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

Key takeaways

• Linear regression is a type of regression analysis that predicts a specific numeric value based on how variables relate to one another, whereas logistic regression predicts the probability of a categorical outcome.

• You might use linear regression to analyze consumer choices by time of year, but use logistic regression to predict whether a consumer will make a purchase based on historical data.

• An example of linear regression versus logistic regression is when a sports analyst uses linear regression to predict a player's performance and logistic regression to predict whether the team will win or lose the game.

Linear and logistic regression differ in their outcome variables, equations, error measures, and output formats. Read on to discover the intricacies of linear and logistic regression, including their key features, differences, and examples of when to use each. If you’re ready to begin your career in data analytics, enroll in the Google Data Analytics Professional Certificate to develop in-demand skills in data structures, Tableau, SQL, Python, data cleaning, data analysis, data visualization, and more in as little as six months.

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 of your exercise and eating patterns. Regression analysis shows how your dependent variable changes as your independent variable or variables change.

Regression uses

You can use regression for several purposes, 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 the relationship between dependent and independent variables. For instance, a health care researcher might use regression to estimate the impact of different factors such as 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, such as product quality, customer service, and marketing efforts, significantly impact overall revenue.

Read more: Good Customer Service: Definition, Examples, and Tips

What is linear regression?

Linear regression is a common type of regression analysis that expresses the relationship between your dependent and independent variables in a straight line when you plot your data on a graph. You might choose it if you anticipate that one factor will change the other by a constant amount, such as how a vehicle's fuel economy is affected by its weight.

Linear regression aims to identify the line of best fit that represents the relationship between your variables using the "least squares" method. You can define the best-fit line as the line that minimizes the total distance between this line and all your data points above and below it. You can then use the equation Y = aX + b to predict the value of one variable when you know the value of another variable

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

Types of linear regression

You will encounter two main types of linear regression: simple and multiple. 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:

• Health care: Exploring the relationship between patient characteristics and biological measures

• Finance: Assessing investment choices and predicted returns

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

• Marketing: Analyzing consumer choices based on location and time of year

• Environmental science: Exploring climate data and carbon emissions

What is logistic regression?

Logistic regression is a statistical method used to predict an outcome based on several predictor variables. For example, a university might want to predict whether a learner will graduate based on age, high school grades, or SAT scores.

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 likelihood 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). Predicting an outcome with only two possible results, such as pass or fail, is the most common use of logistic regression, but you can also use it 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:

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

• Education: Predicting whether a student will pass an exam

• Marketing: Predicting whether a customer will make a purchase

• Banking: Predicting whether an individual will default on a loan

• Sports: Predicting whether a sports team will win a game

Linear regression vs. logistic regression: What is the main difference?

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, such as 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 of selling.

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. Some careers that use linear and logistic regression include:

• Investment analyst

• Risk analyst

• Marketing analyst

• Health care analyst

• Manufacturer

• Environmentalist

• Business analyst

• Risk management analyst

• Programmer

• Trader

• Portfolio manager

A linear regression vs. logistic regression example

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.

Keep up with trends and job opportunities in data analysis

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• Watch on YouTube: Tutorial: Exploratory Data Analysis in Python

• Follow a tutorial: Google Sheets Linear Regression: Learn Predictive Modeling

• Learn related terminology: Data Analysis Terms & Definitions

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