A simple linear regression is a model that can be used to predict and/or explain one variable from another one. Using machine learning language, this is a case of supervised learning. From a probabilitic perspective, a linear regression model is an extension of the Gaussian model where the mean is not directly estimated but rather computed as a linear function of a predictor variable and some additional parameters. While the Gaussian distribution is the most common choice for the dependent variable, we are free to choose other distributions. One alternative, which is especially useful when dealing with potential outliers, is the Student's t-distribution. In the next chapter, we will explore other alternatives.
In this chapter, we also discussed the Pearson correlation coefficient, the most common measure of linear correlation between two variables, and we learned...