Effect of Transformation on the Parameter Estimates of a Simple Linear Regression Model: A Case Study of Division of Variables by Constants

The ability to forecast accurately the future values of a given variable within the minimum possible time gives organizations, governments and business enterprises the opportunity for appropriate decision and policy making. Accurate predictions can be made with a correctly specified model. It is evident that an estimated model comprises parameter estimates. Hence, different sets of estimates may give rise to different forecasts. Again, researchers and experimenters often report large values in some standard forms which include thousands, millions and billions so as to save time required for compilation and computation. In this study, an attempt was made to provide estimates of the parameters of the models involving the transformation obtained by dividing the variables by constants. The effect of the transformation on the parameter estimates was also emphasized. The relationships between the estimates of the parameters of the original model and those involving the transformed variables were derived. It has been shown that the division of the independent variable by a constant did affect the estimate of the slope only. On the other hand, the estimate of the slope of the original model remained unaffected when both variables were divided by the same constant where as other obtained parameter estimates appeared to differ from those of the original model. The theoretically derived estimates were substantiated by empirical data analysis. Moreover, the regression models fitted based on the various transformed variables differed from that of the original model. As a result, transformation by means of dividing the variables by constants affects the parameter estimates as well as the predictability of the model.