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One of the many problems encountered in coming up with a multiple linear regression model is the presence of severe multicollinearity in the data set. In this work, the focus is on the mathematics of multicollinearity -- what it is, what it does to the model, how it can be detected and combated. Aside from the classical methods, artificial neural networks were also employed to combat multicollinearity. Softwares such as Statistical Package for the Social Science (SPPS) Release 7.0 and 10.0 for Windows, MATLAB version 5.3 and Stuttgart Neural Network Simulator (SNNS) version 4.1 were used to carry out the massive computations.