Regression analysis serves two core purposes: quantifying the relationship between variables and using that relationship to forecast outcomes. It’s one of the most widely used statistical tools across medicine, business, economics, and social science because it turns raw data into specific, actionable numbers. Rather than simply observing that two things seem connected, regression tells you exactly how much one changes when the other does, while accounting for other factors that might muddy the picture.
Measuring How Variables Are Connected
The most fundamental reason to use regression is to put a number on a relationship. Say you suspect that a marketing budget affects sales, or that blood pressure rises with body weight. Regression doesn’t just confirm the connection exists. It produces a coefficient that tells you, for every one-unit increase in the input variable, exactly how much the outcome changes. If a regression on hospital data produces a coefficient of -1.17 for a particular eye measurement, that means the outcome drops by 1.17 units for every one-unit increase in that measurement, holding everything else constant.
This precision matters because intuition is unreliable. Two variables might appear strongly linked when you plot them on a chart, but regression can reveal the effect is actually modest once you account for other factors. It can also reveal the opposite: a relationship that’s invisible in a simple chart becomes clear once confounding variables are stripped away.
Comparing the Strength of Multiple Factors
When several variables all influence the same outcome, you often need to know which one matters most. Raw regression coefficients can’t be directly compared because they depend on the units of measurement. A coefficient tied to income in dollars will look wildly different from one tied to age in years, even if age has the stronger influence.
Standardized regression coefficients solve this. They convert everything to the same scale, making it straightforward to rank which inputs have the strongest relationship with the outcome. This is how a hospital might determine whether a patient’s age, smoking history, or cholesterol level is the single best predictor of readmission, or how a company might figure out whether price, advertising spend, or customer reviews drives the most revenue.
Controlling for Confounding Variables
One of the most powerful reasons to use regression is the ability to isolate a single relationship while holding other variables constant. In a study examining whether body mass index is linked to digestive problems, researchers can’t ignore that age, sex, smoking, alcohol use, and ethnicity also play a role. Multiple regression lets you include all of those covariates in one model, effectively filtering out their influence so you can see the connection between BMI and the outcome on its own.
This process, called adjustment, is essential in medical and social science research where you can’t run a controlled experiment. The adjusted result often looks quite different from the unadjusted one. Comparing the two reveals how much confounders were distorting the picture. Without regression, observational data would be far less trustworthy as a basis for decisions.
Predicting Future Outcomes
Once a regression model is built, it becomes a prediction tool. You feed in new values for the input variables and the model generates a forecast for the outcome. This is how businesses project quarterly revenue, how epidemiologists estimate disease spread, and how lenders assess the risk of a loan default.
During the COVID-19 pandemic, researchers used regression-based time series models to predict weekly deaths from new case counts across different age groups, incorporating viral variants as additional factors. These models caught situations where multiple processes contributed to mortality with different time lags, revealing connections that were invisible to the naked eye. The ability to forecast one variable’s behavior from another, even when both are shifting over time, makes regression indispensable for planning and resource allocation.
Assessing Risk in Health and Medicine
In health research, a specific form called logistic regression is used whenever the outcome is a yes-or-no question: did the patient develop the disease or not, did the treatment succeed or fail. The key output is an odds ratio, which communicates risk in intuitive terms.
An odds ratio of 1 means the exposure has no effect on the outcome. Above 1, and the exposure is associated with higher odds. Below 1, it’s associated with lower odds. For example, one study found that the odds of persistent suicidal behavior were 3.8 times higher among adolescents with borderline personality disorder at baseline compared to those without it. That number, along with its confidence interval and p-value, gives clinicians a concrete way to weigh risk factors against each other rather than relying on vague impressions.
The choice between linear and logistic regression comes down to what you’re measuring. If the outcome is continuous, like days of hospitalization or lung capacity, linear regression is the appropriate tool. If the outcome is categorical, like survival versus death, logistic regression applies.
Knowing How Well the Model Fits
Regression doesn’t just give you an answer. It tells you how much confidence to place in that answer. The most common measure of fit is R-squared, which ranges from 0 to 1. An R-squared of 0.8 indicates a very good model, meaning 80% of the variation in the outcome is explained by the input variables. An R-squared near 0 means the model explains almost nothing, essentially performing no better than just guessing the average value every time. Negative R-squared values are possible in constrained models and signal that something has gone fundamentally wrong.
This built-in quality check is part of what makes regression so useful. You don’t have to take the results on faith. An R-squared of 0.756 for one modeling approach versus 0.423 for another gives you a clear, comparable basis for choosing between them. Researchers increasingly recommend R-squared as the standard evaluation metric because, unlike some alternatives, a value like 0.8 clearly signals strong performance regardless of what the data looks like or how the outcome is distributed.
Supporting Better Decisions
Regression results feed directly into policy and strategy. In healthcare, benefit assessments from observational studies rely on regression-adjusted results, with organizations like Germany’s Institute for Quality and Efficiency in Health Care using significance tests calibrated to account for the residual uncertainty that comes from non-randomized data. In business, regression identifies which operational changes will have the largest impact on the metrics that matter.
The p-value attached to each coefficient tells you how likely it is that the observed relationship is due to chance. Traditionally, a threshold of 0.05 has served as the cutoff for “statistical significance,” but practices are evolving. Starting in 2025, the Journal of Marketing adopted a policy requiring researchers to report exact p-values (like p = .047) rather than just indicating whether a result cleared a threshold. This shift discourages the practice of manipulating analyses until a result barely crosses 0.05, a problem documented across economics, biology, and medicine. Reporting the actual number gives decision-makers a more honest picture of the evidence.
Whether the goal is forecasting revenue, quantifying a health risk, or untangling which of a dozen variables actually drives an outcome, regression analysis provides the structure to move from “these things seem related” to “here is exactly how much this factor matters, and here is how confident we should be in that estimate.”