See more complete description in Linear Regression.

A method used in regression analysis.

The goal is to maximize the accuracy of the model, which is to minimize the error of the model.

The error, or residual, of a single point, is the difference between the actual y and the y predicted by the model.

Squaring the error converts it to an absolute value.

Summing the squared errors of all points gives a scalar to represent the total error of the model, which we then seek to minimize.

Thus we attempt to find the least squared sum, or the “least squares”.

Sum of Squared Residuals $$S = \sum r_i^2$$

The residual is actual y minus the y predicted by the function of x and β, where β represents the specific model.
$$r_i = y_i − f(x_i,β)$$

https://en.wikipedia.org/wiki/Least_squares