# Standard Residual

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## Definition: Standard Residual

A residual is the fitting error i.e. it is the difference between the actual sample value and the observable estimate.

Standard residual is defined as the residual divided by the standard deviation of the residuals.

It can be calculated as follows:

1. If we have n residuals r1, r2,…,rN, then find the mean
2. Calculate the standard deviation of the series
3. For every residual, the standardized residual is given as

sr(i) = (ri-mean)/standard-deviation

This is a method of transforming the data so that its mean is zero and the standard deviation is one. Generally only 5% of the residuals could fall outside -2 and +2

If many of the residuals fall outside the given range, then the distribution is not considered to be normal. It is considered to be normal when more than 95% of the residuals fall in the range of -2 and +2.

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