回归分析中的病态矩阵及其改进_莫惠栋1

Abstract In regression analysis  the information matrix XX is an important factor because of b XX

XY If

the determinant value of XX  detXX is close to zero  the inverse of the XX  XX

 will extremely

respectivelyThe illconditioned XX results from the linear dependency among columns in X matrix Three

diagnostic criteria  including linear correlation coefficient  multiple determination coefficient and condition index 

can measure the degree of the column dependency In order to improve or eliminate the illconditioning of XX 

four methods  i e 1to reduce the original regression model  2to collect the new data  3to add the

restrictive condition for regression coefficients and 4to adopt the noncustomary regression procedure such as the

regression  are suggested The importance of diagnosing the ill

conditioning and the evaluation for improved illconditioning are also discussed briefly 

Key words Regression analysis Illconditioned matrix Diagnosis and improvement of illconditioning



为 XX 的逆阵 Y 为依变数的