oh no, the null is not terrible!

This weekend, I did something that Teresa Huang (JHU) has been suggesting I do for a while in our project on linear regression: Plot the null prediction. That is, how much better do our regression methods do than a trivial prediction of zero, no matter what, for every data point? It turns out that her intuitions were correct: There are many settings for our regression problems in which the null prediction does better than any data-driven regression! What gives? If the training data are noisy, it is possible for any training to move your predictions in the worse direction from the null prediction. Hahaha, that's something we have to think about.