Forecasting with Logistic Regression: A Practical Guide

Can I Forecast with Logit Regression?

Introduction to Logistic Regression

Can I Forecast with Logit Regression? This is a question that many data scientists and analysts often grapple with. The truth is that while logistic regression is a powerful tool for predicting binary outcomes, it is not directly suitable for forecasting numerical values.

Understanding Logistic Regression

Logistic regression is a type of supervised learning algorithm used to predict the probability of a binary outcome. It is particularly useful when the dependent variable is binary, i.e., it can take only two values, such as 1 or 0. The logistic regression model is defined such that the probability of the event occurring, given a set of independent variables, is expressed as:

Probx Pry 1 x 1/1 expa b x

where a and b are parameters that are estimated based on the data you have. These parameters are found using a method called Maximum Likelihood Estimation (MLE).

Estimating Parameters and Predicting Probabilities

Using software such as Generalized Linear Model (GLM), you can estimate the logistic regression model parameters. Once these estimates are obtained, you can use them to predict the probability of the binary outcome for new data points. The predicted probability, however, is not the observed outcome, but rather the expected value, denoted as Ey.

The usefulness of logistic regression predictions depends heavily on the context of the problem. To illustrate, let's consider a scenario where the binary outcome is the probability of a consumer buying a specific brand of detergent, and the independent variable is the price. The relationship between price and the probability of a purchase is often nonlinear. You might observe a strong impact of price on the probability of buying the detergent within a certain range of prices, but little or no impact at other price points.

Properties of Logistic Regression

Logistic regression assumes that the binary outcome, y, is a draw from a Bernoulli distribution with mean and variance given by:

Ey Prob

Vary Prob1-Prob

These properties are useful when making inferences about the binary outcomes. For instance, if you have a group of N people all with the same response probability, the total number of success can be approximated as:

EY NProb
VarY NProb(1-Prob)

With these expected values and variances, it is possible to calculate the error bounds for forecasts. If Y represents the total sales for a group of N consumers, the expected total sales and the associated variance can be calculated, and error bars can be plotted around the sales forecast to visually assess the model fit.

Logistic Regression vs. Forecasting

It is important to note that while logistic regression is powerful for predicting binary outcomes, it is not appropriate for forecasting. Logit models provide probabilities, not numerical forecasts. For predicting numerical values, linear regression or more advanced time series models such as ARIMA, Moving Average, and Exponential Smoothing should be used.

Conclusion

In summary, while logistic regression is an excellent tool for predicting binary outcomes, it is not suitable for forecasting numerical values. Understanding the strengths and limitations of various modeling techniques is crucial for accurate predictive analytics.