Studying the quality requirements (aka Non-Functional Requirements (NFR)) of a system is crucial in Requirements Engineering. Many software projects fail because of neglecting or failing to incorporate the NFR during the software life development cycle. This paper focuses on analyzing the importance of the quality requirements attributes in software effort estimation models based on the Desharnais dataset. The Desharnais dataset is a collection of eighty one software projects of twelve attributes developed by a Canadian software house. The analysis includes studying the influence of each of the quality requirements attributes, as well as the influence of all quality requirements attributes combined when calculating software effort using regression and Artificial Neural Network (ANN) models. The evaluation criteria used in this investigation include the Mean of the Magnitude of Relative Error (MMRE), the Prediction Level (PRED), Root Mean Squared Error (RMSE), Mean Error and the Coefficient of determination (R2). Results show that the quality attribute Language is the most statistically significant when calculating software effort. Moreover, if all quality requirements attributes are eliminated in the training stage and software effort is predicted based on software size only, the value of the error (MMRE) is doubled.