As I understand it, first we check the pattern of data and if it looks that it is not linear, we try to increase the degree to quadratic.If the curve of the data pattern is more abrupt, the degree of the polynomial should be increased.

Is this the idea? Does increasing the degree make the curve more abrupt or it fits the data with increased precision to the point of causing overfitting?

What else should be mentioned about that? Please explain thoroughly.

Showing an example in Python would be greatly appreciated.

  • $\begingroup$ The results of the regression must be evaluated by several criteria. I look to see if the regression errors have a normal distribution with a mean of zero, as they should. I also look to see if a scatterplot of the regression errors has some obvious shape or pattern, because that usually indicates that the polynomial order is too low. I also plot the polynomial curve on top of the data to look for Runge's Phenomenon (en.wikipedia.org/wiki/Runge%27s_phenomenon) which indicates overfitting. To my knowledge, there is no single indicator that works in every situation. $\endgroup$ – James Phillips Oct 22 '19 at 17:24

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