Building Multiple Linear Regression

The OLS class allows you to build Multiple Linear Regression the same way as Simple Linear Regression. But unfortunately, the np.polyfit() function does not handle the multiple features case.

We will stick with the OLS class.

Building X̃ matrix

We have the same dataset from the simple linear regression example, but it now has the mother's height as the second feature. Let's load it and look at its X variable.


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import pandas as pd
import statsmodels.api as sm

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

Remember, we should use OLS(y, X_tilde) to initialize the OLS object. As you can see, the X variable already holds two features in separate columns. So to get the X_tilde, we only need to add 1s as a first column. The sm.add_constant(X) function is doing exactly that!


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import pandas as pd
import statsmodels.api as sm

file_link='https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/heights_two_feature.csv'
df = pd.read_csv(file_link)	# Open the file
# Assign the variables
X = df[['Father', 'Mother']]
y = df['Height']
# Create X_tilde
X_tilde = sm.add_constant(X)
print(X_tilde.head())

Finding the parameters

Great! Now we can build the model, find the parameters and make predictions the same way we did in the previous section.


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import pandas as pd
import statsmodels.api as sm
import numpy as np

file_link='https://codefinity-content-media.s3.eu-west-1.amazonaws.com/b22d1166-efda-45e8-979e-6c3ecfc566fc/heights_two_feature.csv'
df = pd.read_csv(file_link)	  # Open the file
X,y = df[['Father', 'Mother']], df['Height']   # Assign the variables
X_tilde = sm.add_constant(X)	# Create X_tilde
# Initialize an OLS object
regression_model = sm.OLS(y, X_tilde)
# Train the object
regression_model = regression_model.fit()
# Get the paramters
beta_0, beta_1, beta_2 = regression_model.params
print('beta_0 is: ', beta_0)
print('beta_1 is: ', beta_1)
print('beta_2 is: ', beta_2)
# Predict new values
X_new = np.array([[65, 62],[70, 65],[75, 70]])	# Feature values of new instances
X_new_tilde = sm.add_constant(X_new)	# Preprocess X_new
y_pred = regression_model.predict(X_new_tilde)	# Predict the target
print('Predictions:', y_pred)

Note

Now that our training set has 2 features, we need to provide 2 features for each new instance we want to predict. That's why np.array([[65, 62],[70, 65],[75, 70]]) was used in the example above. It predicts y for 3 new instances: [Father:65,Mother:62], [Father:70, Mother:65], [Father:75, Mother:70]

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