Polynomial Linear Regression

Basics:

Why Polynomial Linear Regression required? I.e. Why can't problem be resolved thru just Simple/Multiple Linear?
Ans: For the data points like below, Simple/Multiple Linear Regression works fine (Fig 1). However if the data points are slightly parabolic, Simple/Multiple Linear Regression doesn't works well. (Fig 2). This is where  Polynomial Linear Regression fits well (Fig 3).

Fig 1.

Fig 2 (Not Fitting)

Fig 3.

Code: Polynomial Regression

# Importing the libraries
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

# Importing the dataset
dataset = pd.read_csv('Position_Salaries.csv')
X = dataset.iloc[:, 1:2].values   # Only one column taken
y = dataset.iloc[:, 2].values

# Splitting the dataset into the Training set and Test set is skipped due the dataset size is just 10 rows
"""from sklearn.cross_validation import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)"""

# Feature Scaling (Not required as data is already requires levels in designation)
"""from sklearn.preprocessing import StandardScaler
sc_X = StandardScaler()
X_train = sc_X.fit_transform(X_train)
X_test = sc_X.transform(X_test)"""

# Fitting Linear Regression to the dataset
from sklearn.linear_model import LinearRegression
lin_reg = LinearRegression()
lin_reg.fit(X, y)

# Fitting Polynomial Regression to the dataset
from sklearn.preprocessing import PolynomialFeatures
poly_reg = PolynomialFeatures(degree = 4)
X_poly = poly_reg.fit_transform(X)
poly_reg.fit(X_poly, y)

# Fitting Linear Regression to the Polynomial Result set
lin_reg_2 = LinearRegression()
lin_reg_2.fit(X_poly, y)

# Visualising the Linear Regression results
plt.scatter(X, y, color = 'red')
plt.plot(X, lin_reg.predict(X), color = 'blue')
plt.title('Truth or Bluff (Linear Regression)')
plt.xlabel('Position level')
plt.ylabel('Salary')
plt.show()



# Visualising the Polynomial Regression results
plt.scatter(X, y, color = 'red')
plt.plot(X, lin_reg_2.predict(poly_reg.fit_transform(X)), color = 'blue')
plt.title('Truth or Bluff (Polynomial Regression)')
plt.xlabel('Position level')
plt.ylabel('Salary')
plt.show()

# Visualising the Polynomial Regression results (for higher resolution and smoother curve)
# This is done for more smooth fitting the graph
X_grid = np.arange(min(X), max(X), 0.1)
X_grid = X_grid.reshape((len(X_grid), 1))

# Re-Visualising the Polynomial Regression results (on smoothened result set)
plt.scatter(X, y, color = 'red')
plt.plot(X_grid, lin_reg_2.predict(poly_reg.fit_transform(X_grid)), color = 'blue')
plt.title('Truth or Bluff (Polynomial Regression)')
plt.xlabel('Position level')
plt.ylabel('Salary')
plt.show()

Hope this helps!!!

Arun Manglick