General Mathematics · bivariate data · demo

Residual plots assess the fit

A straight line is only a good model when the residual plot is a random cloud around zero. Switch the data — the pattern is the verdict.

data ŷ = a + bx e = 0

Scatter and fitted line

Residual plot · e = y − ŷ versus x

Same x-scale on both plots · residual axis is locked, so a fan or curve is a real pattern

Data shape

random around 0 — linear OK

Working

The residual plot is how you check the linear assumption — a pretty line on the scatter is not enough.