## Data Creation

Before fitting a model, you need data. In this case, we’ll be examining the impact of study method and hours studied on exam results for a selection of students.

To create a pandas DataFrame, follow these steps:

- Import pandas and create a dictionary with keys for hours studied, study method, and exam result.
- Input the values for each key using lists of data.
- Call the pd.DataFrame function, passing in the dictionary as the argument.

Once created, you can use this DataFrame to visualize the data, identifying trends and patterns and testing hypotheses with confidence.

## Logistic Regression Model Fitting

Once you have your data, the next step is to fit a logistic regression model. This will allow you to examine how the independent variables, hours studied and study method, impact the dependent variable, exam result.

To fit the model, follow these steps:

- Import the statsmodels.api module and call the logit function, passing in the formula and DataFrame as arguments.
- Pass the logistic regression formula in the following format: ‘exam_result ~ study_method + hours_studied’
- Call the .fit() method on the logit object to fit the model
- Call the .summary() method to retrieve information on the fit of the model.

Once you’ve fit the model, you’ll want to look at the coefficients and p-values to determine the impact of the independent variables.

### Coefficients and P-Values Interpretation

The coefficients in a logistic regression model describe the relationship between the independent variables and the outcome in log-odds ratios. To interpret the coefficients, exponentiate them to examine the impact on the odds ratio.

A coefficient greater than 1 indicates an increase in the odds of the outcome, while a coefficient less than 1 indicates a decrease. P-values indicate the significance of a predictor variable, with a p-value below .05 indicating that the variable has a significant impact on the outcome.

In our example of study method and hours studied impacting exam results, we might find that study method has a p-value below .05, while hours studied does not. This would lead us to conclude that study method has a significant impact on exam results, while hours studied may not.

### Model Performance Evaluation

Finally, it’s important to evaluate the performance of our logistic regression model. Two key metrics for this evaluation are pseudo R-squared and LLR p-value.

### Pseudo R-Squared

Pseudo R-squared is an approximation of traditional R-squared used in linear regression. It estimates the proportion of the variance in the response variable that can be explained by the independent variables in the model.

To calculate pseudo R-squared, divide the difference between the log-likelihood of the full model (with predictors) and the log-likelihood of the null model (without predictors) by the log-likelihood of the full model.

### LLR p-value

The LLR p-value tests the usefulness and reliability of the model in predicting the response variable. It is calculated by comparing the log-likelihood of the full model to a model without any predictors.

A p-value below .05 indicates that the model is useful in predicting the response variable.

## Additional Resources

While this article provides a brief overview of performing logistic regression with Statsmodels, there are many more functions and classes available to the analyst. The Statsmodels module provides users with statistical models and econometric analysis tools, including classes and functions for model fitting, data manipulation, and estimation.

## Final Thoughts

Logistic regression is a powerful tool in data analysis, allowing researchers to predict the likelihood of a particular outcome based on independent variables. By following the steps to create a pandas DataFrame, fit a logistic regression model, and evaluate its performance, you can make confident predictions about the outcomes you wish to study.

With resources like the Statsmodels module, the opportunities for analysis are endless. In this article, we explored the steps for performing logistic regression with Statsmodels, from data creation all the way through model performance evaluation.

We covered how to create a pandas DataFrame, fit a logistic regression model, and evaluate its performance using metrics like pseudo R-squared and LLR p-value. With these powerful tools at our disposal, we can confidently predict the likelihood of an outcome based on independent variables like hours studied and study method.

By mastering logistic regression, we empower ourselves with the ability to make informed decisions and predictions that impact a wide range of fields and industries.