Problem
1. Experiment with the effects of feature scaling in linear regression. For a given data set with at least two features (dimensions), multiply all the values of one feature by 10k , for -10 ≤ k ≤ 10. Does this operation cause a loss of numerical accuracy in fitting?
2. Experiment with the effects of highly correlated features in linear regression. For a given (x, y) data set, replicate the value of x with small but increasing amounts of random noise. What is returned when the new column is perfectly correlated with the original? What happens with increasing amounts of random noise?