You have learned so far that observations are not perfect and that we need a mathematical model to describe the relation between the observations and the unknown parameters of interest. Such a mathematical model is by definition an idealisation of the real-world (truth). How to find an estimate of the unknown parameters using the mathematical model is the topic of this module. We will introduce the (weighted) least squares principle, and explain the underlying concept and properties. You will apply (weighted) least squares to various examples that you have seen previously.

By the end of the week you will be able to:

• Explain the concept and properties of (weighted) least squares.
• Apply (weighted) least squares for real-life examples, and interpret the solution.

Note: Least squares is a deterministic concept. It allows you to deal with measurement errors, but does not explicitly consider the fact that observations are stochastic variables.

Optional part: Geometry of least squares

The last part of this module is optional – it is about the geometry of least squares. It provides a geometric interpretation of the least squares principle. It may help you to obtain an even better understanding.