Knowledge-based Comparable Predicted Values in Regression Analysis

Regression analysis has a major role in predicting values of a dependent variable by using values of independent variables. The estimate of predicted values is obtained as projected values in a linear subspace spanned by vectors of independent variables. However, if the data set has been observed simultaneously from multiple different data sources, then we must create different linear subspaces to estimate the different predicted values corresponding to the different data sources. Then, we cannot compare the different predicted values, since the linear subspaces are different. In order to solve this problem, we propose a method to obtain comparable predicted values obtained from different data sources by utilizing a fuzzy clustering result and an orthogonal projector which projects two different vectors corresponded with the two different dependent variables to the same intersection of the two different linear subspaces. From this, since the different predicted values from different data sources can be obtained in the common space, we can compare the different predicted values.