Regression Analysis

Demand Estimation by Regression Method – Some Statistical Concepts for application

In case of demand estimation working with data on sales and prices for a period of say 10 years may lead to the problem of identification. In such a case the different variables that may have changed over time other than price, may have an impact on demand more rather than price. In order to avoid this problem of identification what we adopt is the techniques of demand estimation through regression process in order to distinguish the effects of different variables on demand. In order to understand the basic working and application of the model, let us start with two variable model

Two-variable Regression model

To find out the relation between two variables X & Y, usually a linear relation is estimated. If it is non-linear one then we convert it into log-linear to estimate the equation. Among the scatter of points in plane X-Y, we try to fit in the best line that can estimate the relationship. Here Y is the dependent variable and X is the independent variable. Let us take the example given in Salvatore. Let demand be the function of advertisement expenditure by the particular firm. Then the scatter diagram will show as the ad. Exp. Increases the sales volume will rise. In order to estimate the relationship of Sales (Y), on advertisement Expenditure (X), we regress the following equation,

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In order to establish this relation we need to estimate a and b with the help of the data set on Y and X. we use a technique called ordinary least squares technique in order to find out the best fitted line. In order to do so, we minimize the sum of squared errors

(measure of overall variation of estimated sales from observed sales), assuming that the sum of error is equal to zero. Thus the error is given by,

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Thus we need to minimize the above in such a way that the estimated values minimize the above error variance. Minimizing the above with respect to a and b we get the...