Regression Explorer
Fit a least-squares line, manipulate the data and see how slope, intercept, residual error, R² and prediction change in real time.
Regression turns a relationship into a fitted prediction model.
This explorer uses simple least-squares regression. Learners can change the underlying slope, noise, sample size, prediction point and curvature, then drag individual observations and see the fitted equation and residuals update immediately.
Regression Explorer — Step by Step
Eight locked stages build from the fitted line through noise, residuals, prediction range, nonlinearity, a leverage challenge and management review.
Fitted Line, Residuals and Prediction
Reveal the regression context to begin.
Read the model beyond R².
Build Your Own Regression Scenario
Experiment Mode is isolated from the guided demonstration. Adjust the model controls and drag observations without changing guided progress.
Test regression interpretation.
Regression interpretation cues
Slope
The estimated change in predicted y for a one-unit increase in x, conditional on the fitted simple linear model.
Intercept
The predicted y-value when x = 0. Interpret only when zero is meaningful or reasonably close to the observed range.
R²
The proportion of observed y-variation explained by the fitted line in the sample. It does not establish causality or model adequacy.
RMSE
The typical residual magnitude in the original y-units. Lower values indicate tighter predictions relative to the same outcome scale.
Residuals
Observed y minus predicted y. Patterns in residuals can reveal curvature, changing variance or influential observations.
Extrapolation
Predictions outside the observed x-range rely on the assumption that the fitted relationship continues where evidence is weaker.
Interpret slope and prediction together with residual error, leverage, observed range and evidence of nonlinearity.