What Is Linear Regression? (Types, Examples, Careers)

Professionals use linear regression across many industries to make predictions, inform business decisions, prepare for upcoming events, and explore answers to research questions. You can dive into the intricacies of linear regression throughout this article, including the definition,, different types of linear regression, and how different careers use this statistical tool.

What is regression analysis?

Regression analysis is a statistical method that allows us to understand the relationship between two or more variables. Before diving into linear regression, it’s important to understand a few key definitions:

• Dependent variable: The dependent variable, or response variable, is the variable you’re interested in understanding or predicting. For instance, it could be something like the score a student gets on a test.

• Independent variables: The independent variables, or explanatory variables, are variables that you think might affect your dependent variable. In the above example, this could be the number of hours the student studied, their previous knowledge, the number of hours they slept, and so on.

• Regression equation: The regression equation is the formula that tries to express how your independent variables (like studying, sleep, etc.) relate to your dependent variable (the test score). 

When you perform a regression analysis, your regression equation provides a way to predict future outcomes based on the information you currently have. For instance, if you had data on how much previous students studied, slept, and scored on their test, you could perform a regression analysis to create an equation that predicts a future student’s test score based on how much they studied and slept. As you get more data, you can continue to update your equation to improve its validity and findings.

Read more: What Is Data Analysis? (With Examples)

What is linear regression? 

Linear regression is a specific type of regression analysis that you use when you expect a clear, straight-line relationship between your independent and dependent variables. This is where the term “linear” in linear regression comes from. You describe the straight line by an equation: Y = aX + b.

• Y is the dependent variable.

• X is the independent variable.

• ‘b’ is the y-intercept, or where the line crosses the y-axis.

• ‘a’ is the slope of the line, which indicates how much Y changes when X changes.

In linear regression, you’re trying to find the “best fit” line to represent the relationship between your variables. The idea of accuracy here typically means the line where the total distance between the line and all your data points (both above and below the line) is as small as possible. This is the “least squares” model. Once you have your “best fit” line, you can use it to make predictions. 

Types of linear regression

In linear regression, you can have one or multiple independent variables. If you only have one, it’s called “simple linear regression.” If you have more than one, it’s called “multiple linear regression.” The more variables you include, the more complex your equation becomes, but the basic idea is the same.

1. Simple linear regression

Simple linear regression is the most basic form of linear regression, and it involves just one independent variable and one dependent variable. For example, imagine you’re studying the relationship between the number of hours someone exercises per week (independent variable) and their blood pressure (dependent variable).

In simple linear regression, you would model this relationship using the equation Y = a + bX, where:

• Y is the dependent variable (blood pressure).

• X is the independent variable (hours exercised).

• a is the y-intercept (blood pressure with zero hours exercised).

• b is the slope (how much the blood pressure reading changes for each additional hour exercised).

The aim of simple linear regression is to find the best values for ‘a’ and ‘b’ to make the line of best fit. This line helps us predict the dependent variable (blood pressure) based on the independent variable (hours exercised).

2. Multiple linear regression

Multiple linear regression is a direct extension of simple linear regression and is used when more than one independent variable is present. Using the same study example, consider both the number of hours exercised and the number of hours slept each night before the blood pressure reading. Now you have two independent variables, so you’re dealing with multiple linear regression.

In this case, the equation would look something like this: Y = a + b1(X1) + b2(X2). In this equation:

• Y is still the dependent variable (blood pressure).

• X1 and X2 are the independent variables (hours exercised and hours slept).

• a is the y-intercept (the blood pressure reading with no exercise or sleep hours).

• b1 and b2 are the slopes (how much the blood pressure reading changes for each additional hour exercised and each additional hour slept, respectively).

In multiple linear regression, the objective remains the same: to find the best values for ‘a’, ‘b1’, and ‘b2’ that create the best fit for the data. This allows us to predict the test score based on both hours studied and hours slept.

When building your model, you will often have to make choices on which variables to include. As you might guess, the resulting model will vary depending on which variables you include, which is why it is important to think carefully about your model. 

Examples of linear regression 

Linear regression has applications in almost every field. Some ways you might see linear regression in different industries include:

• Politics: The relationship between state spending and public support

• Business: The relationship between revenue and employee pay

• Environment: The relationship between carbon emissions and taxes

• Sociology: The relationship between professional pay and applicant qualifications

• Psychology: The relationship between culture and inclusive behaviors

• Health: The relationship between patient demographics and body weight

• Education: The relationship between academic grades and geographic location

How to perform linear regression

You can perform linear regression by hand or with the help of statistical software. In general, linear regression is most effectively performed with the help of computer software. This software can perform both simple and multiple linear regression and produce different models with different variable combinations. Some software and programming languages you might consider using for linear regression include R, scikit-learn, MATLAB, Python, Stata, and Excel.

Pros and cons of linear regression

When you choose to use linear regression, being aware of the advantages and disadvantages of this method may help you determine when it is appropriate to use and interpret your findings more accurately. Linear regression is a powerful statistical tool, and you may find several advantages to using this method. 

Advantages

Some advantages you might find include the following:

• Ease of use: Linear regression is generally considered to be a straightforward and manageable algorithm that can be used on many types of computational systems.

• Simplicity and efficiency: The underlying linear regression technique is relatively simple to understand compared to other machine-learning techniques

• Modeling linear relationships: Linear regression can effectively model datasets that are linearly separable, which makes it useful when determining relationships between variables.

• Making informed insights: With linear regression, you can use your data to explore the relationships between different variables and make predictions based on different values. This helps to inform decision-making, such as optimizing a marketing strategy or allocating the right volume of resources for a project.

Limitations

While powerful when used correctly, linear regression is not appropriate for every use case. By being aware of limitations, you can more effectively decide when this is the right algorithm for you to use. Some of the limitations you might encounter include:

• Causation vs. correlation: Regression analysis only shows correlation, not causation. Just because two things seem to move together doesn't mean one is directly affecting the other. There might be other hidden factors at play, or it could be a coincidence. It’s always important to use other forms of research and critical thinking to back up your findings from regression analysis.

• Risk of underfitting: Linear regression might lead to underfitting, which is when the machine learning model fails to represent the data accurately.

• Restricted to linear relationships: When measuring the relationship between naturally occurring variables, the underlying shape may be nonlinear Since linear regression assumes a linear relationship between input and output variables, this type of analysis would fail to fit complex datasets accurately.

• Sensitivity to outliers: Outliers, or extreme values, can significantly impact linear regression by pulling the line of best fit toward them. This may lead to models that don’t represent the data well.

What careers use linear regression? 

Linear regression is a very common type of statistical technique, which makes it a popular tool in many professions making insights from their data. Some careers that use linear regression include:

• Sports analysts: Sports analysts can use linear regression to predict how certain players or teams will perform based on previous seasons.

• Marketing analysts: Marketing teams can look at how previous products or campaigns performed to make predictions about future ones.

• Financial analysts: Financial analysts can forecast how stocks or investments will perform based on a wide variety of factors.

• Environmentalists: Environmentalists can predict pollution, emissions, and other environmental data based on previous years’ environmental data.

Next steps with Coursera

Linear regression, including single and multiple linear regression, is a common statistical analysis method in which you predict how one variable is likely to respond to changes in your other variables. Professionals use this tool in a wide range of fields, such as politics, finance, health care, and marketing. 

You can continue exploring linear regression and statistical analysis with several course offerings on Coursera. As a beginner, you can start with Linear Regression and Modeling by Duke University before taking more advanced courses such as Regression Analysis: Simplify Complex Data Relationships by Google.