Multiple linear regression
In all previous examples we have been working with one dependent variable and one independent variable, but in many cases we will find that we have many independent variables we want to include in our model. Some examples could be:
Perceived quality of wine (dependent) and acidity, density, alcohol level, residual sugar, and sulphate content (independent variables)
Student average grades (dependent) and family income, distance home-school, and mother education (independent variables)
In such a cases, we will have the mean of the dependent variable modeled as:
Notice that this is not exactly the same as the polynomial regression we saw before. Now we have different variables instead of successive powers of the same variable.
Using linear algebra notation we can write a shorter version:
Where 
is a vector of coefficients of length m, that is, the number of dependent variables. The variable 
is a matrix of size 
if n is the number of observations and m is the number of...
