In This Article, You Will Learn About Polynomial Regression.
Machine Learning Multiple Regression – Before moving ahead, let’s take a look at Introduction to Machine Learning Linear Regression.
Polynomial Regression
In the event that your points do not meet the requirements for a linear regression (a straight line across the entire data set) this could be suitable for a polynomial.
Like linear regression, relies on the relationship between variables x and y in order to determine the most effective way to create a line between all the points of data.
How does it work?
Python offers methods for determining the relationship between points of data and drawing lines in polynomial regression.
Example: Use the scatter() method to draw a scatter diagram.
import matplotlib.pyplot as plt
x_axis = [10, 12, 18, 25, 33]
y_axis = [18, 29, 34, 39, 42]
plt.scatter(x_axis, y_axis)
plt.show()
As shown above, it returned a scatter plot from given data.
Example: Import numpy and Matplotlib to draw the line of Polynomial Regression.
import numpy as np
import matplotlib.pyplot as plt
x_axis = [10, 12, 18, 25, 33]
y_axis = [18, 29, 34, 39, 42]
data = np.poly1d(np.polyfit(x_axis, y_axis, 9))
info = np.linspace(1, 30, 200)
plt.scatter(x_axis, y_axis)
plt.plot(info, data(info))
plt.show()
In lines 1 and 2,
The Matplotlib and SciPy module are imported to draw diagrams and lines.
In lines 4 and 5,
The variables x and y are defined as the data points that show points on the graph.
In line 7,
NumPy has a method that to make a polynomial model:
In line 9,
Then specify how the line will display, we start at position 1, and end at position 30.
In line 11,
Draw the original scatter plot:
In line 12,
Draw the line of polynomial regression.
Note: Learn More about Numpy module at Numpy Tutorial.
Note: Learn More about SciPy module at SciPy Tutorial.
R-Squared
It is essential to understand the extent to which the relationship between the the x- and y-axis are in the absence of a connections, then the polynomial cannot be used for predicting anything.
This relationship can be measured using an amount known as the r-squared.
The r-squared values range between 0 and 1 where 0 indicates there is no relationship and 1 indicates 100% connected.
Python as well as the Sklearn module can compute the value for you. all you need to feed the program the two arrays (x and y).
Example: Check whether data fits in polynomial regression or not.
import numpy as np
from sklearn.metrics import r2_score
x_axis = [10, 12, 18, 25, 33]
y_axis = [18, 29, 34, 39, 42]
data = np.poly1d(np.polyfit(x_axis, y_axis, 8))
print(r2_score(y_axis, data(x_axis)))
Output -
sys:1: RankWarning: Polyfit may be poorly conditioned
1.0
As a result, it returned a warning that clearly shows data is not fitted well.
Predict Future Values
Now, we can apply the data we’ve collected to anticipate future value.
Example: Predict the sale of product ‘x’.
import numpy as np
from sklearn.metrics import r2_score
x_axis = [10, 12, 18, 25, 33]
y_axis = [18, 29, 34, 39, 42]
data = np.poly1d(np.polyfit(x_axis, y_axis, 8))
sale = data(5)
print(sale)
Output -
sys:1: RankWarning: Polyfit may be poorly conditioned
-38.04542208235844
Bad Result
Let’s create an example where Linear Regression cannot predict future value.
Example: Create a data that represents bad result for Polynomial Regression.
import numpy as np
from sklearn.metrics import r2_score
import matplotlib.pyplot as plt
x_axis = [10, 12, 18, 25, 33]
y_axis = [18, 29, 34, 39, 42]
info = np.poly1d(np.polyfit(x_axis, y_axis, 9))
data = np.linspace(2, 30, 10)
plt.scatter(x_axis, y_axis)
plt.plot(data, info(data))
plt.show()
As a result, it returned Polynomial Plot that clearly shows data is not fitted well with line.
Example: Check whether ‘r’ returns low value or not.
import numpy as np
from sklearn.metrics import r2_score
x_axis = [10, 12, 18, 25, 33]
y_axis = [18, 29, 34, 39, 42]
info = np.poly1d(np.polyfit(x_axis, y_axis, 3))
print(r2_score(y_axis, info(x_axis)))
Output -
0.9539428530144852
