ML Regression

1.2.3 Regression
Regression is perhaps one of the most well-known and well understood algorithms in statistics and machine learning.
Machine learning, more specifically the field of predictive modeling is primarily concerned with minimizing the error of a model or making the most accurate predictions possible, at the expense of explainability. Linear regression was developed in the field of statistics and is studied as a model for understanding the relationship between input and output numerical variables, but has been borrowed by machine learning. It is both a statistical algorithm and a machine learning algorithm.
Linear regression is a linear model, e.g. a model that assumes a linear relationship between the input variables (x) and the single output variable (y). More specifically, that y can be calculated from a linear combination of the input variables (x). When there is a single input variable (x), the method is referred to as simple linear regression. When there are multiple input variables, the method referred as multiple linear regression. Different techniques can be used to prepare or train the linear regression equation from data, the most common of which is called Least Squares Regression.

1.2.3.1 Linear Regression Model Representation
The representation is a linear equation that combines a specific set of input values (x) the solution to which is the predicted output for that set of input values (y). As such, both the input values (x) and the output value are numeric.
The linear equation assigns one scale factor to each input value or column, called a coefficient that is commonly represented by the Greek letter Beta (?). One additional coefficient is also added, giving the line an additional degree of freedom (e.g. moving up and down on a two-dimensional plot) and is often called the intercept or the bias coefficient. For example, in a simple regression problem (a single x and a single y), the form of the model would be:
y = B0 + B1 × x
In higher dimensions when we have more than one input (x), the line is called a plane or a hyperplane. The representation therefore is the form of the equation and the specific values used for the coefficients (e.g. B0 and B1 in the above example).