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Statistical errors and residuals are two closely related measures of the deviation of a sample from its theoretical value. The error of a sample is the deviation of the sample from the true function value. The residual of a sample is the difference between the sample and the estimated function value.A residual is an observable estimate of the unobservable statistical error. The sum of the residuals within a random sample is necessarily zero, and thus the residuals are necessarily not independent. The statistical errors on the other hand are independent , and their sum within the random sample is almost surely not zero. Standardizing the statistical errors in a z-score , and standardize residuals in a t-statistic, or more generally studentized residuals.
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