4.1 Simple linear regression

Many problems we find in science, engineering, and business are of the following form. We have a variable X and we want to model or predict a variable Y . Importantly, these variables are paired like {(x₁,y₁),(x₂,y₂),,(x_n,y_n)}. In the most simple scenario, known as simple linear regression, both X and Y are uni-dimensional continuous random variables. By continuous, we mean a variable represented using real numbers. Using NumPy, you will represent these variables as one-dimensional arrays of floats. Usually, people call Y the dependent, predicted, or outcome variable, and X the independent, predictor, or input variable.

Some typical situations where linear regression models can be used are the following:

• Model the relationship between soil salinity and crop productivity. Then, answer questions such as: is the relationship linear? How strong is this relationship?

• Find a relationship between average chocolate consumption by country and the number of Nobel...