You can use the following basic syntax to use a regression model fit using the statsmodels module in Python to make predictions on new observations:

model.predict(df_new)

This particular syntax will calculate the predicted response values for each row in a new DataFrame called **df_new**, using a regression model fit with statsmodels called **model**.

The following example shows how to use this syntax in practice.

**Example: Make Predictions Using Regression Model in Statsmodels**

Suppose we have the following pandas DataFrame that contains information about hours studied, prep exams taken, and final score received by students in a certain class:

import pandas as pd #create DataFrame df = pd.DataFrame({'hours': [1, 2, 2, 4, 2, 1, 5, 4, 2, 4, 4, 3, 6], 'exams': [1, 3, 3, 5, 2, 2, 1, 1, 0, 3, 4, 3, 2], 'score': [76, 78, 85, 88, 72, 69, 94, 94, 88, 92, 90, 75, 96]}) #view head of DataFrame df.head() hours exams score 0 1 1 76 1 2 3 78 2 2 3 85 3 4 5 88 4 2 2 72

We can use the **OLS()** function from the statsmodels module to fit a multiple linear regression model, using “hours” and “exams” as the predictor variables and “score” as the response variable:

import statsmodels.api as sm #define predictor and response variables y = df['score'] x = df[['hours', 'exams']] #add constant to predictor variables x = sm.add_constant(x) #fit linear regression model model = sm.OLS(y, x).fit() #view model summary print(model.summary()) OLS Regression Results ============================================================================== Dep. Variable: score R-squared: 0.718 Model: OLS Adj. R-squared: 0.661 Method: Least Squares F-statistic: 12.70 Date: Fri, 05 Aug 2022 Prob (F-statistic): 0.00180 Time: 09:24:38 Log-Likelihood: -38.618 No. Observations: 13 AIC: 83.24 Df Residuals: 10 BIC: 84.93 Df Model: 2 Covariance Type: nonrobust ============================================================================== coef std err t P>|t| [0.025 0.975] ------------------------------------------------------------------------------ const 71.4048 4.001 17.847 0.000 62.490 80.319 hours 5.1275 1.018 5.038 0.001 2.860 7.395 exams -1.2121 1.147 -1.057 0.315 -3.768 1.344 ============================================================================== Omnibus: 1.103 Durbin-Watson: 1.248 Prob(Omnibus): 0.576 Jarque-Bera (JB): 0.803 Skew: -0.289 Prob(JB): 0.669 Kurtosis: 1.928 Cond. No. 11.7 ==============================================================================

From the **coef** column in the output, we can write the fitted regression model:

Score = 71.4048 + 5.1275(hours) – 1.2121(exams)

Now suppose we would like to use the fitted regression model to predict the “score” for five new students.

First, let’s create a DataFrame to hold the five new observations:

#create new DataFrame df_new = pd.DataFrame({'hours': [1, 2, 2, 4, 5], 'exams': [1, 1, 4, 3, 3]}) #add column for constant df_new = sm.add_constant(df_new) #view new DataFrame print(df_new) const hours exams 0 1.0 1 1 1 1.0 2 1 2 1.0 2 4 3 1.0 4 3 4 1.0 5 3

Next, we can use the **predict()** function to predict the “score” for each of these students, using “hours” and “exams” as the values for the predictor variables in our fitted regression model:

#predict scores for the five new students model.predict(df_new) 0 75.320242 1 80.447734 2 76.811480 3 88.278550 4 93.406042 dtype: float64

Here’s how to interpret the output:

- The first student in the new DataFrame is predicted to get a score of
**75.32**. - The second student in the new DataFrame is predicted to get a score of
**80.45**.

And so on.

To understand how these predictions were calculated, we need to refer to the fitted regression model from earlier:

Score = 71.4048 + 5.1275(hours) – 1.2121(exams)

By plugging in the values for “hours” and “exams” for the new students, we can calculate their predicted score.

For example, the first student in the new DataFrame had a value of **1** for hours and a value of **1** for exams.

Thus, their predicted score was calculated as:

Score = 71.4048 + 5.1275(1) – 1.2121(1) = **75.32**.

The score of each student in the new DataFrame was calculated in a similar manner.

**Additional Resources**

The following tutorials explain how to perform other common tasks in Python:

How to Perform Logistic Regression in Python

How to Calculate AIC of Regression Models in Python

How to Calculate Adjusted R-Squared in Python