Polynomial Regression for Housing Price Prediction

The section titled ‘Alternate View’ in the lab on Feature Engineering and Polynomial Regression states
Above, polynomial features were chosen based on how well they matched the target data. Another way to think about this is to note that we are still using linear regression once we have created new features. Given that, the best features will be linear relative to the target. This is best understood with an example.

I don’t quite understand this. Is it saying that y=x^2 which is why the plot of y versus x^2 is linear which in turn implies that linear regression can work in this case? If so, would linear regression not work for x^3 because the plot of y versus x^3 is non-linear?


It will work. However, the straight line will not perfectly fit the values for the features x^1 or x^3.