# Logistic Regression

Logistic regression is a statistical procedure to estimate binary events. Thus, similar to linear regression, any number of independent variables (X) are used to calculate a dependent binary variable Y (with the instances 0 and 1). More precisely, logistic regression is used to estimate the influence of X on Y. For each regressor, a coefficient βi is estimated, usually by means of a maximum likelihood estimation. Coefficients describe the influence strength (value of the coefficient) and influence direction (sign of the coefficient).

Often, the curve of logistic regression runs like an S. The probability is plotted on the Y-axis, whereas the X-axis reflects a specific regressor variable. This s-shape is typical for logistic regressions. It could also be a decreasing s-shape from top left to bottom right.

### Interpretation of Regression Coefficients

The coefficients are transformed by necessary mathematical transformations. Therefore, they are no longer directly interpretable in their strength of influence – in contrast to linear regression. Hence, often the so-called “odds ratios” are formed, as these allow a simpler interpretation. Odds ratios describe the change in the probability ratio. Remember, it is not the same as the change in absolute probability!

Blog posts about the interpretation of the coefficients or the implementation of a logistic regression can be found here:

TowardsDataScience

Finally, it is advisable to pay more attention to the direction of influence rather than the strength of influence when interpreting the data.

### Exemplary Use Case

The application of logistic regression is versatile and transferable to numerous business contexts. From predicting the churn of customers or employees to calculating response probabilities to marketing or sales campaigns. Applied to the sales context, this could mean estimating whether or not customers purchases a product (target variable Y). For example, age, number of logins, gender, and a customer score (for example, frequency of purchases and amount of purchases) can be used as regressors (X).

Purchase probability (0 or 1) = β0 + β1*Age + β2*Number of logins + β3*Gender + β4*Customer score

In the example above, it could be assumed that the number of logins and the customer score have a positive influence on the probability of closing a deal. Likewise, the more active (number of logins) a customer is, the higher his interest in the respective products tends to be. Similarly, the higher the sales volume of a customer (customer score), the greater the willingness to buy additional products (cross-selling). As a result, this could be verified with the help of logistic regression (at least at a correlative level).

Logistic regression is one of the supervised learning methods in machine learning, since the target variable (Y) is known. Logistic regression alone does not yet have any machine learning characteristics. These are added when different models are tested against each other and continuously updated with new data so that the model “learns”.

### Code Snippet

from sklearn.linear_model import LogisticRegression

reg = LogisticRegression().fit(X_train, y_train)

reg.coef

The code snippet is written in Python and based on the module scikit-learn.

## More resources about machine learning

### Data integration

How machine learning benefits from data integration
The causal chain “data integration-data quality-model performance” describes the necessity of effective data integration for easier and faster implementable and more successful machine learning. In short, good data integration results in better predictive power of machine learning models due to higher data quality.

From a business perspective, there are both cost-reducing and revenue-increasing effects. The development of the models is cost-reducing (less custom code, thus less maintenance, etc.). Revenue increasing is caused by the better predictive power of the models leading to more precise targeting, cross- and upselling, and more accurate evaluation of leads and opportunities – both B2B and B2C. You can find a detailed article on the topic here:

### Platform

How to use machine learning with the Integration Platform
You can make the data from your centralized Marini Integration Platform available to external machine learning services and applications. The integration works seamlessly via the HubEngine or direct access to the platform, depending on the requirements of the third-party provider. For example, one vendor for standard machine learning applications in sales is Omikron. But you can also use standard applications on AWS or in the Google Cloud. Connecting to your own servers is just as easy if you want to program your own models there.

### Applications

Frequent applications of machine learning in sales
Machine learning can support sales in a variety of ways. For example, it can calculate closing probabilities, estimate cross-selling and up-selling potential, or predict recommendations. The essential point here is that the salesperson is supported and receives further decision-making assistance, which he can use to better concentrate on his actual activity, i.e., selling. For example, the salesperson can more quickly identify which leads, opportunities or customers are most promising at the moment and contact them. However, it remains clear that the salesperson makes the final decision and is ultimately only facilitated by machine learning. In the end, no model sells, but still the human being.

Here you will find a short introduction to machine learning and the most common applications in sales.

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