Linear regression is probably the first method that anyone will learn in terms of machine learning. The objective of linear regression is to find a relationship between one or more features (independent variables) and a continuous target variable (the dependent variable), which can be seen in the following code.

Import all the necessary libraries and declare all the necessary variables:

%matplotlib inline

#Import all the necessary libraries
import torch
import torch.nn.functional as F
import matplotlib.pyplot as plt


#we will define data points for both x-axis and y-axis
# x data (tensor), shape=(100, 1)
x = torch.unsqueeze(torch.linspace(-1, 1, 100), dim=1) 
# noisy y data (tensor), shape=(100, 1)
y = x.pow(2) + 0.2*torch.rand(x.size()) 

# torch can only train on Variable, so convert them to Variable
# x, y = Variable(x), Variable(y)

# plt.scatter(x.data.numpy(), y.data.numpy())
# plt.show()

We will define the linear regression class and run a simple nn to explain regression: 

class Net(torch.nn.Module):
 def __init__(self, n_feature, n_hidden, n_output):
 super(Net, self).__init__()
 self.hidden = torch.nn.Linear(n_feature, n_hidden) # hidden layer
 self.predict = torch.nn.Linear(n_hidden, n_output) # output layer

def forward(self, x):
 x = F.relu(self.hidden(x)) # activation function for hidden layer
 x = self.predict(x) # linear output
 return x

net = Net(n_feature=1, n_hidden=10, n_output=1) # define the network
print(net) # net architecture

optimizer = torch.optim.SGD(net.parameters(), lr=0.2)
loss_func = torch.nn.MSELoss() # this is for regression mean squared loss

plt.ion() # something about plotting

for t in range(200):
 prediction = net(x) # input x and predict based on x
 loss = loss_func(prediction, y) # must be (1. nn output, 2. target)
 optimizer.zero_grad() # clear gradients for next train
 loss.backward() # backpropagation, compute gradients
 optimizer.step() # apply gradients
 if t % 50 == 0:

Now we will see how to plot the graphs and display the process of learning:

     plt.cla()
     plt.scatter(x.data.numpy(), y.data.numpy())
     plt.plot(x.data.numpy(), prediction.data.numpy(), 'r-', lw=5)
     plt.text(0.5, 0, 'Loss=%.4f' % loss.data.numpy(), fontdict={'size': 20, 'color': 'black'})
     plt.pause(0.1)

plt.ioff()
plt.show()

Let's plot the output of this code on the graph, as follows:

The final plot looks as follows, with the loss (meaning the deviation between the predicted output and the actual output) equaling 0.01:

Now, we will start working toward deeper use cases using PyTorch.