In this chapter, we introduced regression with the simplest algorithm: simple linear regression. We first described a regression problem and where to fit a regressor, and then provided some intuitions underneath the math formulation. Then, we learned how to tune the model for higher performance, and came to deeply understand every parameter of it. In addition, some tricks were described to lower the complexity and scaling of the approach.
To start, we explored the coefficient of correlation between two quantitative variables X and Y, which provides information on the existence of a linear relation between the two variables. We understood that this coefficient does not allow us to determine whether it is X that affects Y, of whether it is Y that affects X, or whether both X and Y are consequences of a phenomenon that affects both of them. Only more knowledge of the problem under study can allow some hypothesis of the dependence of a variable on another.
Then, we analyzed a real-life...
