What is the Regression Workbench multi-solver?

Regression Workbench is a guided workflow that chains 4 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.

Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.

Data & Statistics Pack · Multi-Solver

Regression Workbench

Fit, test, bootstrap. This multi-solver chains 4 solvers into a single guided workflow — run each step in order and carry the result forward.

Workflow steps

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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.

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Hypothesis Test

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Hypothesis Test (z-test)Live

p-values & rejection regions

Controls

Presets

Sample mean x̄

Null mean μ₀

Std deviation s

Sample size n

Two-tailed test

A hypothesis test asks whether a sample mean is far enough from the null value to be surprising by chance alone. The test statistic z measures that distance in standard errors; if it falls in the red rejection region (p below 0.05) we reject the null. Larger samples shrink the standard error and sharpen the test.

▶ Run in Python

Data Inspector

Standard error1.265

z-statistic1.581

p-value0.1138

Decisionfail to reject

Governing equation

z = \frac{x ˉ - μ _{0}}{σ / n} = \frac{52 - 50}{8/ 40} = 1.58

Reading this result: The statistic sits in the white central zone, so the gap between x̄ and μ₀ is within ordinary sampling noise and you fail to reject H₀.

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

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Confidence Interval

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Confidence IntervalsLive

what 95% really means

Controls

Presets

Sample size n

A confidence interval is often misread. It does not mean the true value has a 95% chance of being in one interval — it means that if you repeated the experiment many times, about 95% of the intervals would contain the true mean. The red intervals here are the unlucky ones that miss it.

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Data Inspector

Confidence level95%

Observed coverage0%

Intervals shown50

Governing equation

\overset{x}{ˉ} \pm z \frac{σ}{n} = 50 \pm 1.96 \cdot \frac{10}{30}

Reading this result: About 0% of these 50 intervals captured the true mean — close to the 95% you asked for. Raising n from 30 tightens each interval (SE = σ/√n) but does not change that hit rate: the confidence level, not the sample size, sets how often you are right.

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

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Bootstrap

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Bootstrap ResamplingLive

confidence without formulas

Controls

Presets

Original sample size

Bootstrap resamples B

The bootstrap estimates uncertainty by resampling your data with replacement thousands of times and recomputing the statistic each time. The spread of those bootstrap means gives a confidence interval — no formula or normality assumption required. Powerful when the math is intractable.

▶ Run in Python

Data Inspector

Sample mean0.00

95% CI low0.00

95% CI high0.00

CI width0.00

Governing equation

\hat{θ}^{*} = \frac{1}{25} i = 1 \sum 25 x_{i}^{*}, CI_{95%} = [\hat{θ}_{(2.5%)}^{*}, \hat{θ}_{(97.5%)}^{*}] = [0.00, 0.00]

Reading this result: The spread of the resampled means is the confidence interval — no normality assumption needed. Sample size sets its width; more resamples only sharpen its edges.

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

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More in the Data & Statistics pack

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Frequently asked questions

What is the Regression Workbench multi-solver?: Regression Workbench is a guided workflow that chains 4 individual PolySim solvers into one end-to-end analysis, piping each result into the next step.
Is it free to use?: Yes. Every step runs entirely in your browser using real numerics — no install, no account, no cloud cost. Custom or private solver packs are available as a paid service.