I encountered this statement from Statistical Learning by Stanford University. Can anyone give me an example?
In linear regression, the word "linear" applies to the coefficients: the dependence between $Y$ and the coefficients is linear. This does not mean the dependence between $Y$ and $X$ is linear.
Assume $X$ is a one dimensional variable. Basic linear regression is (I omit the noise and intercept for simplicity): $$Y=\beta X$$
But this is still linear regression:
The latter is the same as basic linear regression with feature vector $(X,X^2,\log(X))$ instead of $X$.