How to Make Predictions Using Regression Model in Statsmodels

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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