residualplott

A residual plot is a graphical diagnostic tool used in regression analysis to examine the residuals, the differences between observed values and those predicted by a fitted model. The plot helps assess key assumptions about the model, such as linearity, constant variance, and independence of errors, and can indicate potential misspecification.

Typically, residuals are plotted on the vertical axis while the corresponding fitted values, an independent variable, or the order of the observations is placed on the horizontal axis. Common variants include raw residuals, standardized residuals, and studentized residuals. While the most common form is a residuals versus fitted values plot, other versions may show residuals against time or a specific predictor.

Interpretation focuses on the pattern of points. A random cloud scattered around zero with no obvious trend supports the adequacy of a linear specification and homoscedasticity. Systematic patterns such as curvature, waves, or funnel shapes suggest nonlinearity, heteroscedasticity, or omitted variables. Outliers or influential observations often appear as isolated points far from the main cluster and may warrant further investigation or robust modeling approaches. Residual plots are frequently used alongside QQ plots of residuals to assess normality and other diagnostic tools to evaluate model fit.

Limitations include sensitivity to outliers and the possibility that some issues may not be evident in a single plot. Proper interpretation often requires considering multiple diagnostics and the context of the data, including study design and potential data transformations.