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Linear least squares
The principle or method by which the fit of a function to data is such that the sum of the squared residuals is minimised. In linear regression, the function is a line.
The sum of the squares of the residuals is used instead of the absolute values because this allows the residuals to be treated as a continuous differentiable quantity. However, because squares of the residuals are used, outlying points can have a disproportionate effect on the fit, a property that may or may not be desirable depending on the particular problem being considered.