How to Perform Quadratic Regression in Python?

The quadratic equation is a method of modeling a relationship between sets of independent variables is quadratic regression or we can say the technique of obtaining the equation of a parabola that best fits a collection of data is known as quadratic regression. We use the R square metric to measure the relative predictive power of a Quadratic Regression. 

The equation of quadratic equation is of the form:

y= 

where a, b , c are constants and a ≠ 0.

The term quadratic refers to an equation that has a power of 2.

Used Dataset: Click here

Quadratic Regression in Python

The code starts with importing the necessary packages, then the CSV file is read using the read_csv() and visualizes the data. visualizing the data using a seaborn scatterplot. Adding a polynomial line to the data to view the fit. np.polyfit() and np.poly1d() is used to create a quadratic fit and a quadratic equation.

Syntax: numpy.polyfit (X, Y, deg, rcond=None, full=False, w=None, cov=False)

parameters:

• X: array like object, it represents the x coordinates.
• Y:array like object, it represents the y coordinates.
• deg: integer, degree of the polynomial .

 R square metric is used to measure the predictive power. R square value determines the proportion of variance for a dependent value. r2 value generally ranges from 0 to 1. an r square value near 1 is fairly good.  

Python3

# importing packages and modules
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from sklearn.metrics import r2_score
import scipy.stats as stats

dataset = pd.read_csv('ball.csv')
sns.scatterplot(data=dataset, x='time',
                y='height', hue='time')

plt.title('time vs height of the ball')
plt.xlabel('time')
plt.ylabel('height')
plt.show()

# degree 2 polynomial fit or quadratic fit
model = np.poly1d(np.polyfit(dataset['time'],
                             dataset['height'], 2))

# polynomial line visualization
polyline = np.linspace(0, 10, 100)
plt.scatter(dataset['time'], dataset['height'])
plt.plot(polyline, model(polyline))
plt.show()

print(model)

# r square metric
print(r2_score(dataset['height'],
               model(dataset['time'])))

Output:

       2
2.008 x - 21.69 x + 121.7
0.8133556222534604

R square value is above 0.7 so it implies quadratic fit is a fit for the data.