Building Linear Regression Using NumPy

You already know what simple linear regression is and how to find the line that fits the data best. Let's go through all the steps of building a linear regression for a real dataset.

Loading data

We have a file, simple_height_data.csv, with the data from our examples. Let's load the file and take a look at it.


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import pandas as pd

file_link = 'https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/simple_height_data.csv'
df = pd.read_csv(file_link)	# Read the file

print(df.head())	# Print the first 5 instances from a dataset

So the dataset has two columns, one is 'Height', which is our target, and the second column, 'Father', is the father's height. That is our feature.
Let's assign our target values to the y variable and feature values to X and build a scatterplot.


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import pandas as pd
import matplotlib.pyplot as plt

file_link = 'https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/simple_height_data.csv'
df = pd.read_csv(file_link)	# Read the file

X = df['Father']	# Assign the feature
y = df['Height']	# Assign the target
plt.scatter(X,y)	# Build scatterplot
plt.show()

Finding parameters

Now, NumPy has a nice function to find the parameters of linear regression.

Linear Regression is a Polynomial Regression of degree 1(we will talk about Polynomial Regression in later sections). That's why we need to put deg=1 to get the parameters for the linear regression.
Here is an example:


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import pandas as pd
import numpy as np

file_link = 'https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/simple_height_data.csv'
df = pd.read_csv(file_link)	# Read the files
X, y = df['Father'], df['Height']	# Assign the variables

beta_1, beta_0 = np.polyfit(X, y, 1)	# Get the parameters
print('beta_0 is', beta_0)
print('beta_1 is', beta_1)

Note
If you are unfamiliar with the syntax beta_1, beta_0 = np.polyfit(X,y,1), that is called unpacking.
If you have an iterator (e.g., list or NumPy array or pandas series) that has two items writing
is the same as
And since the return of a polyfit() function is a NumPy array with two values, we are allowed to do that

Making the predictions

Now we can plot the line and predict new variables using the parameters.


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

file_link = 'https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/simple_height_data.csv'
df = pd.read_csv(file_link)	# Read the file
X, y = df['Father'], df['Height']	# Assign the variables
beta_1, beta_0 = np.polyfit(X, y, 1)	# Get the parameters

plt.scatter(X,y)	# Build a scatter plot
plt.plot(X, beta_0 + beta_1 * X)	# Plot the line

Now that we have the parameters, we can use the linear regression equation to predict new values.


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import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
file_link = 'https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/simple_height_data.csv'
df = pd.read_csv(file_link)	# Read the file
X, y = df['Father'], df['Height']	# Assign the variables
beta_1, beta_0 = np.polyfit(X, y, 1)	# Get the parameters

X_new = np.array([65, 70, 75])	# Feature values of new instances
y_pred = beta_0 + beta_1 * X_new	# Predict the target
print('Predicted y: ', y_pred)

So it is pretty easy to get the parameters of the linear regression. But some libraries can also give you some extra information. Let's look at one such library.

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Seção 1. Capítulo 3