Because of the natural dispersion of data, a regression model will make erroneous predictions. The best one can hope for is that the model embodies a function close to the true (and forever unknown) regression function, which is the "average distribution" of the data.
The error of a regression model on a particular observation is called the residual of the model for that observation. Usually, the parameters of a regression model are calculated so as to minimize the sum of the squares of the residuals ("Least Squares" method).
For one particular observation to have a high or low value residual tells absolutely nothing about the model being good or bad in the region around that observation.
* A model may be excellent around a point, yet an observation sitting at this point may have a high value residual because of dispersion.
* For similar reasons, an
observation with a very low residual may be sitting in a region where the model
But of course if all residuals in a particular area are low (resp. large), then the model is good (resp. bad) in this area.
A detailed analysis of the residuals can be conducted only within the framework of Linear Regression (Simple or Multiple). The objective of such analysis is to :
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