حل معادلات برآوردکننده مدل‌های رگرسیون با اندازه خطای تصادفی روی متغیر مستقل به روش بهینه سازی

Measurements of some variables in statistical analysis are often encountered with random errors. Therefore, investigating of the effects of these errors seems to be important. This event in regression analysis seems to be more necessary. Because the aim of the fitting a regression model is estimating the effect of an independent variable on a response variable. Then measurements of an independent variable in a regression model are subject to random error, this may affect the parameter estimating processes. In this article, we first investigate how random errors occur on the measurements of a random variable. Then we show that exist such an error on the measurements of the independent variable has an impact on the estimating of the parameters, such that it makes impossible to directly solve the estimating equations for the estimating of the regression model parameters. We also show with an optimization procedure by solving the estimating equations the estimation of model parameters can be achieved. Finally, we test the results of the optimization procedure on two practical examples, and we illustrate the effects of ignoring random errors in estimating model parameters in these two examples.