Predictive modeling on multivariate linear regression

Based on the historical data, predictive method of multivariate linear regression model was discussed, where both future multivariate regression parameters and the performance evaluation statistics were estimated without future data. Prediction to the regression parameters was converted to predict cross product matrix of the variable augmented matrix. By applying spectral decomposition, cross product matrix was decomposed of eigenvectors and eigenvalues. Predictive method of orthonomal matrix based on rotations of principal axes was adopted to predict eigenvector matrix, where rotated angles from Givens transformation were obtained, and regular predictive models were built on both the angles and eigenvalues, respectively. The experimental simulation illustrates main computational procedures of the predictive model. Besides, the results show a high precise of the fitted values and a statistical validity of the predictive values. The agreement of the final computation results with the experimental data indicates this method could be used to analyze and forecast regression relationships of dependent variable to independent variables in many application fields.