Polynomial Regression - Lab

Introduction

In this lab, you'll practice your knowledge on adding polynomial terms to your regression model!

Objectives

You will be able to:

Use sklearn's built in capabilities to create polynomial features

Dataset

Here is the dataset you will be working with in this lab:

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline

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

df.head()

Run the following line of code. You will notice that the data is clearly of non-linear shape. Begin to think about what degree polynomial you believe will fit it best.

plt.scatter(df['x'], df['y'], color='green', s=50, marker='.');

Train-test split

The next step is to split the data into training and test sets. Set the random_state to 42 and assign 75% of the data in the training set.

# Split data into 75-25 train-test split 
from sklearn.model_selection import train_test_split
y = df['y']
X = df.drop(columns='y', axis=1)
X_train, X_test, y_train, y_test = None

Build polynomial models

Now it's time to determine the optimal degree of polynomial features for a model that is fit to this data. For each of second, third and fourth degrees:

Instantiate PolynomialFeatures() with the number of degrees
Fit and transform the X_train features
Instantiate and fit a linear regression model on the training data
Transform the test data into polynomial features
Use the model you built above to make predictions using the transformed test data
Evaluate model performance on the test data using r2_score()
In order to plot how well the model performs on the full dataset, transform X using poly
Use the same model (reg_poly) to make predictions using X_poly

# Import relevant modules and functions
from sklearn.preprocessing import PolynomialFeatures
from sklearn.linear_model import LinearRegression
from sklearn.metrics import r2_score

colors = ['yellow', 'lightgreen', 'blue']
plt.figure(figsize=(10, 6))
plt.scatter(df['x'], df['y'], color='green', s=50, marker='.', label='plot points')

# We'll fit 3 different polynomial regression models from degree 2 to degree 4
for index, degree in enumerate([2, 3, 4]):
    
    # Instantiate PolynomialFeatures
    poly = None
    
    # Fit and transform X_train
    X_poly_train = None
    
    # Instantiate and fit a linear regression model to the polynomial transformed train features
    reg_poly = None
    
    # Transform the test data into polynomial features
    X_poly_test = None
    
    # Get predicted values for transformed polynomial test data  
    y_pred = None
    
    # Evaluate model performance on test data
    print("degree %d" % degree, r2_score(y_test, y_pred))
    
    # Transform the full data
    X_poly = None
    
    # Now, we want to see what the model predicts for the entire data 
    y_poly = None
    
    # Create plot of predicted values
    plt.plot(X, y_poly, color = colors[index], linewidth=2, label='degree %d' % degree)
    plt.legend(loc='lower left')

Summary

Great job! You now know how to include polynomials in your linear models.