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Ordinary least squares regression (OLSR) is a generalized linear modeling technique. It is used for estimating all unknown parameters involved in a linear regression model, the goal of which is to minimize the sum of the squares of the difference of the observed variables and the explanatory variables.
Ordinary least squares regression is also known as ordinary least squares or least squared errors regression.
Invented in 1795 by Carl Friedrich Gauss, it is considered one of the earliest known general prediction methods. OLSR describes the relationship between a dependent variable (what is aimed to be explained or predicted) and its one or more independent variables (explanatory variable). OLSR application can be found in myriad fields such as psychology, social sciences, medicine, economics and finance.
There are two relationships that may occur: linear and curvilinear. A linear relationship is a straight line that is drawn through the central tendency of the points; whereas a curvilinear relationship is a curved line. Associations between said variables are depicted by using a scatterplot. The relationship could be positive or negative, and result variation also differs in strength.
At a basic level, OLSR it can be easily understood even by non-mathematicians, and its solutions could be easily interpreted. Its added regard is due to its affordance with recent computers’ built-in algorithms from linear algebra. Thus it can quickly be applied to problems with hundreds of independent variables efficiently delivering results to tens of thousands of data points.
OLSR is often used in econometrics, as it provides the best linear unbiased estimator (BLUE) given the Gauss-Markov assumptions. Econometrics is branch of economics where statistical methods are applied to economic data. It aims to extract simple relationships by dissecting existing huge amounts of data. This statistical algorithm is also being used in machine learning and predictive analytics to dynamically predict outcomes based on dynamically changing variables.