resId

Resid is an informal shorthand for residuals in statistics and data analysis. It may also refer to a residuals-related function in statistical software that returns the residuals of a fitted model. In regression and related models, a residual for observation i is the difference between the observed value y_i and the fitted value ŷ_i produced by the model: e_i = y_i − ŷ_i. Residuals quantify the portion of the data not explained by the model.

Several forms of residuals are used in diagnostics. Raw residuals are e_i themselves. Standardized residuals scale these by an estimate of variability. Studentized residuals adjust for observation-specific leverage, computed as e_i divided by ŝ_i√(1 − h_ii). In generalized linear models, Pearson residuals take the form (y_i − ŷ_i) / √Var(y_i | x_i). Deviance residuals reflect each observation’s contribution to the model’s deviance.

Residual analysis supports model diagnostics. Plotting residuals against fitted values or predictors helps assess linearity and homoscedasticity; patterning or funnel shapes can indicate misspecification. Large residuals may indicate outliers or influential observations, while systematic trends suggest missing variables or an incorrect functional form.

In software, resid is commonly available as a function or attribute. In R, resid(object) is a generic function that returns residuals from fitted model objects. Other environments provide similar access, often via a residuals attribute or method.

Notes: Residuals are model-dependent and should be interpreted within the context of the chosen model and data. They are tools for diagnostic evaluation rather than evidence of causal relationships.