Apprendre Building Linear Regression Using Statsmodels

Building a Linear Regression Model

In statsmodels, the OLS class can be used to create a linear regression model.

We first need to initialize an OLS class object using sm.OLS(y, X_tilde). Then train it using the fit() method.

model = sm.OLS(y, X_tilde)
model = model.fit()

Which is equivalent to:

model = sm.OLS(y, X_tilde).fit()

Note

The constructor of the OLS class expects a specific array X_tilde as an input, which we saw in the Normal Equation. So you need to convert your X array to X_tilde. This is achievable using the sm.add_constant() function.

Finding Parameters

When the model is trained, you can easily access the parameters using the params attribute.


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import statsmodels.api as sm
import pandas as pd

df = pd.read_csv('https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/simple_height_data.csv')
X, y = df['Father'], df['Height']
X_tilde = sm.add_constant(X)
model = sm.OLS(y, X_tilde).fit()
beta_0, beta_1 = model.params
print(beta_0, beta_1)

Making the Predictions

New instances can easily be predicted using predict() method, but you need to preprocess the input for them too:


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import numpy as np

X_new = np.array([65, 70, 75])
X_new_tilde = sm.add_constant(X_new)
print(model.predict(X_new_tilde))

Getting the Summary

As you probably noticed, using the OLS class is not as easy as the polyfit() function. But using OLS has its benefits. While training, it calculates a lot of statistical information. You can access the information using the summary() method.


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print(model.summary())

That's a lot of statistics. We will discuss the table's most important parts in later sections.

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Section 1. Chapitre 4

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