Linear Regression with Corrected Errors of Independent and Dependent Variables

Abstract:

This paper presented a new linear regression method where the errors of dependent and independent variables and correlations of errors were adequately captured. The iteration formulae for calculating the regression parameters were derived at the same time. Taking univariate linear regression problem as an example, analytical formulas for linear regression parameters that similar to those from leastsquares method were derived, with which the essential difference between leastsquares method and new method were demonstrated. In addition, for the multiple linear regression that with multiple independent variables, the corresponding method, which considers the errors of both independent and dependent variables and the correlations of errors, for calculating the linear regression parameters were also shown. The experiment results shown that the new method and leastsquares method were equivalent to each other when independent variables were nonrandom; whereas, the regressive parameters from new method were more closer to the true values than those from the leastsquares method when both independent and dependent variables were all random (no matter their errors were correlated or not).