below is the xample file # ================= Polynomial Regression =================== # Thus far, we have assumed that the relationship between the explanatory # variables and the response variable is linear. This assumption is not always # true. This is where polynomial regression comes in. Polynomial regression # is a special case of multiple linear regression that adds terms with degrees # greater than one to the model. The real-world curvilinear relationship is captured # when you transform the training data by adding polynomial terms, which are then fit in # the same manner as in multiple linear regression. # We are now going to us only one explanatory variable, but the model now has # three terms instead of two. The explanatory variable has been transformed # and added as a third term to the model to captre the curvilinear relationship. # The PolynomialFeatures transformer can be used to easily add polynomial features # to a feature representation. Let's fit a model to these features, and compare it # to the simple linear regression model: import numpy as np import matplotlib.pyplot as plt from sklearn.linear_model import LinearRegression from sklearn.preprocessing import PolynomialFeatures # Training set x_train = [[6], [8], [10], [14], [18]] #diamters of pizzas y_train = [[7], [9], [13], [17.5], [18]] #prices of pizzas # Testing set x_test = [[6], [8], [11], [16]] #diamters of pizzas y_test = [[8], [12], [15], [18]] #prices of pizzas # Train the Linear Regression model and plot a prediction regressor = LinearRegression() regressor.fit(x_train, y_train) xx = np.linspace(0, 26, 100) yy = regressor.predict(xx.reshape(xx.shape[0], 1)) plt.plot(xx, yy) # Set the degree of the Polynomial Regression model quadratic_featurizer = PolynomialFeatures(degree = 2) # This preprocessor transforms an input data matrix into a new data matrix of a given degree X_train_quadratic = quadratic_featurizer.fit_transform(X_train) X_test_quadratic = quadratic_featurizer.transform(x_test) # Train and test the regressor_quadratic model regressor_quadratic = LinearRegression() regressor_quadratic.fit(X_train_quadratic, y_train) xx_quadratic = quadratic_featurizer.transform(xx.reshape(xx.shape[0], 1)) # Plot the graph plt.plot(xx, regressor_quadratic.predict(xx_quadratic), c = 'r', linestyle = '--') plt.title('Pizza price regressed on diameter') plt.xlabel('Diameter in inches') plt.ylabel('Price in dollars') plt.axis([0, 25, 0, 25]) plt.grid(True) plt.scatter(X_train, y_train) plt.show() print (X_train) print (X_train_quadratic) print (X_test) print (X_test_quadratic) # If you execute the code, you will see that the simple linear regression model is plotted with # a solid line. The quadratic regression model is plotted with a dashed line and evidently # the quadratic regression model fits the training data better.

below is the xample file # ================= Polynomial Regression =================== # Thus far, we have assumed that the relationship between the explanatory # variables and the response variable is linear. This assumption is not always # true. This is where polynomial regression comes in. Polynomial regression # is a special case of multiple linear regression that adds terms with degrees # greater than one to the model. The real-world curvilinear relationship is captured # when you transform the training data by adding polynomial terms, which are then fit in # the same manner as in multiple linear regression. # We are now going to us only one explanatory variable, but the model now has # three terms instead of two. The explanatory variable has been transformed # and added as a third term to the model to captre the curvilinear relationship. # The PolynomialFeatures transformer can be used to easily add polynomial features # to a feature representation. Let's fit a model to these features, and compare it # to the simple linear regression model: import numpy as np import matplotlib.pyplot as plt from sklearn.linear_model import LinearRegression from sklearn.preprocessing import PolynomialFeatures # Training set x_train = [[6], [8], [10], [14], [18]] #diamters of pizzas y_train = [[7], [9], [13], [17.5], [18]] #prices of pizzas # Testing set x_test = [[6], [8], [11], [16]] #diamters of pizzas y_test = [[8], [12], [15], [18]] #prices of pizzas # Train the Linear Regression model and plot a prediction regressor = LinearRegression() regressor.fit(x_train, y_train) xx = np.linspace(0, 26, 100) yy = regressor.predict(xx.reshape(xx.shape[0], 1)) plt.plot(xx, yy) # Set the degree of the Polynomial Regression model quadratic_featurizer = PolynomialFeatures(degree = 2) # This preprocessor transforms an input data matrix into a new data matrix of a given degree X_train_quadratic = quadratic_featurizer.fit_transform(X_train) X_test_quadratic = quadratic_featurizer.transform(x_test) # Train and test the regressor_quadratic model regressor_quadratic = LinearRegression() regressor_quadratic.fit(X_train_quadratic, y_train) xx_quadratic = quadratic_featurizer.transform(xx.reshape(xx.shape[0], 1)) # Plot the graph plt.plot(xx, regressor_quadratic.predict(xx_quadratic), c = 'r', linestyle = '--') plt.title('Pizza price regressed on diameter') plt.xlabel('Diameter in inches') plt.ylabel('Price in dollars') plt.axis([0, 25, 0, 25]) plt.grid(True) plt.scatter(X_train, y_train) plt.show() print (X_train) print (X_train_quadratic) print (X_test) print (X_test_quadratic) # If you execute the code, you will see that the simple linear regression model is plotted with # a solid line. The quadratic regression model is plotted with a dashed line and evidently # the quadratic regression model fits the training data better.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

