## Linear regression

As explained in Chapter 2, *Data Pipelines and Modeling*, most complex machine learning problems can be reduced to optimization as our final goal is to optimize the whole process where the machine is involved as an intermediary or the complete solution. The metric can be explicit, such as error rate, or more indirect, such as **Monthly Active Users** (**MAU**), but the effectiveness of an algorithm is finally judged by how it improves some metrics and processes in our lives. Sometimes, the goals may consist of multiple subgoals, or other metrics such as maintainability and stability might eventually be considered, but essentially, we need to either maximize or minimize a continuous metric in one or other way.

For the rigor of the flow, let's show how the linear regression can be formulated as an optimization problem. The classical linear regression needs to optimize the cumulative error rate:

Here, is the estimate given by a model, which, in the case of linear regression, is as follows...