Simple linear regression

Many problems we find in science, engineering, and business are of the following form. We have a variable  and we want to model/predict a variable . Importantly, these variables are paired like . In the most simple scenario, known as simple linear regression, both  and  are uni-dimensional continuous random variables. By continuous, we mean a variable represented using real numbers (or floats, if you wish), and using NumPy, you will represent the variables  or  as one-dimensional arrays. Because this is a very common model, the variables get proper names. We call the  variables the dependent, predicted, or outcome variables, and the  variables the independent, predictor, or input variables. When  is a matrix (we have different variables), we have what is known as multiple linear regression. In this and the following...