA is widely used as a preprocessing step in machine learning, in multivariate data exploration, and as a solution to multicollinearity in regression.
Unlike Exploratory Factor Analysis, PCA makes no assumptions about latent structures or measurement error — it is purely a mathematical decomposition of the covariance or correlation matrix. The components themselves are not latent theoretical constructs but algebraic summaries of the observed data. Biplots allow you to visualise both the observations and the original variables in the reduced two-dimensional principal component space, revealing clusters and variable groupings at a glance.
StatRyx performs PCA on standardised variables (from the correlation matrix, appropriate when variables are on different scales), generates a scree plot to aid in deciding how many components to retain (Kaiser criterion: eigenvalue > 1, or parallel analysis), computes component loadings and scores, explains the percentage of variance each component accounts for, and produces a biplot — all formatted for APA 7 reporting.
| Component | Eigenvalue | % Variance | Cumulative % |
|---|---|---|---|
| 1 | 4.83 | 48.3 | 48.3 |
| 2 | 1.91 | 19.1 | 67.4 |
| 3 | 0.87 | 8.7 | 76.1 |
| 4 | 0.62 | 6.2 | 82.3 |
Principal component analysis on 10 financial indicators yielded two components with eigenvalues exceeding 1.0, together accounting for 67.4% of total variance. Component 1 (eigenvalue = 4.83, 48.3% variance) loaded most strongly on revenue growth, EBITDA margin, and return on equity. Component 2 (eigenvalue = 1.91, 19.1% variance) was defined primarily by debt-to-equity ratio and current ratio.
Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.
No coding required. Specify the variables you want to reduce in plain English and StatRyx handles standardisation, eigendecomposition, component extraction, and all visualisations.
PCA results become more stable with larger samples. A common guideline is at least 5–10 observations per variable. Very small samples (fewer than 50 total) can produce highly variable component solutions that do not replicate well.
The two most common rules are the Kaiser criterion (retain components with eigenvalue > 1) and the scree plot (look for the 'elbow' where eigenvalues level off). Parallel analysis is the most statistically defensible criterion: retain components with eigenvalues that exceed those expected from random data. StatRyx provides all three guides.
A biplot displays both the original variables (as vectors, or arrows) and the observations (as points) in principal component space. Variables with long arrows contribute strongly to the components shown. Variables whose arrows point in similar directions are positively correlated; those pointing in opposite directions are negatively correlated. Clusters of points indicate groups of similar observations.
Run a Principal Component Analysis on your data →