Implementing an ordinary least squares linear regression model

At the beginning of this chapter, we discussed that linear regression can be understood as finding the best-fitting straight line through the sample points of our training data. However, we have neither defined the term best-fitting nor have we discussed the different techniques of fitting such a model. In the following subsections, we will fill in the missing pieces of this puzzle using the Ordinary Least Squares (OLS) method to estimate the parameters of the regression line that minimizes the sum of the squared vertical distances (residuals or errors) to the sample points.

Solving regression for regression parameters with gradient descent

Consider our implementation of the ADAptive LInear NEuron (Adaline) from Chapter 2, Training Machine Learning Algorithms for Classification; we remember that the artificial neuron uses a linear activation function and we defined a cost function , which we minimized to learn the weights via...