In the seminar, we define linear models of several variables in general. Then we introduce the model using the least squares method, where we look at the main features of the model and highlight the main disadvantages for different types of data. We continue to introduce a related model of principal component regression, where we present the main ideas of the principal component method. After we are familiar with how this method works, we apply a similar principle to the method of partial least squares. The theory of the model is supported by examples of how the method works in prediction. Finally we look also at the problem of classification and nonlinear models, where we show the operation on some simple examples.
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