Regression Meaning: Definition, Examples, Uses

Key takeaways

• Regression is a statistical method used to examine how a dependent variable changes in relation to one or more independent variables.

• Linear regression refers to modeling a continuous outcome using a linear equation that predicts future values based on relationships between variables.

• Regression in real life occurs across fields such as economics, sociology, psychology, business, education, and health care, where analysts use variable relationships to make predictions and guide decisions.

The difference between correlation and regression is that correlation measures the strength and direction of a relationship between variables, while regression models that relationship to predict how a dependent variable changes when independent variables change. Discover the meaning of regression analysis, foundational concepts, the advantages and disadvantages of this method, and more. Then, consider enrolling in the IBM Machine Learning Professional Certificate. In as little as three months, you can have the opportunity to master the most up-to-date practical skills and knowledge machine learning experts use in their daily roles. You can predict course ratings by training a neural network and constructing regression and classification models.

Regression meaning: What is regression analysis?

Regression analysis is a statistical methodology that explores the relationship between a dependent variable and one or more independent variables. The letter “Y” generally denotes the dependent variable, and the independent variable is an “X.”

In simpler terms, you can think of regression as a way to predict a future outcome based on what has happened in similar scenarios (i.e., based on our existing data sets). We can use this mathematical model to predict the outcome (the dependent variable) based on the input or changes in the other variables (the independent variables). In a linear regression model, you would have a continuous outcome and create a line equation to predict future outcome values. In a logistic regression model, your outcome is a fixed categorical event (e.g., yes/no or pass/fail), and you predict the probability that your outcome will be in a certain category.

Researchers also use regression analysis to determine which independent variables affect the dependent variable. If you suspect that a set of variables is impacting your outcome, you can use regression analysis to determine which variables are the most important in your model and have the biggest impact on your outcome.

Foundational concepts

When you perform regression analysis, you will work with a certain key set of concepts. Understanding these concepts supports the design and application of regression analysis: independent variables, dependent variables, correlation, and causation.

1. Independent variables

In a regression model, the independent variables, or the explanatory variables, are the factors that you believe will impact the outcome of the variable you are interested in understanding or predicting. As the name suggests, they are independent, and the researcher can manipulate them to observe the corresponding changes in the dependent variable.

For example, if you are trying to predict someone’s likelihood of developing a disease, your independent variables might be their age, health status, activity level, and biological metrics.

2. Dependent variables

The dependent variable, or response variable, is the outcome in a regression model. This is the variable you aim to understand, predict, or explain. Its value is dependent on the changes in the independent variables.

For example, in a business scenario, the dependent variable could be sales, which might depend on independent variables like marketing budget, pricing, and competition.

3. Correlation

Correlation is a statistical measurement representing the magnitude of the relationship between several variables. You can represent this measure as a correlation coefficient (denoted as “r”), ranging from negative to one.

If r is positive, the correlation is positive, meaning both variables increase or decrease together. If r is negative, one variable decreases as the other increases. If r equals zero, it represents no correlation between the variables. It is important to note that correlation does not equal causation.

Read more: Correlation vs. Causation: What’s the Difference?

4. Causation

While correlation can signal a relationship between variables, it does not infer causation. Correlation means two variables relate and change with one another. Causation means that a change in one variable causes a change in the other. If a causal relationship between variables is present, regression analysis can predict the outcome of our dependent variable based on changes to the independent variables.

Saying changes in one or multiple variables definitively cause an outcome is a stronger claim than saying two variables relate. Because of this, determining causal relationships requires much stricter assumptions and analysis than correlation.

How does regression analysis work?

Regression analysis begins with data, or information about the variables you would like to assess. Using this data, you can create a mathematical model, typically a line or curve, that best illustrates the relationship between the dependent and independent variables.

Once you have your estimate or prediction from your model, you can look at the standard error of the prediction to see whether your prediction is strong or weak. This tells you how much you can trust your model and helps you build a confidence interval to better represent your true regression coefficient.

You can also examine statistical metrics to see how each independent variable you include affects your model. This can show you how important each variable is and help you decide which independent variables to include in your model to predict the value of your response variable most accurately.

Origins of regression analysis

The term “regression” dates back to the 19th century. Sir Francis Galton, a British scientist, pioneered the method in his studies of heredity. He noted that extreme traits in parents often “regressed” toward the average in their offspring, leading to the term “regression.”

Examples of regression analysis

Regression analysis is present in almost every professional field. Usually, an investigator in a certain industry shows interest in the causal effect of certain variables on another. These variables are changed by industry, but the principle of the regression analysis is the same. Some ways in which you might use regression analysis include the following:

• Economics: Predicting a family’s spending patterns based on their location, number of children, and income

• Political science: Determining how much money politicians should allocate to a certain government-funded program based on the need in previous years

• Sociology: Looking at how the social status of different universities predicts application patterns

• Psychology: Assessing the relationship between someone’s level of acceptance and their cultural background

• Business: Understanding how business practices affect sales or employee retention

• Education: Predicting a student’s GPA based on their extracurricular activities

• Health care: Predicting whether someone will recover from an illness based on their age, blood pressure, weight, and medical history

Benefits of using regression analysis

One of the primary benefits of regression analysis is its ability to quantify and model the relationship between different variables, allowing you to make predictions. It allows us to estimate the strength and direction of one or more independent variables' impact on the dependent variable.

Regression analysis is flexible and can deal with more than one independent variable simultaneously. This enables professionals to consider complex, multifactor scenarios. For instance, a company might use regression analysis to understand how pricing, advertisement spending, and market competition collectively impact sales.

Drawbacks of regression analysis

Despite its many strengths, regression analysis does come with a set of limitations. For one, while regression analysis can suggest relationships and correlations, it does not prove causation. It may provide evidence of a causal effect under certain conditions, which require careful study design to meet in practice.

In addition to this, regression analysis can include pitfalls such as:

• Overfitting: Overfitting occurs if the model fits too closely to the training data and cannot generalize to new information.

• Nonconstant variances (heteroskedasticity): Nonconstant variance happens when the error term is not constant, preventing the model from being well-defined. This can cause prediction intervals to be too wide or too narrow with new information.

• Multicollinearity: Multicollinearity can occur if the independent variables correlate with one another. This can skew results.

• Missing data: When data is missing, this can lead to a small sample size and reduced power.

• Small sample size: A small sample size can induce biased results.

• Low power: Low power is when the probability of a significant finding is low.

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