Nazirul Hazim A. Khalim Monash University Malaysia
Starting engine…
About
Vector Studio
An interactive 3D studio for seeing the geometry of vectors and Ordinary Least Squares — column space, projection, residuals and the orthogonality that ties them together.
OLS Geometry
Watch how Ordinary Least Squares projects the data vector y onto the column space Col(X). The residual e = y − ŷ is what's left over — always perpendicular to the fit.
OrbitDrag to rotate · scroll to zoom
SlidersSet the angle, tilt and length of y
TogglesReveal the plane, ŷ, residual & ⊥
PlayAnimate the projection step by step
Vector Sandbox
A free playground for 3D vector algebra. Spawn vectors, feed them into operations — add, subtract, cross product, projection — and watch results update live as you drag.
SpawnAdd vectors, operations & planes from the dock
DragMove a box to reposition · an arrowhead to edit
FeedDrop a vector's box onto an operation to use it
TasksWork the checklist or take the guided tour
Nazirul Hazim A. Khalim · Monash University Malaysia, 2026. Inspired by ImDat and MathVR by Matt Cabanag, UNSW.
Geometry of OLS
logged in as: z12345
Tasks
Nothing selected
Click a vector box, arrowhead, operation, or plane to select it.
Vectors
Operations
Plane
Scene
✕Drag a box to move a vector · drag an arrowhead to change its value ·
drag empty space to orbit · scroll to zoom · right-drag to pan.
Drag a vector's box onto an operation to feed it in.
MathVR — after Cabanag (2023), SIGGRAPH Asia Educator's Forum