Linear Regression Calculator

Paste paired observations, inspect the fitted relationship, and remember that association and prediction do not by themselves establish causation.

Paired data (x, y per line)

Prediction x (optional)

At least two paired points are required, and x values cannot all be identical.

—Best-fit line

—Pearson r

—R²

—Residual RMSE

—Prediction and model summary

Residual & fit-quality evidence

Independently recompute the least-squares line, correlation, R², RMSE and row-level residuals.

Regression audit

Prediction x

Residual rows

Precision

x	y	ŷ	residual

Use the tool above, then refresh this verification.

Verification uses the visible inputs and keeps the original tool workflow intact.

Analysis reproducibility & method-fit audit

Capture the current inputs, analysis settings and visible result as stable fingerprints, then flag structural method-fit issues that can be checked from the entered data. This complements the page’s existing mathematical audit; it does not prove distributional assumptions or causal validity.

Run the analysis above, then refresh this reproducibility audit.

Browser-local provenance evidence. Statistical assumptions still require subject-matter and study-design judgment.

Core describe → test → interpret workflows

Use descriptive context first, choose the method that matches the design, then keep inputs, settings and result evidence reproducible instead of copying a p-value without its analysis recipe.

Start: Statistics Calculator Choose a statistical test

All 51 statistics tools

T-Test CalculatorOne-sample, Welch and paired mean tests Box Plot MakerQuartiles, spread, outliers and export Linear RegressionLine of best fit, R² and residuals Probability CalculatorEvents, odds and repeated trials CorrelationPearson, Spearman and paired association Standard ErrorSampling uncertainty and CI context One-Way ANOVACompare 3+ independent group means Chi-SquareCounts, independence and goodness of fit

Practical guide and verification

A fitted line is a model, not proof of causation

Simple linear regression estimates a relationship between variables under a model. A strong slope or high R² does not establish that changing x causes the change in y.

Inspect residuals and influential points

A single line can hide curvature, unequal variance, clusters or influential outliers. Plot the data and residuals rather than judging the model only from the equation and R².

Common mistake

Extrapolating far beyond the observed x range can produce precise-looking but unsupported predictions. The fitted relationship may not continue outside the data used to estimate it.

Interpret statistical results in context

Use plots and descriptive summaries before formal tests. Check the sampling/design assumptions that matter for the chosen method, report effect size and uncertainty where available, and avoid treating a threshold such as p < .05 as proof of importance, causation, or truth. Browser calculations are educational/planning utilities, not domain-specific professional advice.