What this answers

This tool answers "does this model's error look like patternless noise, or does it show a systematic shape that a good model should not leave behind?" A model can have a high R-squared and still violate its own assumptions in ways only a residual plot reveals.

How it is calculated

Every point is plotted with its fitted value on the horizontal axis and its residual (observed minus fitted) on the vertical axis, along with a zero reference line. You can either supply raw x and y data, in which case this calculator fits a simple linear regression first, or supply already-computed fitted values and residuals directly from a model you fit elsewhere.

Worked example

For nearly exact linear data with only small random noise, the resulting residual plot shows points scattered randomly around the zero line with no visible pattern, exactly what a well-specified linear model's residuals should look like: patternless noise, not a remaining signal the model failed to capture.

Assumption audit

Calculated from your data: every point's fitted value and residual, plotted against each other with a zero reference line.

Evidence to review: the shape of the point cloud itself. A curved pattern suggests a missing nonlinear term; a funnel shape (residuals spreading wider as fitted values increase) suggests non-constant variance; a few far-flung points suggest outliers worth investigating individually.

You must verify: that any pattern you see reflects a genuine model limitation and not just a small sample producing an unclear picture; residual plots from very small samples can look patterned by chance alone.

What this result does not mean

A residual pattern is evidence to investigate, not automatic proof a model is unusable; every model is an approximation, and the real question is whether the specific departure visible here matters for your particular use of the model.

Common mistakes

Reading too much into a residual plot from a very small sample is a common mistake; with only a handful of points, some visual pattern will appear essentially by chance even when the model is perfectly well specified, so treat apparent structure in small samples as a weak signal rather than a firm conclusion. A second mistake is checking R-squared and stopping there, since a model with a high R-squared can still show clear residual patterns that a good model should not leave behind.

Limitations

This calculator's raw x,y mode fits a simple one-predictor linear regression only; for a multi-predictor model, compute fitted values and residuals with the Multiple Linear Regression Calculator and paste them here directly using the "already-computed" input mode.