# How to Perform Logistic Regression Using Statsmodels

The statsmodels module in Python offers a variety of functions and classes that allow you to fit various statistical models.

The following step-by-step example shows how to perform logistic regression using functions from statsmodels.

## Step 1: Create the Data

First, let’s create a pandas DataFrame that contains three variables:

• Hours Studied (Integer value)
• Study Method (Method A or B)
• Exam Result (Pass or Fail)

We’ll fit a logistic regression model using hours studied and study method to predict whether or not a student passes a given exam.

The following code shows how to create the pandas DataFrame:

```import pandas as pd

#create DataFrame
df = pd.DataFrame({'result': [0, 1, 0, 0, 0, 0, 0, 1, 1, 0,
0, 1, 1, 1, 0, 1, 1, 1, 1, 1],
'hours': [1, 2, 2, 2, 3, 2, 5, 4, 3, 6,
5, 8, 8, 7, 6, 7, 5, 4, 8, 9],
'method': ['A', 'A', 'A', 'B', 'B', 'B', 'B',
'B', 'B', 'A', 'B', 'A', 'B', 'B',
'A', 'A', 'B', 'A', 'B', 'A']})

#view first five rows of DataFrame

result	hours	method
0	0	1	A
1	1	2	A
2	0	2	A
3	0	2	B
4	0	3	B```

## Step 2: Fit the Logistic Regression Model

Next, we’ll fit the logistic regression model using the logit() function:

```import statsmodels.formula.api as smf

#fit logistic regression model
model = smf.logit('result ~ hours + method', data=df).fit()

#view model summary
print(model.summary())

Optimization terminated successfully.
Current function value: 0.557786
Iterations 5
Logit Regression Results
==============================================================================
Dep. Variable:                 result   No. Observations:                   20
Model:                          Logit   Df Residuals:                       17
Method:                           MLE   Df Model:                            2
Date:                Mon, 22 Aug 2022   Pseudo R-squ.:                  0.1894
Time:                        09:53:35   Log-Likelihood:                -11.156
converged:                       True   LL-Null:                       -13.763
Covariance Type:            nonrobust   LLR p-value:                   0.07375
===============================================================================
coef    std err          z      P>|z|      [0.025      0.975]
-------------------------------------------------------------------------------
Intercept      -2.1569      1.416     -1.523      0.128      -4.932       0.618
method[T.B]     0.0875      1.051      0.083      0.934      -1.973       2.148
hours           0.4909      0.245      2.002      0.045       0.010       0.972
===============================================================================
```

The values in the coef column of the output tell us the average change in the log odds of passing the exam.

For example:

• Using study method B is associated with an average increase of .0875 in the log odds of passing the exam compared to using study method A.
• Each additional hour studied is associated with an average increase of .4909 in the log odds of passing the exam.

The values in the P>|z| column represent the p-values for each coefficient.

For example:

• Studying method has a p-value of .934. Since this value is not less than .05, it means there is not a statistically significant relationship between hours studied and whether or not  a student passes the exam.
• Hours studied has a p-value of .045. Since this value is less than .05, it means there is a statistically significant relationship between hours studied and whether or not  a student passes the exam.

## Step 3: Evaluate Model Performance

To assess the quality of the logistic regression model, we can look at two metrics in the output:

1. Pseudo R-Squared

This value can be thought of as the substitute to the R-squared value for a linear regression model.

It is calculated as the ratio of the maximized log-likelihood function of the null model to the full model.

This value can range from 0 to 1, with higher values indicating a better model fit.

In this example, the pseudo R-squared value is .1894, which is quite low. This tells us that the predictor variables in the model don’t do a very good job of predicting the value of the response variable.

2. LLR p-value

This value can be thought of as the substitute to the p-value for the overall F-value of a linear regression model.

If this value is below a certain threshold (e.g. α = .05) then we can conclude that the model overall is “useful” and is better at predicting the values of the response variable compared to a model with no predictor variables.

In this example, the LLR p-value is .07375. Depending on the significance level we choose (e.g. .01, .05, .1) we may or may not conclude that the model as a whole is useful.