Linear Regression vs. Logistic Regression: What You Need to Know

Professionals across many industries use linear and logistic regression to better understand the relationship between their variables. This information can inform key business decisions by evaluating trends, estimating sales, analyzing pricing elasticity, predicting disease, and more. 

Gain a deeper insight into the intricacies of linear and logistic regression, including their key features, differences, and how to decide which type of regression is right for your needs.

Read more: What Is Data Analysis? (With Examples)

What is regression analysis?

Regression analysis lets you model and analyze relationships between variables. When performing regression analysis, you'll look at two critical variables: independent and dependent. Independent variables aren’t influenced by other factors. Examples may include how many hours you exercise in a day or how many vegetables you eat in a week. 

On the other hand, a dependent variable is directly affected by the independent variable. In this example, your physical health would be a dependent variable to your exercise and eating patterns. Regression analysis shows how your dependent variable changes based on the behavior and value of your independent variable or variables.

Regression uses 

You can use regression for several reasons, depending on your industry and needs. Some primary purposes of regression analysis are:

• Predictive analysis: Regression analysis allows you to make predictions. You can predict the dependent variable's value based on the independent variables' values. For example, an online retailer might use regression to predict future sales based on past purchasing behavior and other factors, such as advertising spend or time of the year.

• Estimating relationships: Another major function of regression is to assess the strength and direction of relationships between dependent and independent variables. For instance, a health care researcher might use regression to estimate the impact of different factors (like diet, exercise, age, and genetics) on the likelihood of developing a particular health condition.

• Understanding variable importance: Regression can help understand the importance of different predictors. For instance, in a company’s revenue model, regression can help determine which factors (product quality, customer service, marketing efforts) significantly impact overall revenue.

Read more: Logistic Regression: An Overview

Linear regression 

Linear regression is a common type of regression analysis you might choose if you anticipate a linear correlation between your dependent and independent variables. This approach expresses the relationship between your variables through a straight line, which is where the term “linear” in linear regression comes from. This line of best fit uses the equation: Y = aX + b.

In this equation:

• Y represents the dependent variable

• X is the independent variable

• ‘a’ represents the slope of the line, which shows how much Y changes based on each unit change in X 

• ‘b’ is the Y-intercept, which is the point where the line intersects the Y-axis

Linear regression aims to identify the best line to represent the relationship between your variables. You can define the best-fit line as the line where the total distance between this line and all your data points (either above or below the line) is minimal, following the “least squares” method. After obtaining the “best fit” line, you can use the equation to make predictions.

Types of linear regression 

You will encounter two main types of linear regression: simple and multiple linear regression. These two types of regression are similar, with multiple linear regression being an extension of simple linear regression.

In simple linear regression, you have one independent and one dependent variable. For instance, you might examine the connection between a person’s weekly vegetable consumption (independent variable) and blood pressure (dependent variable). In this case, use the equation Y = aX + b.

Multiple linear regression comes into play when you have multiple independent variables. For instance, in the same study, you might consider not just vegetable consumption but also the sleep duration each night before the blood pressure measurement. Now, you have two independent variables, meaning you're working with multiple linear regression. The equation in this scenario would look something like Y = a + b1(X1) + b2(X2). Here, X1 and X2 are the independent variables (vegetable consumption and sleep duration), and b1 and b2 are their slopes.

Examples of linear regression 

Linear regression benefits several industries, with many professionals and organizations using this analytical technique. Some examples of where you might see linear regression in different fields include:

• Exploring the relationship between patient characteristics and biological measures

• Assessing investment choices and predicted returns

• Predicting whether an applicant will repay a loan based on past behavior

• Analyzing consumer choices based on location and time of year

• Exploring climate data and carbon emissions

Logistic regression 

Logistic regression, specifically binary logistic regression, is a statistical method used to predict an outcome with only two possible results based on several predictor variables. For example, a university might want to predict whether a learner will graduate based on age, high school grades, SAT scores, etc.

