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In statistics, the mean signed difference, deviation, or error is a sample statistic that summarises how well a set of estimates θ ^ i {\displaystyle {\hat {\theta }}_{i}} match the quantities θ i {\displaystyle \theta _{i}} that they are supposed to estimate. It is one of a number of statistics that can be used to assess an estimation procedure, and it would often be used in conjunction with a sample version of the mean square error.
For example, suppose a linear regression model has been estimated over a sample of data, and is then used to extrapolate predictions of the dependent variable out of sample after the out-of-sample data points have become available. Then θ i {\displaystyle \theta _{i}} would be the i-th out-of-sample value of the dependent variable, and θ ^ i {\displaystyle {\hat {\theta }}_{i}} would be its predicted value. The mean signed deviation is the average value of θ ^ i − θ i . {\displaystyle {\hat {\theta }}_{i}-\theta _{i}.}
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