below is the xample file

# ================= Polynomial Regression ===================

# Thus far, we have assumed that the relationship between the explanatory

# variables and the response variable is linear. This assumption is not always

# true. This is where polynomial regression comes in. Polynomial regression

# is a special case of multiple linear regression that adds terms with degrees

# greater than one to the model. The real-world curvilinear relationship is captured

# when you transform the training data by adding polynomial terms, which are then fit in

# the same manner as in multiple linear regression.

# We are now going to us only one explanatory variable, but the model now has

# three terms instead of two. The explanatory variable has been transformed

# and added as a third term to the model to captre the curvilinear relationship.

# The PolynomialFeatures transformer can be used to easily add polynomial features

# to a feature representation. Let's fit a model to these features, and compare it

# to the simple linear regression model:

import numpy as np

import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression

from sklearn.preprocessing import PolynomialFeatures

# Training set

x_train = [[6], [8], [10], [14], [18]] #diamters of pizzas

y_train = [[7], [9], [13], [17.5], [18]] #prices of pizzas

# Testing set

x_test = [[6], [8], [11], [16]] #diamters of pizzas

y_test = [[8], [12], [15], [18]] #prices of pizzas

# Train the Linear Regression model and plot a prediction

regressor = LinearRegression()

regressor.fit(x_train, y_train)

xx = np.linspace(0, 26, 100)

yy = regressor.predict(xx.reshape(xx.shape[0], 1))

plt.plot(xx, yy)

# Set the degree of the Polynomial Regression model

quadratic_featurizer = PolynomialFeatures(degree = 2)

# This preprocessor transforms an input data matrix into a new data matrix of a given degree

X_train_quadratic = quadratic_featurizer.fit_transform(X_train)

X_test_quadratic = quadratic_featurizer.transform(x_test)

# Train and test the regressor_quadratic model

regressor_quadratic = LinearRegression()

regressor_quadratic.fit(X_train_quadratic, y_train)

xx_quadratic = quadratic_featurizer.transform(xx.reshape(xx.shape[0], 1))

# Plot the graph

plt.plot(xx, regressor_quadratic.predict(xx_quadratic), c = 'r', linestyle = '--')

plt.title('Pizza price regressed on diameter')

plt.xlabel('Diameter in inches')

plt.ylabel('Price in dollars')

plt.axis([0, 25, 0, 25])

plt.grid(True)

plt.scatter(X_train, y_train)

plt.show()

print (X_train)

print (X_train_quadratic)

print (X_test)

print (X_test_quadratic)

# If you execute the code, you will see that the simple linear regression model is plotted with

# a solid line. The quadratic regression model is plotted with a dashed line and evidently

# the quadratic regression model fits the training data better.

Compulsory Task
Follow these steps:
Read the example file.
• Try to think of a relationship you can model and create a new Python file
in this folder called poly.py.
Inside poly.py, identify a relationship, and use Polynomial regression to
train, predict, and plot your results.

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