Understanding regression analysis: overview and key uses

Regression analysis is a statistical method that predicts and explains how different factors (the independent variables) influence a specific outcome (the dependent variable).

Say you’re trying to predict the value of a house. Regression analysis helps you build a formula that estimates the house’s value from variables like the home’s size and the neighborhood’s average income. The same logic lets you predict and analyze trends in any dataset.

That example is straightforward, but the technique scales to far more complex situations, delivering valuable insights in economics, healthcare, marketing, and beyond.

3 uses for regression analysis in business

Businesses can use regression analysis to improve nearly every aspect of their operations. Used correctly, it’s a powerful tool for learning how adjusting variables can improve outcomes. Here are three applications:

1. Prediction and forecasting

Predicting future scenarios gives businesses a real advantage. No method guarantees certainty, but regression analysis offers a reliable framework for forecasting trends from past data. Companies use it to anticipate future sales for financial planning and to predict inventory requirements for more efficient space and cost management. Similarly, an insurance company can use regression analysis to predict the likelihood of claims for more accurate underwriting.

2. Identifying inefficiencies and opportunities

Regression analysis shows how the relationships between different business processes affect outcomes. Because it can model complex relationships, it highlights the variables driving inefficiencies—ones intuition alone may miss. That lets businesses improve performance through targeted interventions. For instance, a manufacturing plant experiencing production delays, machine downtime, or labor shortages can use regression analysis to determine the underlying causes.

3. Making data-driven decisions

Regression analysis can sharpen decision-making in any situation that relies on dependent variables. For example, a company can analyze how various price points affect sales volume to find the best pricing strategy for its products. Understanding the factors behind buying behavior can also help segment customers into buyer personas for better targeting and messaging.

Types of regression models

There are several types of regression models, each suited to a particular purpose. Picking the right one is vital to getting correct results.

• Simple linear regression analysis is the simplest form. It examines the relationship between exactly one dependent variable and one independent variable, fitting a straight line to the data points on a graph.
• Multiple regression analysis examines how two or more independent variables affect a single dependent variable. It extends simple linear regression and requires a more complex algorithm.
• Multivariate linear regression suits multiple dependent variables. It analyzes how independent variables influence multiple outcomes.
• Logistic regression applies when the dependent variable is categorical, such as binary outcomes (true/false or yes/no). It estimates the probability of a category based on the independent variables.

6 mistakes people make with regression analysis

Ignoring key variables is a common mistake in regression analysis. Here are a few more pitfalls to avoid:

1. Overfitting the model

If a model is too complex, it can over-adjust to fit every variable—a problem known as overfitting. It’s especially likely when the independent variables don’t actually impact the dependent data. The model starts memorizing noise rather than meaningful patterns. Its results will fit the training data perfectly but fail to generalize to new, unseen data, making it useless for prediction or inference.

2. Underfitting the model

A simpler model is less likely to draw false conclusions, but make it too simplistic and you get the opposite problem: underfitting. The model fails to capture the underlying patterns in the data, so it performs poorly on both the training data and new, unseen data. Without enough complexity, it can’t make accurate predictions or draw meaningful inferences.

3. Neglecting model validation

Model validation is how you confirm a model isn’t overfitting or underfitting. Imagine teaching a child to read. If you always read the same book, they might memorize and recite it perfectly, seeming like they’ve learned to read. Hand them a new book, though, and they might struggle.

A model that performs well on its training data but fails with new data is doing the same thing. Model validation means testing the model on data it hasn’t seen before. If it performs well on that new data, it has truly learned to generalize. If it only performs well on the training data, it has overfitted—much like the child who can only recite the memorized book.

4. Multicollinearity

Regression analysis works best when the independent variables are genuinely independent. Sometimes, though, two or more variables are highly correlated. This multicollinearity makes it hard for the model to accurately determine each variable’s impact.

If a model gives poor results, checking for correlated variables may reveal the issue. You can fix it by removing one or more correlated variables, or by using principal component analysis (PCA), which transforms the correlated variables into a set of uncorrelated components.

5. Misinterpreting coefficients

Errors aren’t always the model’s fault—human error is common, and it often involves misreading the results. Someone might misunderstand the units of measure and draw incorrect conclusions. Another frequent issue is confusing correlation and causation. Regression analysis can only provide insights into correlation, not causation.

6. Poor data quality

The adage “garbage in, garbage out” strongly applies to regression analysis. Feed a model low-quality data and it analyzes noise rather than meaningful patterns. Poor data quality shows up as missing values, unrepresentative data, outliers, and measurement errors. The model may also be missing essential variables that significantly impact the results. All of these issues distort the relationships between variables and lead to misleading conclusions.

