David Lindow: Metoden minstakvadratavstånd, matematiken bakom och några av metodens användningsområden

Abstract.

The least squares method is used in mathematics to estimate a function based on points in a coordinate system. For one or more parameters \(X\) and outcomes \(Y_1, \dotsc, Y_n\) for the least squares method involves finding a vector \(b\) that minimizes the absolute value \(|e|^2\) in the equation \(Y=Xb+e\). This can be applied to lines, quadratic curves, trigonometric functions, and more which is shown by examples in this paper. The method can also be used when the outcome is not continuous, as in statistics, provided that the outcome is normally distributed.