regression | Definition

Regression is a statistical method for examining the relationship between one dependent variable and one or more independent variables.

What Is Regression Analysis?

Regression is a common statistical technique that helps researchers understand how variables are related. Specifically, regression allows social scientists to predict the value of one variable (called the dependent variable) based on the values of one or more other variables (called independent variables).

In social science research, regression tests hypotheses, identifies patterns, and determines the strength and direction of relationships between variables. It is especially useful when trying to explain or predict outcomes, such as how education level influences income or how political beliefs shape voting behavior.

Regression can handle both simple relationships (with one independent variable) and complex ones (with multiple predictors). It provides not only a mathematical equation for the relationship but also tells researchers how strong the relationship is, whether it is statistically significant, and how much of the variation in the dependent variable can be explained by the independent variables.

Key Terms in Regression

Before diving deeper, it’s helpful to understand a few basic terms used in regression analysis:

Dependent variable: The outcome or variable researchers are trying to predict or explain.
Independent variable(s): The variable(s) believed to influence or predict the dependent variable.
Coefficient: A number that represents the strength and direction of the relationship between each independent variable and the dependent variable.
Intercept: The expected value of the dependent variable when all independent variables are equal to zero.
Residual: The difference between the observed value and the predicted value of the dependent variable.
R-squared: A measure of how much of the variance in the dependent variable is explained by the regression model.

Understanding these terms helps researchers interpret their results and determine whether the model is useful.

Types of Regression

There are several types of regression methods used in social science research, depending on the kind of data and research question. Here are the most common types:

Simple Linear Regression

Simple linear regression is used when there is only one independent variable. It tests how well one variable can predict another. For example, a researcher might use simple regression to see how years of education predict annual income.

The model takes the form:

Y = a + bX

Where:

Y is the dependent variable,
a is the intercept,
b is the slope (or regression coefficient), and
X is the independent variable.

This model shows how much Y changes for each one-unit change in X.

Multiple Linear Regression

Multiple regression involves more than one independent variable. This method allows researchers to control for other variables and assess their separate effects on the outcome.

For example, in a study of job satisfaction, a researcher might include variables like income, work environment, and education level. Multiple regression helps determine which of these has the strongest relationship with job satisfaction, while accounting for the others.

The model looks like this:

Y = a + b1X1 + b2X2 + b3X3 + … + bnXn

This version allows for more complex analysis and is widely used in social sciences.

Logistic Regression

Logistic regression is used when the dependent variable is categorical, especially when it is binary (e.g., yes/no, pass/fail, vote/don’t vote). Instead of predicting a number, logistic regression estimates the probability of an event happening.

For example, researchers may use logistic regression to predict whether someone will vote based on age, education, and political interest. The output is a probability between 0 and 1.

Logistic regression is useful when outcomes are not continuous but still need prediction and analysis.

Other Types

There are many other types of regression, including:

Ordinal regression (for ranked outcomes)
Multinomial regression (for outcomes with more than two categories)
Hierarchical regression (adding variables in steps to see how each set affects the outcome)
Interaction models (testing if the effect of one variable depends on another)
Nonlinear regression (used when the relationship between variables is not a straight line)

Each of these serves different purposes depending on the type of data and the research question.

Why Regression Is Important in Social Science

It Tests Relationships

Regression helps researchers move beyond basic descriptions and correlations. It allows for testing whether a change in one variable is associated with a change in another, and how strong that relationship is.

For example, a correlation might show that income and education are related, but regression can show how much income increases, on average, with each additional year of schooling.

It Helps Control for Confounding Variables

In real-world research, variables are often interconnected. Regression allows researchers to include multiple variables at once and control for their effects. This is especially helpful when trying to isolate the impact of one specific variable.

For example, in a study on gender and income, researchers can control for education and work experience to better understand whether gender alone affects income differences.

It Supports Prediction

Regression models are not just used to test theories—they are also used to make predictions. For instance, policy analysts might use regression to predict crime rates based on unemployment levels, or schools might predict graduation rates using test scores and attendance data.

It Offers Quantitative Evidence

Regression provides numerical estimates that show how variables relate. These numbers are critical when making evidence-based decisions or arguing for policy changes. Having concrete estimates, significance levels, and confidence intervals increases the credibility of research findings.

Assumptions of Regression

Regression analysis relies on certain assumptions. If these are not met, the results may be misleading. Understanding these assumptions is key to applying regression properly.

Linearity: The relationship between the independent and dependent variables should be linear.
Independence: Observations should be independent of one another.
Homoscedasticity: The variance of the residuals should be constant across all levels of the independent variable.
Normality: Residuals should be normally distributed (especially for small samples).
No multicollinearity: Independent variables should not be too closely related to each other.

Researchers must check these assumptions using diagnostic tests and graphs. If the assumptions are violated, other methods or transformations may be necessary.

Steps in Conducting a Regression Analysis

Running a regression model involves several steps:

Define the research question and identify the variables.
Collect and clean the data to ensure accuracy and completeness.
Explore the data using descriptive statistics and graphs.
Choose the appropriate regression model based on the type of data.
Run the regression using statistical software.
Check assumptions using diagnostics like residual plots or variance inflation factors.
Interpret the output, focusing on coefficients, p-values, and model fit.
Report the results in clear, accessible language.

Each step requires thoughtful decisions to ensure the analysis supports valid conclusions.

Example Applications of Regression in Social Science

Sociology

A sociologist might study how parental income, education, and neighborhood characteristics affect a child’s academic performance. Regression helps identify which factors are most important after controlling for others.

Psychology

Psychologists may use regression to examine how stress, sleep, and social support predict symptoms of anxiety. Multiple regression can reveal which predictors have the strongest effects.

Political Science

In voting behavior research, regression helps examine how variables like income, education, political interest, and media exposure influence the likelihood of voting.

Education

Educational researchers often use regression to assess the effects of teacher quality, class size, and school funding on student outcomes such as test scores or graduation rates.

Criminology

In criminology, researchers may use regression to explore how unemployment, poverty, and policing levels influence crime rates in different neighborhoods.

How to Interpret Regression Output

Statistical software provides many results, but some key parts include:

Coefficients: Show how much the dependent variable is expected to change for a one-unit increase in the independent variable.
Significance levels (p-values): Tell whether the relationships are likely due to chance. A p-value less than 0.05 is often considered statistically significant.
R-squared: Shows how much of the variation in the dependent variable is explained by the model. Higher values indicate a better fit.
Standard errors: Indicate how precise the coefficient estimates are.

Together, these elements help researchers determine whether their model supports their hypothesis and how confident they can be in their conclusions.

Limitations of Regression

While powerful, regression has its limits:

It cannot prove causation unless strong experimental or longitudinal designs are used.
It can be sensitive to outliers, which may distort results.
It assumes linear relationships, which may not always be true.
It relies on quality data, and poor data can lead to misleading results.
It can oversimplify complex processes if important variables are missing or poorly measured.

Understanding these limits helps researchers use regression wisely and avoid drawing overly broad conclusions.

Conclusion

Regression is a foundational statistical method in social science research. It helps researchers test relationships, make predictions, and control for confounding factors. From simple models with one predictor to complex models with multiple variables, regression provides valuable insights into how the social world works.

Used correctly, regression supports clear, evidence-based conclusions. But it requires thoughtful application and careful attention to assumptions, data quality, and interpretation. With practice and precision, regression becomes a powerful tool for answering important research questions.

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Last Modified: 03/23/2025