## Regression Analysis

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# REGRESSION ANALYSIS

The dictionary meaning of the term ‘regression’ is the act of returning or going back. The term ‘regression’ was first sued by Sir Francis Galton in 1877 while studying the relationship between the height of fathers and sons. This term was introduced by him in the paper ‘Regression’ towards Mediocrity in Hereditary Stature.’

2. “The term ‘regression analysis’ refers to the methods by which estimates are made of the values of a variable from a knowledge of the values of one or more other variables and to the measurement of the errors involved in this estimation process.”

It is clear from the above definitions that regression analysis is a statistical device with the help of which we are in a position to estimate (or predict) the unknown values of one variable from known values of another variable. The variable which is used to predict the variable of interest is called the independent variable or explanatory variable and the variable we are trying to predict is called the dependent variable or “explained” variable. The independent variable is denoted by X and the dependent variable by Y. The analysis used is called the simple linear regression analysis – simple because there is only one predictor or independent variable, and linear because of the assumed linear relationship between the dependent and the independent variables.

The term “linear’’ means that an equation of a straight line of the form Y = a+bX where a and b are constants, is used to describe the average relationship when change in the independent variable (say X) by one unit leads to constant absolute change in the dependent variable (Y). When two variables have linear relationship the regression lines can be used to find out the values of dependent variable. When we plot two variables (say X and Y) on a scatter diagram and draw two lines of best fit which pass through the plotted points, these lines are called regression lines.

In linear regression, these lines are straight ones. These regression lines are based on two equations called regression equations which give best estimate of one variable when the other is exactly known or given.

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## A few definitions of the term regression

1. “Regression is the measure of average relationship between two or more variables in terms of the original units of the data.”2. “The term ‘regression analysis’ refers to the methods by which estimates are made of the values of a variable from a knowledge of the values of one or more other variables and to the measurement of the errors involved in this estimation process.”

It is clear from the above definitions that regression analysis is a statistical device with the help of which we are in a position to estimate (or predict) the unknown values of one variable from known values of another variable. The variable which is used to predict the variable of interest is called the independent variable or explanatory variable and the variable we are trying to predict is called the dependent variable or “explained” variable. The independent variable is denoted by X and the dependent variable by Y. The analysis used is called the simple linear regression analysis – simple because there is only one predictor or independent variable, and linear because of the assumed linear relationship between the dependent and the independent variables.

The term “linear’’ means that an equation of a straight line of the form Y = a+bX where a and b are constants, is used to describe the average relationship when change in the independent variable (say X) by one unit leads to constant absolute change in the dependent variable (Y). When two variables have linear relationship the regression lines can be used to find out the values of dependent variable. When we plot two variables (say X and Y) on a scatter diagram and draw two lines of best fit which pass through the plotted points, these lines are called regression lines.

In linear regression, these lines are straight ones. These regression lines are based on two equations called regression equations which give best estimate of one variable when the other is exactly known or given.

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