Multivariate Linear Model And Multi-index Prediction

The essay has mainly studied about two aspect content: The recognitions and revision of multicollinearity in linear model; Multi -index modelling and prediction. 1. The recognitions and revision of multicollinearityThe prime task includes qualitative and the quantitative analysis of the mechanism and the consequence which produces to the multicollinearity, the analysis and the value comparison of the commonly measures which used of judging the extent of multicollinearity (including condition number indicator, data redundancy measure , Theil indicator, variance inflation factor), then make analysis about a concrete example. The conclusion is: although four kinds of measures are carried on the description from the different aspect to the multicollinearity questions, the obtained conclusion is consistent. On the other hand, they all cannot give which variables exist multicollinearity. Finally we utilize the above methods to carry on the diagnoses of multicollinearity in the concrete model, and make the improvement using the ridge regression, its result improves the model fitting and the effect of the prediction.2. multi-index modellings and prediction.This article utilizes multivariate linear model method to establish the multi-index prediction model. Under the matrix loss, we find the best linear estimate class of the prediction index. Then obtain several best linear estimates, and finally we analyse carefully about the nature of obtained estimate.