Hey there! Let's clear this up for you—Statsmodels doesn't expose a standalone f() function for your model, but the fitted OLS object already contains everything you need to compute that f(X)=Y mapping, and it's easy to access or wrap into a function of your own.

How to get your f(X) mapping from the fitted OLS model #

First, remember that when you fit an OLS model with Statsmodels, you're estimating a linear function:

f(X) = β₀ + β₁X₁ + β₂X₂ + ... + βₖXₖ
where β₀ is the intercept, and β₁ to βₖ are the coefficients for your features.

1. Access the model coefficients directly

Once you've fitted your model like this:

import statsmodels.api as sm
# Assume X is your feature matrix, y is your target variable
X_with_intercept = sm.add_constant(X)  # Add intercept term (critical for OLS!)
model = sm.OLS(y, X_with_intercept).fit()

You can get all the β values from model.params—this is a Series where the first entry is β₀ (intercept), followed by coefficients for each feature in your X matrix.

2. Compute f(X) using predict()

The easiest way to calculate f(X) for new or existing data is to use the model's built-in predict() method:

# For your original X (with intercept)
y_pred = model.predict(X_with_intercept)
# For new data X_new (make sure to add the intercept if you didn't include it in training!)
X_new_with_intercept = sm.add_constant(X_new)
y_new_pred = model.predict(X_new_with_intercept)

This is exactly equivalent to evaluating your f(X) function.

3. Wrap it into a custom f() function if you want

If you really want a standalone function named f, you can wrap the predict logic like this:

def f(X_input):
    # Add intercept if your training data included it (which it should for OLS)
    X_input_with_intercept = sm.add_constant(X_input, has_constant='add')
    return model.predict(X_input_with_intercept)

Now you can call f(X) directly to get your predicted Y values.

Why you won't find a named f() in the docs #

Statsmodels designs its models as objects that hold all the model information (coefficients, residuals, summary stats, etc.) rather than exposing a single function. The predict() method is the official way to compute the model's output for any input X, which is exactly what you're looking for when you say f(X)=Y.

内容的提问来源于stack exchange，提问作者Bilbo