On Mathematical and Statistical Aspects of Linear Models

Abstract

This research article presentssome mathematical and statistical aspects of linear models and their characteristic properties. In Statistics, the term linear model is used in different ways according to the context. The most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. However, the term is also used in time series analysis with a different meaning. In each case, the designation “linear” is used to identify a subclass of models for which substantial reduction in the complexity of the related statistical theory is possible. In this research article an attempt is made to presentsome specific forms of simple and multiple linear regression models. Here mathematical aspects of linear models are depicted in a lucid manner. A large number of mathematical models are discussed here and the methods of fitting transformed models are presented. Moreover specific form of linear statistical model is proposed and the crucial assumptions of general linear model are extensively discussed. Finally the method of ordinary least squares estimation of parameters of a linear model has been proposed