# Statistical Regression

• A. M. Mathai
• P. N. Rathie

## Abstract

Regression and correlation analyses are often used in problems in Econometrics, Biometry, Social Sciences and so on. Regression analysis is a widely used tool in evaluating the relationship among a number of variables and then using this relationship to predict the value of a variable or to forecast the value that will be taken by a variable at a particular time. The word regression means ‘going back’. The theory of regression analysis started when statisticians investigated the genetical problem of making inference regarding the parents by observing the offsprings. But in the present day statistical discussion this branch is the study of structural relationship among observable (on which numerical observations can be made) variables. For example, the price of a commodity may be related to the demand for that commodity. Both the price and demand are observable, but the exact nature of the relationship is unknown. This is evidently not a mathematical relationship such as y=2x+3. In the mathematical relationship y=2x+3 there is one and only one value for y, which is determinate, corresponding to a given value for x. For example if x=2 then y=7. But in the case of demand and price suppose that we estimate the relationship between the demand and price based on a given data but for a given price we won’t be able to say that the demand will be exactly a particular number.

## Keywords

Conditional Expectation Stochastic Variable Scatter Diagram Mathematical Relationship Linear Regression Coefficient