In recent years, the backpropagation neural network has been shown to be a good modelling method for complex problems because of its self-adjusting ability, and the fact that it can be used with small amounts of data. However, some factors in the data may be insignificant and correlated, or there may be some noise present. These phenomena will cause the model to predict inaccurately. In this research, we propose a statistical method to avoid such situations, by screening variables and testing for normality. The model built by using screened variables shows a better fit and yields accurate predictions. To demonstrate the proposed method, we conduct cutting experiments and build cutting tool life models as an example. Then we compare the results of the constructed models among the backward stepwise regression, the neural network and the proposed neural network methods. The proposed neural network method shows the most accurate prediction.