Residual plot

A residual plot graphs regression residuals against fitted values or a predictor. A random horizontal band supports the OLS assumptions; systematic patterns reveal heteroskedasticity, non-linearity or omitted variables.

ByHoang TruongUpdated July 2, 2026

FrameworkClassical linear regression model

See it move

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Plotting residuals against fitted values tests whether a regression's assumptions hold. A random horizontal band around zero, with roughly constant spread, is the sign of a well-specified model. A funnel shape that widens as fitted values increase signals heteroskedasticity, a curved pattern signals non-linearity, and a trend correlated with an excluded variable signals omitted-variable bias.

Where it fits

SubjectData Analysis & StatisticsCoreTopicSimple Linear Regression & OLSCoreTopicRegression Diagnostics & ProblemsCore

The formula

LaTeX

e_i = y_i - \hat{y}_i

Variables

$e_{i}$: Residual for observation i
$y_{i}$: Observed value of the dependent variable for observation i
$\overset{y}{^}_{i}$: Fitted (predicted) value from the regression for observation i

Residuals plotted against ŷ or each predictor should form a random horizontal band if OLS assumptions hold. Systematic patterns indicate heteroskedasticity, non-linearity or omitted variables.

Check yourself

PracticeCORE

A researcher regresses factory output on machine hours and plots residuals against fitted values. The residuals form a funnel shape that widens from left to right. What does this pattern signal?

Select an answer to check your understanding.