Logistic Regression, Its Purpose and Calculations

Why is logistic regression needed?

Predicting the likelihood of an event is useful when using logistic regression analysis. It aids in calculating the odds between any two classes.

Logistic regression aims to find the most accurate model to explain the association between the dichotomous features of interest and a collection of independent variables.

In binary classification issues, where the outcome variable discloses one of the two groups, logistic regression is frequently utilized (0 and 1).

How is it calculated?

A logistic function known as the sigmoid function is used in logistic regression to map predictions and their probability. An S-shaped curve known as the sigmoid function transforms any real value into a range between 0 and 1.

Additionally, the model predicts that the instance belongs to that class if the sigmoid function’s output (estimated probability) is higher than a predetermined threshold on the graph. The model predicts that the instance does not belong to the class if the calculated probability is less than the set threshold.

For logistic regression, the sigmoid function is known as an activation function and is described as follows:

Logistic regression is represented by the following equation:

,

where:

• χ– input value,

• 

  – expected result,

• 

  – bias or intercept term,

• 

  – the input coefficient (χ)

Like linear regression, this equation uses weights or coefficient values to predict the output value by linearly combining the input values. In contrast to linear regression, the output value described here is a binary value (0 or 1) rather than a numeric value.

How are the results used?

Fraud detection

Teams can find data anomalies indicative of fraud using logistic regression models. In order to better safeguard their customers, banking and other financial organizations may find that certain behaviors or attributes are more frequently associated with fraudulent operations.

Disease prediction

In medicine, this analytics strategy can forecast the likelihood of a specific population developing a disease or condition. Healthcare institutions can set up preventative treatment for people with a higher risk of developing a particular ailment.

Churn in various organizational tasks may be indicated by specific actions. If strong performers risk leaving the firm, human resources, and management teams may be interested in finding out. This information might spark discussions about the company’s culture or pay practices.

Advantages vs. Disadvantages

In machine learning, logistic regression analysis has both advantages and downsides.

• Training and testing are critical components in the setup of a machine learning model. Through training, patterns in the input data are found and linked to the output. Regression algorithms can train logistic models without requiring more processing resources. As a result, compared to other ML techniques, logistic regression is simpler to apply, understand, and train.
• A graph with a straight line dividing the two data classes is referred to as a linearly separable dataset. The y variable in logistic regression only accepts two values. Therefore, if linearly separable data is used, it can effectively divide the data into two groups.
• The direction of their relationship or association is also revealed by the coefficient size of a logistic regression, which quantifies how important or appropriate an independent/predictor variable is (positive or negative).

• Logistic regression should not be employed if there are fewer data than features because this could result in overfitting.
• Since the result of logistic regression is constantly dependent on the total of the inputs and parameters, it is referred to as a generalized linear model. The decision border in a logistic regression model is a straight line.
• The assumption of linearity between the dependent and independent variables is the main drawback of logistic regression.

References

Bartosik, A., & Whittingham, H. (2021). Evaluating safety and toxicity. The Era of Artificial Intelligence, Machine Learning, and Data Science in the Pharmaceutical Industry, 119–137.

Schober, P., & Vetter, T. R. (2021). Logistic regression in medical research. Anesthesia and Analgesia, 132(2), 365–366.