# Linear regression example

In this example, we want to approximate the following scatter plot with a single layer neural network. Blue points are the training set given by an input $$x_i$$ and an expected output $$y′_i$$. The red line is the output of the network $$y=f(x)$$ after training.

The following perceptron will be used for the single layer network:

$$x$$ is the input. The activation function is given by $$f(x)=x$$.

## Update rule

As explained on the previous page, the weights will be updated according to this formula:

$$w_i'= w_i + \eta(y'-y)x_i$$

Let's detail for each weight $$w_1$$ and $$w_2$$:

$$w_1'= w_1 + \eta(y'-y)x$$ $$w_2'= w_2 + \eta(y'-y)$$