In this assignment we will explore the well known fact that sometimes a simple neu- ral network featuring an identity activation function can improve model forecasting capabilities by a proper transformation of the input information. This procedure is generally known as feature engineering. To this aim let us again consider the problem of forecasting the water vapor pressure data shown in the following Figure: To simplify calculations let us consider a single layer neuron as shown in the next Figure: 3 y x where y stands for the output response (vapor pressure), r is the first input data (saturation temperature), whereas r = f(xl) is the second input data. In general the f() function can take several forms, and it should mimic the output response as much as possible. You are asked two carry out the following tasks: 1. What do you think the characteristics of f() should be? Why? 2. Let us consider the following forms of the f() function: f(1) = x2 f() =23 f = e" For each one of the above three forms of the f() function formulate and solve the neural network water vapor pressure forecasting