In this study, friction tests are performed, via a custom-built friction tester, on specimens of natural rubber used in automotive suspension bushings. By analyzing the problematic suspension bushings, the eleven candidate factors that influence squeak noise are selected: surface lubrication, hardness, vulcanization condition, surface texture, additive content, sample thickness, thermal aging, temperature, surface moisture, friction speed, and normal force. Through friction tests, the changes are investigated in frictional force and squeak noise occurrence according to various levels of the influencing factors. The degree of correlation between frictional force and squeak noise occurrence with the factors is determined through statistical tests, and the relationship between frictional force and squeak noise occurrence based on the test results is discussed. Squeak noise prediction models are constructed by considering the interactions among the influencing factors through both multiple logistic regression and neural network analysis. The accuracies of the two prediction models are evaluated by comparing predicted and measured results. The accuracies of the multiple logistic regression and neural network models in predicting the occurrence of squeak noise are 88.2% and 87.2%, respectively.