# Regression Analysis for Demand Estimation

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 void 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

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Test of Goodness of fit ( Coefficient of Determination)

In order to see whether the overall regression has been a good fit or not, we take the help of Coefficient of Determination, which is given as follows

(to be remembered) where the numerator is the explained variation in Y and denominator is the total variation ion Y. There is adjusted R2 as well which incorporates the degrees of freedom and is a more accurate measure of goodness of fit. (to be remembered). A higher R2 implies that the fit of the line is good to relate changes in X to changes in Y and the line is the good estimator of the relationship.

Multiple Regression Model

Here the number of explanatory variables may be more than one. There may be several variables that have an impact on demand. With one variable the coefficient of determination may be very less than with several variables. This explains why we shall estimate demand with several variables. In order to get a better fitness we shall include several variables that can lead to more accuracy. On the other hand this will lead to the problem of estimating more number of coefficients or parameters attached to these variables, thus degrees of freedom will get reduced. In order to solve this problem we shall have to work with a large number of data set or number of observations must increase. In case of a multiple regression model, instead of calculating the t- statistic to