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2.3 Linear Models

A general modeling principle is to "try simple things first." The idea behind this principle is that there is no reason to make a model more complex than necessary. The simplest type of model is often a linear model. Figure 2.2 illustrates a linear model. Each arrow in the figure symbolizes a parameter in the model.

Figure 2.2. A linear model.

Mathematically, the linear model gives rise to the following simple equation for the output

Linear models are called regression models in traditional statistics. In this case the output is said to regress on the inputs ,..., plus a bias parameter b.

Using the Neural Networks package, the linear model in Figure 2.2 can be obtained as a feedforward network with one linear output neuron. Section 5.1.1, InitializeFeedForwardNet describes how this is done.

A linear model may have several outputs. Such a model can be described as a network consisting of a bank of linear neurons, as illustrated in Figure 2.3.

Figure 2.3. A multi-output linear model.

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