Course Content

Linear Regression with Python

## Linear Regression with Python

# Building Linear Regression Using Statsmodels

In the previous chapter, we used a function from NumPy to calculate the parameters.

Now we will use the class object instead of the function to represent the linear regression. This approach takes more lines of code to find the parameters, but it stores a lot of helpful information inside the object and makes the prediction more straightforward.

## 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.

Which is equivalent to:

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.

`import statsmodels.api as sm # import statsmodels 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) # Open the file X, y = df['Father'], df['Height'] # Assign the variables # Get the correct form of input for OLS X_tilde = sm.add_constant(X) # 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 = regression_model.params print('beta_0 is: ', beta_0) print('beta_1 is: ', beta_1)`

## Making the predictions

New instances can easily be predicted using `predict()`

method, but you need to preprocess the input for them too:

`import statsmodels.api as sm 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) # Open the file X, y = df['Father'], df['Height'] # Assign the variables X_tilde = sm.add_constant(X) # Preprocess regression_model = sm.OLS(y, X_tilde) # Initialize an OLS object regression_model = regression_model.fit() # Train the object # Predict new values X_new = np.array([65,70,75]) # 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(y_pred)`

## 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.

`import statsmodels.api as sm 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 X, y = df['Father'], df['Height'] X_tilde = sm.add_constant(X) # Preprocess X regression_model = sm.OLS(y, X_tilde) # Initialize an OLS object regression_model = regression_model.fit() # Train the object # Print the summary print(regression_model.summary())`

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

Everything was clear?