Linear Regression
In linear regression, the target variable, Y, is a continuous variable, meaning that it assumes all possible values in a bounded or unbounded interval, (a,b) 
R, where R is the set of real numbers. In this way, the preceding equation assumes the following concrete form:
Figure 3.17: Linear regression equation
Let's denote the right-hand side of the preceding equation with Ŷ, as follows:
Figure 3.18: Linear regression equation
Then, if we have n samples in our data (where for each i ϵ {1,..., n}, we denote the entries for the m features with xi,1,....xi,m and the target variable with y_i), we can rewrite the previous equation in a more specific form, as follows:
Figure 3.19: Linear regression equation in a specific form
Note that in Figure 3.17 and Figure 3.19, we assume that the dependency of Y from the feature vectors X1,...,Xm is either linear or can be approximated...