Explain how a polynomial regression works.

405    Asked by Ajit yadav in Data Science , Asked on Dec 25, 2019
Answered by Ajit yadav

Polynomial Regression is linear on the coefficients since we don’t have any power of the coefficients (all the coefficients are raised to the power of 1: b0, b1, ..., bn). However, Polynomial Regression is a nonlinear function of the input x, since we have the inputs raised to several powers: x (power 1), x2 (power 2), ..., xn (power n). That is how we can also see the Polynomial Regression as a nonlinear model. Besides indeed, Polynomial Regression is appropriate when the data is non linearly distributed (meaning you can’t fit a straight line between y and x).

We don’t apply feature scaling in our polynomial regression model.It’s simply because, since y is a linear combination of x and x2, the coefficients can adapt their scale to put everything on the same scale. For example if y takes values between 0 and 1, x takes values between 1 and 10 and x2 takes values between 1 and 100, then b1 can be multiplied by 0.1 and b2 can be multiplied by 0.01 so that y, b1x1 and b2x2 are all on the same scale.



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