Explain how a polynomial regression works.
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.