Logistic regression is a statistical method used to model a binary dependent variable. It is widely used in various fields, including marketing, to predict the probability of an event occurring based on one or more independent variables. The output of logistic regression is a probability that the given input point belongs to a certain class, which can then be mapped to a binary outcome.
The logit function (or logistic function) is used to model the binary dependent variable:
where:
Market basket analysis is a data mining technique used to discover patterns or associations between items. This method is commonly used in retail to understand the purchasing behavior of customers. For example, it helps in identifying items that are frequently bought together. Unlike logistic regression, which predicts the probability of a single binary outcome, market basket analysis focuses on identifying associations and co-occurrences between multiple items.
Let's consider a business case where we want to use logistic regression to predict whether a customer will make a purchase based on various factors. Here is a sample dataset:
Using logistic regression, we aim to predict the Purchase variable.
After fitting a logistic regression model to the data, we might get the following coefficient output:
| Variable | Coefficient | Standard Error | z value | Pr(>|z|) |
|-------------|-------------|----------------|---------|----------|
| Intercept | -3.0 | 1.0 | -3.0 | 0.0027 |
| Revenue | 0.002 | 0.0005 | 4.0 | <0.0001 |
| Campaign A | 0.5 | 0.2 | 2.5 | 0.0123 |
| Campaign B | -0.3 | 0.2 | -1.5 | 0.1343 |
| Campaign C | 0.7 | 0.2 | 3.5 | 0.0004 |
| Income | 0.00001 | 0.00001 | 1.0 | 0.3162 |
| Size hh | -0.1 | 0.1 | -1.0 | 0.3173 |
| Education | 0.2 | 0.1 | 2.0 | 0.0455 |
To evaluate the performance of our logistic regression model, we can use a confusion matrix. Suppose our initial confusion matrix looks like this:
From this confusion matrix, we can calculate various performance metrics such as accuracy, precision, recall, and F1-score.
Let's say we introduce a new variable, Promotion, into our model and re-run the logistic regression. The updated confusion matrix might look like this:
Lift charts are useful for visualizing the performance of a predictive model. They show how much better the model performs compared to a random guess. The lift chart plots the lift (ratio of model's performance to random performance) on the y-axis against the percentage of the population on the x-axis.
Using the lift chart, we can determine how deep into the population we should target our marketing efforts. For example, if the lift chart shows that the top 20% of the population yields a lift of 2.5, it indicates that targeting this segment will be 2.5 times more effective than a random selection.
Logistic regression is a powerful tool for predicting binary outcomes in marketing analytics, allowing businesses to make data-driven decisions. By evaluating the model's performance using confusion matrices and lift charts, marketers can optimize their campaigns and achieve better results. Understanding when and how to apply logistic regression and market basket analysis can provide valuable insights and drive strategic actions in marketing efforts.
