By following our experiments throughout the book, you may have noticed that adding new variables is always a great success in a linear regression model. That's especially true for training errors and it happens not just when we insert the right variables but also when we place the wrong ones. Puzzlingly, when we add redundant or non-useful variables, there is always a more or less positive impact on the fit of the model.
The reason is easily explained; since regression models are high-bias models, they find it beneficial to augment their complexity by increasing the number of coefficients they use. Thus, some of the new coefficients can be used to fit the noise and other details present in data. It is precisely the memorization/overfitting effect we discussed before. When you have as many coefficients as observations, your model can become saturated (that's the technical term used in statistics) and you could have a perfect prediction because basically you have...