title: Linear regression with tensorflow
body: <p>I trying to understand linear regression... here is script that I tried to understand:</p>
  
  <pre><code>'''
  A linear regression learning algorithm example using TensorFlow library.
  Author: Aymeric Damien
  Project: https://github.com/aymericdamien/TensorFlow-Examples/
  '''
  
  from __future__ import print_function
  
  import tensorflow as tf
  from numpy import *
  import numpy
  import matplotlib.pyplot as plt
  rng = numpy.random
  
  # Parameters
  learning_rate = 0.0001
  training_epochs = 1000
  display_step = 50
  
  # Training Data
  train_X = numpy.asarray([3.3,4.4,5.5,6.71,6.93,4.168,9.779,6.182,7.59,2.167,
                           7.042,10.791,5.313,7.997,5.654,9.27,3.1])
  train_Y = numpy.asarray([1.7,2.76,2.09,3.19,1.694,1.573,3.366,2.596,2.53,1.221,
                           2.827,3.465,1.65,2.904,2.42,2.94,1.3])
  
  train_X=numpy.asarray(train_X)
  train_Y=numpy.asarray(train_Y)
  n_samples = train_X.shape[0]
  
  
  # tf Graph Input
  X = tf.placeholder("float")
  Y = tf.placeholder("float")
  
  # Set model weights
  W = tf.Variable(rng.randn(), name="weight")
  b = tf.Variable(rng.randn(), name="bias")
  
  # Construct a linear model
  pred = tf.add(tf.multiply(X, W), b)
  
  
  # Mean squared error
  cost = tf.reduce_sum(tf.pow(pred-Y, 2))/(2*n_samples)
  # Gradient descent
  optimizer = tf.train.GradientDescentOptimizer(learning_rate).minimize(cost)
  
  # Initializing the variables
  init = tf.global_variables_initializer()
  
  # Launch the graph
  with tf.Session() as sess:
      sess.run(init)
  
      # Fit all training data
      for epoch in range(training_epochs):
          for (x, y) in zip(train_X, train_Y):
              sess.run(optimizer, feed_dict={X: x, Y: y})
  
          # Display logs per epoch step
          if (epoch+1) % display_step == 0:
              c = sess.run(cost, feed_dict={X: train_X, Y:train_Y})
              print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(c), \
                  "W=", sess.run(W), "b=", sess.run(b))
  
      print("Optimization Finished!")
      training_cost = sess.run(cost, feed_dict={X: train_X, Y: train_Y})
      print("Training cost=", training_cost, "W=", sess.run(W), "b=", sess.run(b), '\n')
  
      # Graphic display
      plt.plot(train_X, train_Y, 'ro', label='Original data')
      plt.plot(train_X, sess.run(W) * train_X + sess.run(b), label='Fitted line')
      plt.legend()
      plt.show()
  </code></pre>
  
  <p>Question is what this part represent:</p>
  
  <pre><code># Set model weights
  W = tf.Variable(rng.randn(), name="weight")
  b = tf.Variable(rng.randn(), name="bias")
  </code></pre>
  
  <p>And why are there random float numbers?</p>
  
  <p>Also could you show me some math with formals represents cost, pred, optimizer variables?</p>