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Polynomial regression

Python notebook: https://github.com/daviskregers/data-science-recap/blob/main/10-polynomial-regression.ipynb

  • Not all relationships are linear

  • We can use higher orders of polynomials to produce more complex curves.

  • First order: \(y = mx + b\)

  • Second order: \(y = ax^2 + bx + c\)
  • Third order: \(y = ax^3 + bx^2 + cx + d\)

Beware of overfitting

  • Don't use more degrees than you need to
  • Visualize your data first to see how complex of a curve there might be
  • Visualize the fit - is your curve going out of it's wat to accommodate outliers?
  • A high r-squared simply means your curve fits your training data well, but it may not be a good predictor.
  • Later we'll talk about more principled ways to detect overfitting (train/test)