Linear regression is a private case of polynomial regression

• The formula of linear regression: y=mx+b .This formula represents a straight line but not all relationships are linear.
• Linear regression is just one example of all class of regressions.It's actually a first-degree polynomial regression.
• Polynomial regressions:

  

  first degree polynomial regression - linear regression

  
  

  

  second degree polynomial regression

  

  third degree polynomial regression

  
  
• python code example
  

  import numpy as np
  import matplotlib.pyplot as plt
  
  np.random.seed(2)
  numberOfVisitors = np.random.normal(3, 1, 1000)
  numberOfClicks = np.random.normal(50, 10, 1000) / numberOfVisitors
  
  x = np.array(numberOfVisitors)
  y = np.array(numberOfClicks)
  
  # create a line from x=0 to x=7 width 100 evenly spaced values
  xp = np.linspace(0, 7, 100)
  
  # 4 degree polynomial fit
  p4 = np.poly1d(np.polyfit(x, y, 4))
  plt.scatter(x, y)
  plt.plot(xp, p4(xp), c='r')
  plt.show()

4 degree polynomial fit