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Simple And Multiple
Linear Regression Analysis

The regression has a much wider perspective in the statistics. Regression analysis, now, means the estimation or prediction of the unknown value of one variable on the basis of known value of the other variable. It is one of the very important statistical tools which are widely used in almost all sciences natural, social and physical. It has particular application in business and economics to study the relationship between two or more variables that ate closely related to each other and for estimating the demand and supply curves, cost function, etc.

Prediction or estimation is one of the major problems in all spheres of human activity. The predictions of future production, consumptions, prices, investments, sales etc. are vital important to a businessmen and economist, Regression analysis is the scientific technique for making such prediction. M.M. Blair has described Regression analysis as a mathematical measures of the average relationship two or more variables in terms of the original units of the data. Therefore, it is clear that regression analysis is a statistical device for estimating the unknown values of one variable from known values another variable on the basis of average relationship between these two variables. The variable which is used to estimate the another variable, is called independent variable or explained variable. In statistics, the independent variable is usually denoted by X and the dependent variable by Y. When the regression analysis is confined to the study of only two variables at the time, then it is known as simple liner regression analysis. It is simple regression because there is only one independent variables. On the other hand, the regression analysis for studying more than two variables at a time is known as multiple regressions. The scope of this lesson is restricted to simple linear analysis and multiple linear regression analysis upto three variables.

Simple Linear Regression Analysis:

In simple linear regression analysis, the analysis is limited to two variables i.e., one independent and another dependent variables. Here we assume linear relationship for estimating the value of dependent variable on the basis of independent variable.

Regression Equation:

Regression equations are the algebraic expression of the regression lines. Like regression lines, there are two regression equations, the regression equation Y on X and regression equation X on Y. These equations could be used for estimation and judging the degree of correlation.

Graphing the Regression Lines:

It is very simple to graph the regression lines on the basis of regression equations as computed above. The involves the following steps:

  • Compute the estimated values of X and Y with the help of regression equations X and Y and Y on X. In order to draw regression lines, it is preferable to estimate two values of each variable X and Y. Because by adjoining two values of one variable, we can draw straight line for that variable.
  • Plot the estimated values of X variable in the graph and draw a straight line through these plotted points. This will give us regression line of X on Y.
  • Plot the estimated values of Y variable in the graph and draw a straight line through these plotted points. This will give us regression line Y on X.

Multiple Regression Analysis:

It is possible through multiple regression analysis to measure the joint effect of any number of independent variables upon a dependent variable. In fact, multiple regression equation explains the average relationship between these variables, and such relationship is useful to estimate the value of dependent variable. Here, the discussion on multiple regression analysis is limited to three variables, i.e., one dependent variable and two independent variables. Moreover, the relationship between these variables is assumed to be linear. In case of three variables, a linear regression equation for estimating the value of the dependent variable X2 and X2 in down as a regression equation of X1 and X and X2. It can be written as: X1 = F(X2, X2)

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