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Applying polynomial regression comes with an extra responsibility of managing overfitting. PCA might help but for polynomial functions, choosing the exponents of the parameters can be a much better option. Based on data available, choosing the parameters efficiently is necessary. For example, say we are making a model to predict the grade a student obtains based on his attendance, class interaction, the professor who teaches the subject and mode of transport. Clearly, the last parameter is useless in modelling hence it is necessary that we remove parameters from the model and efficiently use the model.
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