# Logistic Regression and Its Application in Predicting Dependent Variables

In simplest terms, logistic regression is used to evaluate the likelihood of a class or event, such as like win or lose, or living or dead. The model can even classify multiple different classes of events, like figuring out if an image contains a hat, a shoe, a shirt, and a briefcase. As a statistical technique, it holds a lot of value for businesses because it can be applied towards predictive use cases, which is a strategic business objective for organizations that want to use their data to help them better prepare for the future.

Logistic regression aims to measure the relationship between a categorical dependent variable and one or more independent variables (usually continuous) by plotting the dependent variables' probability scores. A categorical variable is a variable that can take values falling in limited categories instead of being continuous.

Logistic regression techniques have recently experienced a surge in demand due to the increasing use of Machine Learning, as this is one of the most commonly used algorithms. Its applications aren’t limited to specific industries or use cases, making it a commonly used and flexible analytics technique compared to other analytics methods.

## Logistic Regression and Its Applicability

Interestingly, about 70% of data science problems are classification problems. Classification is a critical component of advanced analytics, like machine learning, predictive analytics, and modeling, which makes classification techniques such as logistic regression an integral part of the data science process.

Logistic regression forecasts categorical results, including binomial and multinomial values of y. It’s a widely used statistical technique for forecasting binary classes and computes the likelihood of an event occurring or a decision being made. For example, a business might want to understand the probability of different demographics of guests accepting a promotional offer on their website (dependent variable). In this case, logistic regression would examine known characteristics of the guests, like if they’ve made other visits to the business’s website (independent variables) and what other websites they might have originated from. This would help the business develop their decision-making process regarding promotional content.

There are three different types of logistic regression:

• Multinomial Logistic Regression There are only two potential results for a categorical response, like click-through or not.
• Binary Logistic Regression There are three or more categories that don’t follow an ordering system, like forecasting the weather conditions such as sunny, rainy, partly cloudy, etc.
• Ordinal Logistic Regression There are three or more categories that do follow an ordering system, like a customer satisfaction rating from 1 to 10.

As a statistical method, this approach can be applied to a variety of analytics contexts, such as nonlinear regression, conjoint analysis, Monte Carlo simulation, and descriptive statistics.

Based on y being the dependent variable, and x1, x2, and Xn are explanatory variables, the statistical formula for logistic regression is:

The formula is based on assumptions, like there being no outliers contained within the data and no correlations between the independent variables.

## Logistic Regression in Business

This statistical method can have a significant, positive impact on a business, especially if predictive models are developed using this analytics process. It can augment decision-making capabilities based on accurately identified relationships and prediction and equip organizations with the information they need to tailor their sales and marketing strategies, improve customer services, shape product development, anticipate future events, and more. Basically, logistic regression uncovers patterns in complicated digital data, a key driver in areas like improved employee retention or understanding consumer behaviors.

Below are just a few examples of logistic regression in various business scenarios:

• #### Eliminate manufacturing errors

In Industry 4.0, logistic regression is indispensable and can identify the connection between equipment parts or machine failures and how long those particular pieces of equipment were kept unused in inventory or storage.

• #### Reduce credit risks

In banking and financial services, logistic regression can help loan officers evaluate credit risk by using customer data to understand the characteristics of customers who typically default, and those customers who have good credit.

• #### Preventative care

In healthcare, logistic regression is used to forecast the likelihood of disease for a specific population so that the right preventative care treatment or therapy can be put into effect.

• #### Improve product marketing

In marketing, logistic regression can be used to build profiles of customers who buy a specific product, like a pre-packaged nutritional bar, for example. Customers with different profile types, such as active lifestyle, age, gender, etc., can taste test the product, and from that data, models can be built to shape marketing strategies for the product.

## Logistic Regression in Machine Learning

As previously mentioned, logistic regression has a very robust role in machine learning because this form of advanced analytics relies on statistical concepts in order for the machines to continuously learn without being programmed. But logistic regression is best for this when the machine learning action or task is based on binary classification, meaning there are two values involved. Also, there are some different predictive models that use logistic regression, including ordered logit, multinomial logit, discrete choice, probit, and generalized linear models.

• Maximum likelihood estimation A popular learning algorithm that makes assumptions about the data distribution.
• Logistic function Sometimes referred to as the sigmoid function, this is used to describe the properties of population growth in ecological fields.
• Probability prediction This technique models the probability of the first class, or the probability that an X input is connected to the Y=1 default class. Or, P(X) = P(Y=1|X).
• Gaussian Distribution As a linear algorithm, logistic regression assumes that there’s a linear relationship across the input and output variables. So if the input variables can be transformed by data, the linear relationship can be more clearly visible.

## Benefits of Logistic Regression

Getting the best outcomes from logistic regression depends on an understanding of when this analytics technique is useful, and when it might not be the best fit for the scenario. Generally, the rules of thumb are to be cautious of overfitting, circumvent continuous outcomes, ensure variables are complete and accurate and avoid using interrelated data. This is true whether from a statistical standpoint, or a business perspective.

However, when aware of these guidelines, analytics and data science professionals are set up to produce results that can provide strong benefits.

• ### Reduce business expenses

Businesses can use insights produced from logistic regression to optimize their processes through more streamlined, efficient solutions.

• ### Build accurate predictive models

Logistic regression can help market researchers and data scientists determine the ideal variable sets to use when developing predictive models.

• ### Versatile and efficient

This analytics technique is very efficient and doesn’t rely on numerous different computational resources to produce dependable predictive probabilities.

• ### Develop more profitable products

Companies can use logistic regression to predict customer actions and behaviors and use the information to develop profitable products.

• ### Risk detection

This technique is beneficial for risk detection, such as the risk of developing a specific disease, based on certain patient characteristics.

## Take an Expert’s Assistance for Making Use of Logistic Regression

Research Optimus (ROP) uses both open-source and commercial software to effectively analyze data and apply logistic regression methods to perform data analysis for an expansive variety of business scenarios and use cases. We know how to help businesses make the most of their data with practical logistic regression services and numerous other analytics solutions.

As natural problem solvers, our skilled researchers and analysts are able to work with your organization to help you overcome your pain points and address your most urgent business objectives. Apart from a plethora of research services such as market research, financial research, and media monitoring, reach out to ROP today for personalized research and analysis services based on your unique requirements.

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