Is this good for educators?

Yes — this version of "Factor Model for a Monte-Carlo forecast" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.

Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Educators · Factor Model

Factor Model for a Monte-Carlo forecast

Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate a Monte-Carlo forecast live below — adjust the inputs and watch it respond, right in your browser.

Linear Regression

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Linear RegressionLive

least squares & R²

Controls

Presets

True slope

Noise level

Data points

Ordinary least squares finds the line that minimizes the sum of squared vertical residuals (the gray drop-lines). R² measures the fraction of variance the line explains — 1 is perfect, 0 is useless. Add noise or remove points to watch the fit and R² degrade.

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Data Inspector

Fitted slope0.000

Intercept0.000

R²0.000

Correlation r0.000

Governing equation

\overset{y}{^} = 0.00 + 0.00 x, β_{1} = \frac{\sum ( x - x ˉ ) ( y - y ˉ )}{\sum ( x - x ˉ ) ^{2}}, R^{2} = 0.00

Reading this result: R² = 0.00: noise (2) swamps the signal, so least squares can barely tell the slope from flat — adding data points would tighten the estimate.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

PCA

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Principal Component AnalysisLive

finding the axes of variation

Controls

Presets

Correlation

Spread (x)

PCA finds the directions along which data varies most. The eigenvectors of the covariance matrix are the principal components (cyan = most variance, green = least), and their eigenvalues are the variances along each. Projecting onto the top components is the basis of dimensionality reduction.

▶ Run in Python

Data Inspector

Variance PC10.00

Variance PC20.00

PC1 explains0%

PC1 angle0°

Governing equation

C v = λ v, \frac{λ _{1}}{λ _{1} + λ _{2}} = \frac{0.00}{0.00} = 0.00

Reading this result: PC1 explains 0% of the variance here; the stronger the correlation between features, the more PCA concentrates information on that first component.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Frequently asked questions

Is this good for educators?: Yes — this version of "Factor Model for a Monte-Carlo forecast" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.