I am working through the book Applied Predictive Modeling and came across something that was a bit confusing.

It discussed adding non linearity to a model to improve its fit - I get this part.

For example: $x^2 + 2x - 4$

What is the interpretation of these values though?

When we are using just a normal linear regression or a multivariate regression, we would say that the coefficients like 2 would suggest its relative importance relative to the other features being included in the model. However, what does this mean in the context of quadratic functions?

ie. Fuel efficiency of a car based on 2 Displacement + Displacement$^2$ -4

What exactly does displacement squared mean?

Any help would be greatly appreciated.



$Displacement$ component gives us a "line" to fit over the data points. To get more freedom add $Displacement^{2}$ a "curve" element. This adds to the flexibility - with same feature/ variable - to map the data points. Please refer page 90, 91 on Introduction to Statistical Learning in R - Hastie, Tibshirani

  • $\begingroup$ I understand that we are using a non linear fit vs a linear fit. My question is what is the conceptual understanding for displacement$^2$ in words? $\endgroup$ – user67797 Jun 20 at 23:56
  • $\begingroup$ Seems that even Hastie, Tibshirani did not provide answer your query. Also, I'm sure that know the meaning/ difference of x-y relationship in: y = x, y = x$\^2$ curves on a graph. Further ahead, you definitely know what is meaning of x in both graphs/ curves. If you're clear about all of the above, and you've referred the free pdf of book, then I'll curious to see an answer, that resolves your query. Regards. $\endgroup$ – Continue2Learn Jun 21 at 1:56

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