Please answer each of the following questions in detail and provide examples for better clarity,

wherever applicable. Provide in-text citations.

Figure 1 shows a typical composition of neurons in a net. This discussion questions aimed at

learning how natural composition of neural nets can be mimicked to derive algorithms that can

provide prediction at higher levels of complexity.

1. Consider a multiple regression model of your choice containing two predictors.

Calculate the values of the regression equation with a range chosen by you for the

values of the predictors. Provide the graph of the regression equation which is a plane.

2. Augment your regression model by a sigmoid posterior filter. Calculate the values of the

regression equation within the range chosen in part 1. Provide the graph of the

regression equation, which will be a sigmoidal surface. Show that this graph cannot

have a local extremum.

3. Now, add another regression model with sigmoid posterior containing the same two

predictors in the previous part. Repeat parts 1 and 2 for this new regression model.

4. Now consider a model of a neural net, which has two parallel hidden layers, which are

the two regression models considered above. The output of the net is simply the

superposition of the two regression models. Show that by proper choice of the

parameters you can have an output, which has a local extremum within the choice for

the range of the values of the predictor. Provide the graph of the regression equation.

5. How does this observation indicate an application of neural networks modeling in

practice?

Figure 1 Typical Composition of Neurons in a Net lngut Lam Hidden Mar