Least squares regression
In the previous section, we saw an example of simple linear regression, built the model, and now have a brief description of it. Next, we will explain the results in detail. We will get started by introducing the key concepts, with another simple linear regression example; we will just use data in the form of a spreadsheet containing the number of vehicles registered in Italy and the population of the different regions. Using this data we will try to determine the line that best estimates the relationship between the population and number of registered vehicles. We can do this in various different ways; we will begin with the simplest. Previously, we said that a linear relationship is represented by the following formula:
If we have a set of observations in the form (x1, y1), (x2, y2), ... (xn, yn), for each of these pairs we can write an equation of the type just seen. In this way, we get a system of linear equations. Represent this equation in matrix form as follows...
