So far, regression analysis is used to model the mean of response variable as a function of some independent variables, using the least squares (LS) method. In general, the LS method is able to describe well the measure of central tendency, however it is not robust against outliers. Therefore, in certain cases, a regression analysis that minimizes the sum of absolute residuals (least absolute deviation - LAD) is required, which is more robust against outliers. So far, the value of the regression coefficient is not modeled and only depends entirely on the data processed. In some cases, the sign and the value of regression coefficients need to be controlled, in order to be in the meaningful range. The results of this study showed that the modification of the constraints on the LAD regression able to control the regression coefficients to be in the meaningful range. The results of bootstrap showed that distribution of controlled regression coefficients were different from distribution of uncontrolled regression coefficients.