The inner mechanics of the linear regression algorithm

In its most fundamental form, the expression for the linear regression algorithm can be written as follows:

In the preceding equation, the output of the model is a numeric outcome. In order to obtain this numeric outcome, we require that each input feature be multiplied with a parameter called Parameter1, and we add the second parameter, Parameter2, to this result.

So, in other words, our task is to find the values of the two parameters that can predict the value of the numeric outcome as accurately as possible. In visual terms, consider the following diagram:

Two-dimensional plot between the target and input feature

The preceding diagram shows a two-dimensional plot between the target that we want to predict on the y axis (numeric output) and the input feature, which is along the x axis. The goal of linear regression is...