How to detect the change of model for fitting

2 dimensional polynomial 3 dimensional polynomial Prepare for simple model (for example, 2D polynomial function) and complex model (for example, 3D polynomial function). The fitting accuracy (RMSE (root mean squared error)) for fitting is almost the same when x is small ． x y Case study: model for fitting when x is small is not the same as when x is large

If x is large, the fitting accuracy (RMSE (root mean squared error)) becomes different; The RMSE with 3D polynomial function is small while the RMSE with 2D polynomial function is large. x y Case study: model for fitting when x is small is not the same as when x is large 2 dimensional polynomial 3 dimensional polynomial