What are the assumptions that must hold for regression models?

To correctly interpret the output of a regression model, these key assumptions about the underlying data must hold:

• The relationship between variables is linear.
• There must be homoscedasticity, meaning the variance of the error term remains constant.
• All explanatory variables are independent of one another.
• The residuals (error terms) are normally distributed.

Real-life examples of regression analysis

Here’s how a few industries use regression analysis to improve their outcomes:

Healthcare

Regression analysis has many applications in healthcare, but two of the most common are improving patient outcomes and optimizing resources.

For any medical condition, you can find research that identifies the risk factors for that condition. The condition is the dependent variable, and the risk factors are the independent variables. By plugging a patient’s risk factors into a regression analysis, healthcare providers can estimate that person’s risk of developing the condition.

Hospitals need to use resources effectively to ensure the best patient outcomes. Regression models help forecast patient admissions, equipment and supply usage, and more—letting hospitals plan ahead and maximize their resources.

Finance

The finance industry depends on predicting stock prices, economic trends, and financial risks. Regression analysis helps finance professionals make informed decisions about all three.

For example, analysts often use regression analysis to assess how changes in GDP, interest rates, and unemployment rates impact stock prices. Armed with this information, they can make better portfolio decisions.

Banking uses regression analysis, too. When a loan underwriter decides whether to grant a loan, regression analysis lets them calculate the probability that a borrower will repay it.

Marketing

Imagine how much more effective a company’s marketing could be if it could predict customer behavior. Regression analysis makes that possible with a degree of accuracy. Marketers can analyze how price, advertising spend, and product features combine to influence sales. Once they’ve identified the key sales drivers, they can adjust their strategy to maximize revenue—often in stages.

For instance, if ad spend turns out to be the biggest driver, they can run regression analysis on advertising-specific data to improve the ROI of their ads. The opposite holds too: if ad spending has little to no impact on sales, something is wrong—and regression analysis might help identify what.

Regression analysis tools and software

Regression analysis by hand isn’t practical—the process involves large numbers and complex calculations. Computers make even the most complex regression analysis possible, and many machine learning algorithms are, at their core, sophisticated regression calculations. Plenty of tools exist to help you build these regressions.

R

R is a powerful open-source programming language and software environment designed for statistical computing, making it a favorite for regression analysis. It has packages for every type of regression you might perform, so you can plug in numbers and get meaningful results quickly. There are also packages to visualize data and create reports, adding to its utility.

MATLAB

MATLAB is a commercial programming language built for complex mathematical operations, including regression analysis (the open-source project Octave implements much of the same functionality). Its computation and visualization tools have made it popular in academia, engineering, and industry for calculating regressions and displaying the results. MATLAB integrates with other toolboxes, so developers can extend its functionality for application-specific solutions.

Python

Python is a more general programming language, but its libraries cover regression thoroughly. Packages like scikit-learn and statsmodels provide the computational tools, while Pandas and Matplotlib handle large amounts of data and display the results. Python is simple to learn and easy to read, which can give it a leg up over more specialized math and statistics languages.

SAS

SAS (Statistical Analysis System) is a commercial software suite for advanced analytics, multivariate analysis, business intelligence, and data management. Its PROC REG procedure lets users efficiently perform regression analysis on their data. SAS is well known for its data-handling capabilities, extensive documentation, and technical support—common reasons it’s chosen for large-scale enterprise use and industries requiring rigorous statistical analysis.

Stata

Stata is a statistical software package providing an integrated environment for data analysis, management, and graphics. It includes tools for a wide range of regression tasks. Its popularity comes from its ease of use, reproducibility, and intuitive handling of complex datasets, and its extensive documentation helps beginners get started quickly. Stata is widely used in academic research, economics, sociology, and political science.

Excel

Most people know Excel, but you might not know that Microsoft’s spreadsheet software has an add-in called Analysis ToolPak that performs basic linear regression and visualizes the results. Excel isn’t a great choice for complex regression or very large datasets. But for quick analysis of smaller datasets, it’s a convenient option that’s already in many tech stacks.

SPSS

SPSS (Statistical Package for the Social Sciences) is a versatile statistical analysis tool widely used in social science, business, and health. It offers tools for various analyses, including regression, through a user-friendly interface. SPSS lets users manage and visualize data, perform complex analyses, and generate reports without coding. Its extensive documentation and support make it popular in academia and industry for handling large datasets reliably.