# Application Of A Regression Analysis

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Since electricity demand and the regressors are in logarithms, the demand elasticities are directly derived from the coefficients. Monthly binary dummy covers from January to November and does not include dummy for December to avoid dummy variable trap. Severe multicollinearity between price variables of on-peak, mid-peak and off peak limited the estimation of cross price elasticity. We assume that individual error components are uncorrelated with each other. With regards to choice of econometric technique, we used Cochrane-Orcutt estimation to adjust serial correlation in error terms. Due to the same explanatory variables appear in the log-log equations, which is in fact OLS is equivalent to seemingly unrelated regression, it is not…show more content…
Multicollinearity occurs when two or more predictors in the model are correlated and provide redundant information about the response. That is, a multiple regression model with correlated predictors can indicate how well the entire bundle of predictors predicts the outcome variable, but it may not give valid results about any individual predictor, or about which predictors are redundant with respect to others. Consequences of high multicollinearity is that increase in standard error of estimates of the b’s so that decrease in reliability (Farrar and Glauber 1967). In case of perfect multicollinearity the predictor matrix is singular and therefore cannot be inverted. Under these circumstances, the ordinary least-squares estimator b '=(X 'X)-1X 'y does not exist. To detect multicollinearity, we calculate the variance inflation factors for each predictors in RHS (Mansfield and Helms 1982). The VIF (variance inflation factors) for each predictor xj is: VIFj = 1/( 1−R2j). R2j is the coefficient of determination of the model that includes all predictors except the jth predictor. The models for the VIF test are: VIF for ln Pon: ln Ponm = ln I + b2 ln Pmidm + b3 ln Poffm + b4 ln GPPt + cmDm + uont VIF for ln Pmid: ln Pmidm = ln I + b2 ln Ponm + b3 ln Poffm + b4 ln GPPt +