Visual simulations for analytics intuition.

Explore how models react to data. Each simulation is interactive, lightweight, and designed to make assumptions visible—so you can see how decisions change outcomes.

Browse by category below.

Regression

Linear Regression

Linear Fit Explorer

Drag points and compare least‑squares vs. robust fits with instant residual updates.

Launch simulation →
What you'll see
Residuals expand/contract as the line rotates.
Try this
Drag an outlier and watch fit sensitivity.
Tags
Slope Residuals Outliers
Metrics
MSE • R²
Equation
y = β0 + β1x

Sampling & Inference

Central Limit Theorem

Sampling Distribution Lab

Draw repeated samples from skewed, bounded, or bimodal populations and watch the means converge to normal.

Launch simulation →
What you'll see
Sample means tighten and turn bell‑shaped as n increases.
Try this
Use a bimodal population, then push n to 40+.
Tags
Sampling Means Normality
Metrics
SE • Mean
Equation
x̄ ~ N(μ, σ/√n)

Classification

Support Vector Machine

Margin Slider

Adjust the soft‑margin strength and watch the boundary shift while support vectors update in real time.

Launch simulation →
What you'll see
Margins widen/tighten as C changes; support vectors update live.
Try this
Push C down, then drag a point across the boundary.
Tags
Boundary Margin Support vectors
Metrics
Margin width • Violations
Equation
f(x) = w·x + b
Logistic Regression

Curve Builder

Place binary points, fit a logistic curve, and explore how cutoff probability changes misclassifications.

Launch simulation →
What you'll see
Probability curve shifts as points move; cutoff changes errors.
Try this
Set cutoff to 0.8, then add a few y=1 points.
Tags
Probability Cutoff Misclassification
Metrics
Log-likelihood • Accuracy
Equation
p(x) = 1 / (1 + e-(b0 + b1x))
k-Nearest Neighbors

Neighborhood Explorer

Move a query point through feature space and see the nearest-neighbor vote update in real time.

Launch simulation →
What you'll see
Neighbor sets and class votes shift as query position and k change.
Try this
Use a larger k near overlapping clusters and compare the prediction.
Tags
Distance Neighbors Voting
Metrics
Vote count • Neighborhood radius
Equation
ŷ = mode(Nk(x))

Neural Networks

Neural Networks

Neural Network Sandbox

Build a tiny network and watch activations and decision regions change as you tweak weights.

Launch simulation →
What you'll see
Hidden units carve decision regions; activations light up.
Try this
Increase one weight and watch the boundary bend.
Tags
Activations Layers Nonlinearity
Metrics
Loss • Accuracy
Equation
a = σ(Wx + b)
Neural Networks

Activation Compare

See how sigmoid and ReLU respond to the same input as you sweep through w · x + b.

Launch simulation →
What you'll see
Sigmoid saturates while ReLU clips; slopes tell gradient story.
Try this
Push b negative to see ReLU go flat.
Tags
Activation Gradient Nonlinearity
Metrics
z • σ(z) • ReLU(z)
Equation
z = w·x + b

Overfitting

Model Complexity

Overfitting Tradeoff Studio

Increase polynomial degree and watch training error fall while test/validation error curves back up.

Launch simulation →
What you'll see
Training error drops while test/validation error forms a U‑curve.
Try this
Switch to Piecewise data and raise degree.
Tags
Bias Variance Generalization
Metrics
Train vs. test/validation error
Equation
y = Σ βk xk
Cross-Validation

Cross-Validation Motion Lab

Cycle through folds, watch the model refit, and track how validation error changes across splits.

Launch simulation →
What you'll see
Fold roles swap with each cycle; validation errors build a bar chart.
Try this
Increase folds and raise degree to watch variance spike.
Tags
Folds Generalization Validation
Metrics
Fold MSE • Avg MSE
Equation
CV = (1/k) Σ MSE
Nested CV

Nested Cross-Validation Studio

Outer folds estimate generalization while inner folds select polynomial degree.

Launch simulation →
What you'll see
Inner CV picks a model; outer fold tests it.
Try this
Watch inner scores shift while the best degree locks in.
Tags
Nested Model selection Generalization
Metrics
Inner CV error • Outer test error
Equation
Nested CV = outer test error

Clustering

Clustering

K‑Means Playground

Seed centroids, iterate, and watch clusters converge while inertia updates.

Launch simulation →
What you'll see
Centroids shift, clusters reassign, inertia drops.
Try this
Move a centroid near overlap and iterate.
Tags
Centroids Inertia Assignment
Metrics
SSE • Iterations
Equation
argmin‖x − μk‖²
Clustering

Hierarchical Clustering

Explore linkage choices and watch dendrogram merges reshape clusters.

Launch simulation →
What you'll see
Dendrogram merges change with linkage choice.
Try this
Compare single vs. complete linkage at the same cut.
Tags
Linkage Dendrogram Cut height
Metrics
Merge distance
Equation
d(A,B) = min / max / avg

About this collection

Categories

Model families

Simulations are grouped by model family: classification, regression, clustering, and probabilistic inference. New items will appear as the course progresses.

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