Python for R Users by Ajay Ohri

Author:Ajay Ohri
Language: eng
Format: epub, pdf
ISBN: 9781119126782
Publisher: Wiley
Published: 2017-10-02T00:00:00+00:00

5.1.1 OLS

Ordinary least squares (OLS) or linear least squares is a method for estimating the unknown parameters in a linear regression model, with the goal of minimizing the differences between the observed responses in some arbitrary dataset and the responses predicted by the linear approximation of the data (visually this is seen as the sum of the vertical distances between each data point in the set and the corresponding point on the regression line—the smaller the differences, the better the model fits the data) (https://en.wikipedia.org/wiki/Ordinary_least_squares). The primary assumption of OLS is that there are zero or negligible errors in the independent variable, since this method only attempts to minimize the mean squared error in the dependent variable. The method of least squares is a standard approach in regression analysis to the approximate solution of overdetermined systems, that is, sets of equations in which there are more equations than unknowns. “Least squares” means that the overall solution minimizes the sum of the squares of the errors made in the results of every single equation.

The most important application is in data fitting. The best fit in the least‐squares sense minimizes the sum of squared residuals, a residual being the difference between an observed value and the fitted value provided by a model.

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

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