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Here’s What You Should Know About Logistic Regression

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Logistic regression is an invaluable regression analysis technique in situations where linear regression simply cannot work.

To quote prominent statistician Andy Field, “Logistic Regression is based on this principle: it expresses the multiple linear regression equation in logarithmic terms(called the logit) and thus overcomes the problem of violating the assumption of Linearity.”

In this article, we’ll understand what is logistic regression analysis, how it works with a logistic regression example, and how it is applied in data analytics.

What is Logistic Regression?

To understand what is logistic regression, we must begin by understanding how it’s different from linear regression.

In order to understand the difference between linear and logistic regression, we need to first understand the difference between a continuous and a categoric variable.

Continuous variables are numeric values. They have an infinite number of values between any two given values. Examples include the length of a video or the time a payment is received or the population of a city.

Categorical variables, on the other hand, have distinct groups or categories. They may or may not have a logical order. Examples include gender, payment method, age bracket and so on.

In linear regression, the dependent variable Y is always a continuous variable. If the variable Y is a categorical variable, then linear regression cannot be applied.

In case Y is a categorical variable that has only 2 classes, logistic regression can be used to overcome this problem. Such problems are also known as binary classification problems.

It’s also important to understand that standard logistic regression can only be used for binary classification problems. If Y has more than 2 classes, it becomes a multi-class classification and standard logistic regression cannot be applied.

One of the biggest advantages of logistic regression analysis is that it can compute a prediction probability score for an event. This makes it an invaluable predictive modeling technique for data analytics.

Logistic Regression Source - Machine Learning Plus

Linear & Logistic Regression

Logistic Regression Examples

To find logistic regression examples, we must first find some examples of binary classification problems. Binary classification problems are usually those problems where an outcome either happens or doesn’t happen.

In other words, the dependent variable Y has only two possible values. Logistic regression helps to predict the value as either 0 or 1 or as a probability score that ranges from 0 to 1. Some common binary classification problems include:

(i) Predicting the creditworthiness of a customer; that is whether a customer will default on a loan or not.

(ii) Identifying if a particular user will buy a particular product or not. This is especially used for financial products like mutual funds, insurance, and so on.

(iii) Identifying whether a particular person is likely to develop diabetes or not.

(iv) Identifying whether a particular email constitutes spam or not.

If we use linear regression for these kinds of problems, the resulting model will not restrict the values of Y between 0 to 1. With logistic regression analysis, the other hand, you will get a value between 0 and 1 which will indicate the probability of the event occurring.

Logistic Regression example represented graphically

Logistic Regression Source Wikipedia

Logistic Regression Graph

How does Logistic Regression Work?

Here’s what the logistic equation looks like:

Logistic Regression Source Machine Learning Plus

Logistic Regression Equation

Taking e (exponent) on both sides of the equation results in:

Logistic Regression Source Machine Learning Plus

Equation with E Exponent

Here’s how the equation can be implemented in R:

# Template code

# Step 1: Build Logit Model on Training Dataset

logitMod <- glm(Y ~ X1 + X2, family=“binomial”, data = trainingData)

# Step 2: Predict Y on Test Dataset

predictedY <- predict(logitMod, testData, type=“response”)

Watch this video for a detailed understanding of how logistic regression models can be built in R.

Different Types of Logistic Regression Techniques

Logistic Regression Source Medium

Logistic Regression Model

As discussed, the standard logistic regression technique can only solve binary classification problems. So what about problems with multiple classes? We use extensions of logistic regression to solve multi-class classification problems. Here are the two main ones:

(i) Multinomial Logistic Regression

For instance, say the dependent variable has K=3 classes. The multinomial logistic regression technique fits K-1 independent binary logistic classifier model. To do so, it chooses any one target class randomly as the reference class.

It then fits K-1 regression models that compare the remaining classes to the randomly chosen reference class. This model is not very widely used because it has scalability issues. It doesn’t work well when there are too many target classes. Plus, it requires a much larger data set to achieve accuracy because it uses K-1 models.

(ii) Ordinal Logistic Regression

This technique can only be used when there is an order to the dependent variable. Say, for instance, the years of experience need to be determined.

In this case, there is an order in the values, that is 5>4>3>2>1 and so on. In this method, a single model is built but with multiple threshold values. So if there are K classes, the model will have K-1 threshold points. The method also assumes that on a logit scale, all the thresholds lie on a straight line.

However, it must be kept in mind that logistic regression is not usually the best choice when it comes to multi-class problems. It’s much more valuable in binary classification problems.

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How is Logistic Regression Used in Data Analytics

Like other regression analysis models, logistic regression is also used in data analytics to help companies make decisions and predict outcomes. In the case of logistic regression, the output predicted is binary which simplifies decision making even further.

Companies use insights derived from logistic regression output to achieve a variety of business goals; from minimizing losses and optimizing costs to maximizing profits and ROI.  Here are two logistic regression models that are commonly used by companies to make crucial decisions.

Default Propensity Model

This is a model that is used to determine whether or not a customer will default. Credit card companies often build default propensity models to decide whether or not they should issue credit cards to customers.

The Propensity to Respond Model

This model is often used by e-commerce companies. They use this model to determine whether a customer is likely to respond positively to a promotional offer. In other words, the model predicts whether an existing customer will be a “Responder” or a “Non-Responder”.

What are the Best Resources to Learn Logistic Regression

There are some seminal books on logistic regression that can really help you understand logistic regression better. These include Regression Models for Categorical and Limited Dependent Variables (Advanced Quantitative Techniques in the Social Sciences) by J. (John) Scott Long, and Logistic Regression Using SAS: Theory and Application by Allison Paul D.

Of course, the best resources to learn logistic regression depends upon what you want to do with the information. If it’s just a casual, passing interest, almost any basic online course will do.

If you are looking to learn logistic regression for research purposes, then you will need material that is more formal and academic in nature.

If your goal is to have a career in data science, machine learning, or data analytics then it’s best to go for a course with live sessions that the advantages of a cutting-edge curriculum with two-way interaction, live sessions, assignments, and placement assistance.

Common Mistakes in Regression Analysis

Here are some mistakes that many people tend to make when they first start using regression analysis and why you need to avoid them.

(i) Correlation is Not Causation

Regression analysis can show you relationships between your independent and dependent variables. However, it’s important to understand that this correlation may not always result in causation.

For instance, a logistic regression analysis may give you the result that product sales go above a certain threshold whenever the temperature drops below 30 degrees. However, this doesn’t mean that the temperature drop is causing an increase in sales.

It’s important for you to also do some background work to understand if this is the case. In other words, correlation should not be confused with causation when you make important business decisions.

(ii) Intuition Together With Data

The important thing is not to blindly trust regression results. Regression results can be tainted by unclean data or a large error term. If a particular result doesn’t seem right, do trust your instincts and investigate before acting on the result.


Logistic regression is the next step in regression analysis after linear regression. Regression analysis is one of the most common methods of data analysis that’s used in data science.

If you are serious about a career in data analytics, machine learning, or data science, it’s probably best to understand linear and logistic regression analysis as thoroughly as possible. Luckily, there are a number of good programs and courses that can get you there.

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