DEFINITION of 'Sum Of Squares'

A statistical technique used in regression analysis. The sum of squares is a mathematical approach to determining the dispersion of data points. In a regression analysis, the goal is to determine how well a data series can be fitted to a function which might help to explain how the data series was generated. The sum of squares is used as a mathematical way to find the function which best fits (varies least) from the data.


In order to determine the sum of squares the distance between each data point and the line of best fit is squared and then all of the squares are summed up. The line of best fit will minimize this value.

BREAKING DOWN 'Sum Of Squares'

There are two methods of regression analysis which use the sum of squares: the linear least squares method and the non-linear least squares method. Least squares refers to the fact that the regression function minimizes the sum of the squares of the variance from the actual data points. In this way, it is possible to draw a function which statistically provides the best fit for the data. A regression function can either be linear (a straight line) or non-linear (a curving line).

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