Logistic regression is an algorithm that uses historical data to predict an outcome. This type of regression determines the probability of a specific event or category, such as the probability of a consumer purchase (yes/no), a sporting team's result (win/lose), or a city’s weather on a given day (rain/no rain). Logistic regression can expand to include several additional types of outcome variables, including unordered and ordered categorical variables.

Types of logistic regression 

You can choose between three main types of logistic regression, depending on your variables. These types are:

• Binary logistic regression: Binary logistic regression is the go-to option when the dependent variable, or the outcome you’re interested in predicting, can only adopt two possible values. It includes outcomes such as yes/no, pass/fail, and win/lose.

• Ordinal logistic regression: This type is ideal when you have ordinal categorical variables. This means that the variable can be naturally ranked or ordered. For example, this would include an outcome such as whether a customer chose a small, medium, or large drink size.

• Multinomial logistic regression: This type is similar to ordinal logistic regression in that you have more than two possible outcomes. However, unlike with ordinal, your outcome variable is nominal. This means that your categorical variables are naturally unordered. For example, this may predict whether a customer will choose a red, blue, or yellow bag.

Examples of logistic regression

Similar to linear regression, logistic regression benefits many industries. Some examples of how you might see logistic regression in real-world problems include:

• Predicting whether a city will have a hurricane in a given year

• Predicting whether a student will pass an exam

• Predicting whether a customer will make a purchase

• Predicting whether an individual will default on a loan 

• Predicting whether a sports team will win a game

Key differences between linear and logistic regression 

While linear and logistic regression fall under the umbrella of predictive modeling and share similarities, they are fundamentally distinct methods used for different prediction problems. Some key differences include:

• Outcome variable: Linear regression has an outcome variable that is continuous or quantitative, like predicting house prices, sales amounts, or students’ test scores. Logistic regression has an outcome variable that is categorical or qualitative. This includes binary outcomes, multinomial outcomes, and ordinal outcomes.

• Regression equation: Linear regression uses a linear equation to estimate the dependent variable. This equation takes the form Y = a + bX. Logistic regression uses a logistic function to model the probability that the dependent variable belongs to a particular category. The logistic function transforms the output to lie between 0 and 1, which interprets as a probability.

• Error measurement: In linear regression, the least squares method minimizes the sum of the squared differences between the actual and predicted values, resulting in a “best fit” line. Logistic regression uses a method called maximum likelihood estimation (MLE). This technique maximizes the likelihood of getting the results that you did.

• Output format: Linear regression provides an actual predicted outcome. For example, it might predict that a house will sell for $500,000. Logistic regression outputs the probability of an event occurring. For instance, it might predict that a house has an 80 percent chance a particular house will sell.

How to perform regression analysis 

While you can perform regression analysis by hand, modern computer software programs streamline regression analysis and allow you to quickly analyze large data sets and combinations of variables. Some statistical software packages and programming languages that enable you to perform regression analysis include:

• SAS

• R

• STATA

• Python

• Excel

What careers use regression 

Both linear and logistic regression are helpful in a wide range of careers. While they have different applications, many professions use both techniques.

Example of how linear and logistics regression can be used

Sports analysts might employ linear regression to forecast a player's performance in the coming season based on past performances. On the other hand, they might use logistic regression for binary outcomes, such as predicting whether a team will win or lose a game based on several factors, like team form, head-to-head records, and player fitness levels.

Some other careers that use linear and logistic regression include:

• Investment analyst

• Risk analyst

• Marketing analyst

• Health care analyst

• Manufacturer

• Environmentalist

• Business teams

• Risk management analyst

• Programmer

• Trader

• Portfolio manager

Next steps on Coursera

Regression analysis is an exciting and useful skill you can use across different professions. Regardless of your job title, learning to use logistic and linear regression can help you better understand data and make informed predictions on how your outcome variables will respond to change. To build your skills in this area, consider taking courses, guided projects, and Professional Certificates on Coursera from top universities. Some highly-rated options include:

• Linear Regression and Modeling

• Regression Analysis: Simplify Complex Data Relationships

• Logistic Regression in R for Public Health

• Predictive Modeling with Logistic Regression using SAS