Python for Machine Learning - Polynomial Linear Regression using Scikit Learn - P9

Publicado em: 25 Março 2018
no canal de: technologyCult

5,756

Python for Machine Learning - Polynomial Linear Regression using Scikit Learn - P9
Polynomial Linear Regression using Scikit Learn

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x). Although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(y | x) is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression.

y = 9450x + 25792
y = 16.393x2 + 9259.3x + 26215
y = -122.92x3 + 2099.4x2 - 718.71x + 38863
y = 4.9243x4 - 236.59x3 + 2979.9x2 - 3314.2x + 41165
y = 15.006x5 - 430.13x4 + 4409.7x3 - 19368x2 + 43652x + 8315

Code Starts Here
===============
import matplotlib.pyplot as plt
import pandas as pd

df = pd.read_csv('SalaryData_Train.csv')

features = df.iloc[:,0:1].values
labels = df.iloc[:,1:2].values

plt.scatter(features,labels)
plt.xlabel('Years of Experience')
plt.ylabel('Salary')
plt.title('Salary V/s Years of Experience')
plt.show()

Step 6 - Sampling
from sklearn.cross_validation import train_test_split

X_train, X_test, y_train, y_test = train_test_split(features,
labels,
test_size=0.33,
random_state=0)

Create the REgression Model

from sklearn.linear_model import LinearRegression
regressor = LinearRegression()

Create The Polynomial Features

from sklearn.preprocessing import PolynomialFeatures

poly_reg = PolynomialFeatures(degree=3)

x_poly = poly_reg.fit_transform(features)
regressor.fit(x_poly,labels)

Test the model
y_pred = regressor.predict(poly_reg.fit_transform(X_test))

Calculate the Accuracy

print('Polynomial Linear Regression Accuracy:',regressor.score(poly_reg.fit_transform(X_test),y_test))

for i in range(1,6):
poly_reg = PolynomialFeatures(degree=i)
x_poly = poly_reg.fit_transform(features)
regressor.fit(x_poly,labels)
print('Degree of Equation :', i)
print('Coefficient :', regressor.coef_)
print('Intercept :', regressor.intercept_)
print('Accuracy Score:', regressor.score(poly_reg.fit_transform(X_test),y_test))

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