The following graph shows the different RMSE obtained for the five cross-validations and the different polynomial degrees (1 to 5):
We see that the best fit is obtained for the polynomes of degrees 3 and 4. In the end, the overall RMSE of our models based on polynomial regression models is not good compared to the RMSE obtained with quantile binning. Polynomial regression gives RMSE values at best around 0.85, while the RMSE with quantile binning was found to be around 0.15. Quantile binning, as it is done by Amazon ML, beats polynomial regression by a large factor.
