The baseline model – multiple linear regression
We will begin with the model's specification and objective function, the methods we can use to learn its parameters, and the statistical assumptions that allow the inference and diagnostics of these assumptions. Then, we will present extensions that we can use to adapt the model to situations that violate these assumptions. Useful references for additional background include Wooldridge (2002 and 2008).
How to formulate the model
The multiple regression model defines a linear functional relationship between one continuous outcome variable and p input variables that can be of any type but may require preprocessing. Multivariate regression, in contrast, refers to the regression of multiple outputs on multiple input variables.
In the population, the linear regression model has the following form for a single instance of the output y, an input vector , and the error :
The interpretation of the coefficients...