The basic assumption in regression analysis is that there is a linear relationship between the dependent and the independent variable over the entire range of the independent variable. The resultant regression coefficient conveys qualitative and quantitative information about the relationship. The qualitative information is given by the sign of the regression coefficient, while the quantitative information is given by the magnitude of the coefficient. The main contribution of this paper is to suggest simple graphical tools that can indicate the robustness of the qualitative results. That is, check whether the relationship between the dependent variable and the independent variable is monotonic over the entire range or not and in addition, if the relationship is not monotonic then the graphs can be used to identify the different sections with different signs and inform the user on the possibility and the type of monotonic transformations that can change the sign of the regression coefficient. The new techniques are illustrated by examples from the labor market. The adaptation of the methodology to a multiple regression case is also discussed.