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Regression Analysis

Regression analysis

The dictionary meaning of the term regression' is the scat of returning or going back. The term regression' was first used by Sir Francis Galton (1822-19110 in 1877 while studying the relationship between the height of fathers and send. This term was introduced by him in the paper 'regression towards mediocrity in hereditary stature'. His study of height of about one thousand fathers and some revealed a very intrusting relationship, i.e. tall fathers tend to have tall sons and short fathers short sons, but the average height of the sons of a group of tall fathers is less than that of the fathers than that of the fathers. The line describing the tendency to regress or going back was called by Galton a regression line.' The term is still used to describe that line drawn for a group of points to represent the trend present, but it no longer necessarily carries the original implication of ''stepping back'' that Galton the term estimating line instead of regression line because the expression estimating line is more clarificatory in character.

**Some of its main topics are:**

1. Introduction to regression analysis

2. Uses of regression analysis

**Regression Analysis**

After having established the fact that two variables are closely related we may be interested in estimating (predicting) the value of one variable given the value of another. For example, if we know that advertising and sales are correlated we find out expected amount of sales for a given advertising expenditure or the required amount of expenditure for attaining a given amount of sales. Similarly. If we know that the yield of rice and rainfall are closely related we may find out the amount of rain required to achieve a certain production figure. Regression analysis reveals average relationship between two variables and this makes possible estimation or prediction.

The dictionary meaning of the term regression' is the scat of returning or going back. The term regression' was first used by Sir Francis Galton (1822-19110 in 1877 while studying the relationship between the height of fathers and send. This term was introduced by him in the paper 'regression towards mediocrity in hereditary stature'. His study of height of about one thousand fathers and some revealed a very intrusting relationship, i.e. tall fathers tend to have tall sons and short fathers short sons, but the average height of the sons of a group of tall fathers is less than that of the fathers than that of the fathers. The line describing the tendency to regress or going back was called by Galton a regression line.' The term is still used to describe that line drawn for a group of points to represent the trend present, but it no longer necessarily carries the original implication of ''stepping back'' that Galton the term estimating line instead of regression line because the expression estimating line is more clarificatory in character.

**Let us examine a few definitions of the term regression.**

**1. **''regression is the measure of the 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.''

**3. **''one of the most frequently used techniques in economics and business research. To find a relation between two or more variables that are related causally is regression analysis.''

**4. ** ''regression analysis attempts to establish the 'nature of the relationship' between variables-that is, to study the functional relationship between the variables and thereby provide a mechanism for prediction or forecasting.''

It is clear from 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 of ''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 but Y. the analysis used is called the simple liner regression analysis-simple because there is only one predictor or independent variable and liner because of the assumed liner relationship between the dependent and the independent variables. The term liner'' means that an equation of a straight line of the form Y = α = box, where a and b are constants is used to describe the average relationship that exists between the two variables.

It should be noted that the tern 'dependent' and ''independent refer to the mathematical or functional meaning of dependence-they do not imply that there is necessarily any cause and effect relationship between the variables. What it meant is simply that estimates of values of the dependent variable Y may be obtained for given values of the independent variable X from a mathematical function involving X and Y. in that sense, the values of Y are dependent upon the values of X. the X variable may or may not be product from figures on advertising expenditures, sales is generally taken as the dependent variable. However, there may or may not be causal connection between these two factors in the since that changes in advertising expenditures cause changes in sales. In fact, in certain cases. The cause-effect r3elation may be just opposite of what appears to be the obvious one.

**Uses of regression analysis**

Regression analysis is a branch of statistical theory that is widely used in almost all the scientific disciplines. In economics it is the basic technique for measuring or estimating the relationship among economic variables that constitute the essence of economic theory and economic life. For example, if we know that two variables, price (X) and demand (Y), are closely related we can find out the most probable value of X for a given value of Y or the most probable value of Y for a given value of X. similarly, if we know that the amount of tax and the rise in the price of a commodity are closely related, we can find out the expected price for a certain amount of tax levy. Thus we find that the study of regression is of considerable help to the economists and businessmen. The uses of regression are not confined to economics and business field only. Its applications are extended to almost all the natural, physical and social sciences. The regression analysis attempts to accomplish the following:

**1. **Regression analysis provides estimates of values of the dependent variable from values of the independent variable. The device used to accomplish this estimation procedure is the regression line. The regression line describes the average relationship existing between X and Y variables, i.e. it displays mean values of X for given values of Y. the equation of this line, known as the regression equation, provides estimates of the dependent variable when values of the independent variables are inserted into the equation.

**2. **A second goal of regression analysis is to obtain a measure of the error involved in using the regression line as a basis for estimation. For this purpose the standard error of estimate is calculated. This is a measure of the scatter or scatter of the observations around the regression line, good estimates can be made of the Y variable. On the other hand, if there is a great deal of scatter of the observations around the fitted regression line, the line will not produce accurate estimates of the dependent variable?

**3. **With the help of regression coefficients we can calculate the correlation coefficient. The square of correlation coefficient (r), called coefficient of determination, measures the degree of association of correlation that exists between the two variables. It assesses the proportion of variance in the dependent variable that has been accounted for by the regression equation. In general, the greater the value of r^{2} the better is the fit and the more useful the regression equations as a predictive device.

Uses of regression analysis

Regression analysis is a branch of statistical theory that is widely used in almost all the scientific disciplines. In economics it is the basic technique for measuring or estimating the relationship among economic variables that constitute the essence of economic theory and economic life. For example, if we know that two variables, price (X) and demand (Y), are closely related we can find out the most probable value of X for a given value of Y or the most probable value of Y for a given value of X. similarly, if we know that the amount of tax and the rise in the price of a commodity are closely related, we can find out the expected price for a certain amount of tax levy. Thus we find that the study of regression is of considerable help to the economists and businessmen. The uses of regression are not confined to economics and business field only. Its applications are extended to almost all the natural, physical and social sciences. The regression analysis attempts to accomplish the following:

**1. **Regression analysis provides estimates of values of the dependent variable from values of the independent variable. The device used to accomplish this estimation procedure is the regression line. The regression line describes the average relationship existing between X and Y variables, i.e. it displays mean values of X for given values of Y. the equation of this line, known as the regression equation, provides estimates of the dependent variable when values of the independent variables are inserted into the equation.

**2. **A second goal of regression analysis is to obtain a measure of the error involved in using the regression line as a basis for estimation. For this purpose the standard error of estimate is calculated. This is a measure of the scatter or scatter of the observations around the regression line, good estimates can be made of the Y variable. On the other hand, if there is a great deal of scatter of the observations around the fitted regression line, the line will not produce accurate estimates of the dependent variable.

**3. ** With the help of regression coefficients we can calculate the correlation coefficient. The square of correlation coefficient (r), called coefficient of determination, measures the degree of association of correlation that exists between the two variables. It assesses the proportion of variance in the dependent variable that has been accounted for by the regression equation. In general, the greater the value of r^{2} the better is the fit and the more useful the regression equations as a predictive device.

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