Insyt
All charts in the library

Relationship

Biplot

Displays observations and variable directions together in a low-dimensional projection, often from PCA.

  • Plot
  • Multivariate exploration
  • Relationship

What it answers

Which observations and variables explain the main variation?

Shape
Score points and variable vectors
What it shows
Observation groups and variable contributions.

Example

The question

Which stores are alike, and which measures drive the difference?

Stores on the first two principal components, with measure arrows (biplot)

Stores on the first two principal components, with measure arrows (biplot)Dots are stores placed by their scores; arrows show how each measure loads on the two components. Sales and staff point the same way, so they move together; returns point up, nearly at right angles to sales.Component 2 (27%)-2-1012-3-2-10123Component 1 (48% of variation)SalesStaffReturnsRent
Stores on the first two principal components, with measure arrows (biplot)Dots are stores placed by their scores; arrows show how each measure loads on the two components. Sales and staff point the same way, so they move together; returns point up, nearly at right angles to sales.Component 2 (27%)-2-1012-3-2-10123Component 1 (48% of variation)SalesStaffReturnsRent
Dots are stores placed by their scores; arrows show how each measure loads on the two components. Sales and staff point the same way, so they move together; returns point up, nearly at right angles to sales.

Illustrative data. It belongs to no company.

When to use it

Use it when

Exploring a valid low-dimensional PCA or related projection.

Avoid it when

When explained variance is low or vector geometry is overinterpreted.

How to read it

Read observation positions and variable vectors under the stated scaling.

Note

State projection, scaling and variance explained.

The data you need

Layout
Wide observation table
Fields
ObservationID: text; V1...Vp: numeric columns
One row is
One observation with several measured numeric variables. What is the grain?
Rules
Align variables by observation. Decide scaling, missing-data handling and which columns are features.
Optional
Optional Group. PCA, clustering and correlations require calculations before rendering their derived results.
Preparation
Scale variables appropriately, fit the chosen projection and retain observation scores, loadings and explained variation.
Units
Scores/loadings are projection-dependent and may be standardised. State scaling and explained-variance percentages.
Example of the input layout: Wide observation tableA wide table: one row per item, with a separate column for each measure or period.ObservationV1V2V3V4V5ABC
A wide table: one row per item, with a separate column for each measure or period.

Worked example

If a PCA fit supplies PC1 scores A=-2, B=0, C=2 and positive PC1 loadings for sales, C lies in the higher-sales direction under that scaling.

IDV1V2V3
A10305
B12208
C18256
All charts in the library