Residualplottar

Residualplottar, or residual plots, are diagnostic plots used in regression analysis to assess how well a model fits data by visualizing residuals, the differences between observed responses and model-fitted values. The most common form is the residuals versus fitted values plot, where residuals are plotted on the vertical axis against the predicted values on the horizontal axis. This plot helps detect nonlinearity, nonconstant variance, and outliers. Other common plots include residuals versus each predictor to assess individual covariate effects, and the scale-location plot (also called spread-location plot), which plots the square root of the absolute residuals against fitted values to assess homoscedasticity. A normal probability plot (Q-Q plot) of residuals is used to assess whether residuals are approximately normally distributed, a key assumption for many inference procedures.

Interpretation: A random scatter with no apparent pattern in residual plots suggests that the linear model is appropriate and assumptions are reasonably satisfied. Systematic curves indicate nonlinearity, increasing or decreasing spread indicates heteroscedasticity, and unusual points can signal outliers or influential observations.

Applications: Residual plots are standard practice in linear regression, generalized linear models, and time-series regression as a quick diagnostic tool. They guide transformations (such as log or Box-Cox), the addition of predictors, or switching to robust or nonlinear modeling.

Limitations: Residual plots are diagnostic rather than prescriptive; they cannot confirm model adequacy on their own and may be inconclusive with small samples. They should be used alongside quantitative tests and other diagnostics.