Polynomial Regression

Polynomial regression is just as simple linear regression except most of the data points are located at the same side of best fit line, therefore making a quadratic kind of curve. 

In this model we would make predictions using both simple linear regression and polynomial regression and compare which best describes this dataset.

Dataset:-

It contains the salary of all the positions of an employee of a company. We need to predict the salary of an former employee who claims to be a Region Manager for half a year.

Data-set

Code:-

#importing libraries

import numpy as np

import matplotlib.pyplot as plt

import pandas as pd

#importing dataset

dataset=pd.read_csv('Position_Salaries.csv')

x=dataset.iloc[:,1:2].values

y=dataset.iloc[:,2].values

#splitting datase into training and test set

"""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)"""

Fitting the result into regression model 

#fitting linear regression to dataset

from sklearn.linear_model import LinearRegression

lin_reg=LinearRegression()

lin_reg.fit(x,y)

#fitting polynomial regression to dataset

from sklearn.preprocessing import PolynomialFeatures

poly_reg=PolynomialFeatures(degree=4)

x_poly=poly_reg.fit_transform(x)

lin_reg2=LinearRegression()

lin_reg2.fit(x_poly,y)

Comparing the result of linear and polynomial model graphically

#visualing linear regression result

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()

#visualing polynomial regression result

plt.scatter(x,y,color='red')

plt.plot(x ,lin_reg2.predict(poly_reg.fit_transform(x)),color='blue')

plt.title('Truth or Bluff(Polynomial Regression)')

plt.xlabel('Position level')

plt.ylabel('Salary')

plt.show()

Comparing the predictions made by linear regression model and polynomial regression model

#predicting new result with linear regression

lin_reg.predict(6.5)

#predicting new result with polynomial regression

lin_reg2.predict(poly_reg.fit_transform(6.5))

Result:-

This is our first non linear model so we will compare it to linear just to make a smooth transition from linear to non-linear.

Prediction using Linear regression is 330378.78787879

Prediction using polynomial regression is 158862.45265153

You can see how much more accurate non linear models are.