Understanding regression analysis: overview and key uses

Regression analysis is a fundamental statistical method that helps us predict and understand how different factors (aka independent variables) influence a specific outcome (aka dependent variable). 

Imagine you're trying to predict the value of a house. Regression analysis can help you create a formula to estimate the house's value by looking at variables like the home's size and the neighborhood's average income. This method is crucial because it allows us to predict and analyze trends based on data. 

While that example is straightforward, the technique can be applied to more complex situations, offering valuable insights into fields such as economics, healthcare, marketing, and more.

Businesses can use regression analysis to improve nearly every aspect of their operations. When 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 can give businesses significant advantages. No method can guarantee absolute certainty, but regression analysis offers a reliable framework for forecasting future trends based on past data. Companies can apply this method to anticipate future sales for financial planning purposes and predict inventory requirements for more efficient space and cost management. Similarly, an insurance company can employ regression analysis to predict the likelihood of claims for more accurate underwriting. 

2. Identifying inefficiencies and opportunities

Regression analysis can help us understand how the relationships between different business processes affect outcomes. Its ability to model complex relationships means that regression analysis can accurately highlight variables that lead to inefficiencies, which intuition alone may not do. Regression analysis allows businesses to improve performance significantly 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 of these issues.

3. Making data-driven decisions

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

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

• Simple linear regression analysis is the simplest form of regression analysis. 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 is suitable for multiple dependent variables. It allows the analysis of how independent variables influence multiple outcomes.

• Logistic regression is relevant when the dependent variable is categorical, such as binary outcomes (e.g., true/false or yes/no). Logistic regression estimates the probability of a category based on the independent variables.

Ignoring key variables is a common mistake when working with regression analysis. Here are a few more pitfalls to try and avoid:

1. Overfitting the model

If a model is too complex, it can become overly powerful and lead to a problem known as overfitting. This mistake is an especially significant problem when the independent variables don't impact the dependent data, though it can happen whenever the model over-adjusts to fit all the variables. In such cases, the model starts memorizing noise rather than meaningful data. When this happens, the model’s results will fit the training data perfectly but fail to generalize to new, unseen data, rendering the model ineffective for prediction or inference.  

2. Underfitting the model

A less complex model is unlikely to draw false conclusions mistakenly. However, if the model is too simplistic, it will face the opposite problem: underfitting. In this case, the model will fail to capture the underlying patterns in the data, meaning it won't perform well on either the training or new, unseen data. This lack of complexity prevents the model from making accurate predictions or drawing meaningful inferences. 

3. Neglecting model validation

Model validation is how you can be sure that a model isn't overfitting or underfitting. Imagine teaching a child to read. If you always read the same book to the child, they might memorize it and recite it perfectly, making it seem like they’ve learned to read. However, if you give them a new book, they might struggle and be unable to read it.

This scenario is similar to a model that performs well on its training data but fails with new data. Model validation involves testing the model with data it hasn’t seen before. If the model performs well on this new data, it indicates having truly learned to generalize. On the other hand, if the model only performs well on the training data and poorly on new data, it has overfitted to the training data, much like the child who can only recite the memorized book.

4. Multicollinearity

Regression analysis works best when the independent variables are genuinely independent. However, sometimes, two or more variables are highly correlated. This multicollinearity can make 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 using a principal component analysis (PCA) technique, which transforms the correlated variables into a set of uncorrelated components.

5. Misinterpreting coefficients

Errors are not always due to the model itself; human error is common. These mistakes often involve misinterpreting the results. For example, someone might misunderstand the units of measure and draw incorrect conclusions. Another frequent issue in scientific analysis 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. When low-quality data is input into a model, it analyzes noise rather than meaningful patterns. Poor data quality can manifest as missing values, unrepresentative data, outliers, and measurement errors. Additionally, the model may have excluded essential variables significantly impacting the results. All these issues can distort the relationships between variables and lead to misleading results. 

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

• The relationship between variables is linear.

• There must be homoscedasticity, meaning the variance of the variables and the error term must remain constant.

• All explanatory variables are independent of one another.

• All variables are normally distributed.

Let's turn our attention to examining how a few industries use the 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 tells you the risk factors for that condition. The condition is the dependent variable, and the risk factors are the independent variables. By plugging the risk factors for a patient into a regression analysis, healthcare providers can determine that person's estimated risk for developing the condition. 

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

Finance

Predicting stock prices, economic trends, and financial risks benefits the finance industry. Regression analysis can help finance professionals make informed decisions about these topics. 

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

The banking industry also uses regression analysis. When a loan underwriter determines whether to grant a loan, regression analysis allows them to calculate the probability that a potential lender will repay the loan.

Marketing

Imagine how much more effective a company's marketing efforts could be if they could predict customer behavior. Regression analysis allows them to do so with a degree of accuracy. For example, marketers can analyze how price, advertising spend, and product features (combined) influence sales. Once they've identified key sales drivers, they can adjust their strategy to maximize revenue. They may approach this analysis in stages. 

For instance, if they determine that ad spend is the biggest driver, they can apply regression analysis to data specific to advertising efforts. Doing so allows them to improve the ROI of ads. The opposite may also be true. If ad spending has little to no impact on sales, something is wrong that regression analysis might help identify. 

Regression analysis by hand isn't practical. The process requires large numbers and complex calculations. Computers make even the most complex regression analysis possible. Even the most complicated AI algorithms can be considered fancy regression calculations. Many tools exist to help users create these regressions.

R

R is a powerful open-source programming language and software environment. The software is designed with statistical computing in mind, making it a favorite tool for regression analysis. The language has a suite of packages that assist developers with these analyses. There are packages for every type of regression analysis you can perform, making it easy to plug in numbers and get meaningful results. There are also packages to visualize data and create reports, adding to its utility. 

MATLAB

Another programming language—while MATLAB is a commercial tool, the open-source project Octave aims to implement much of the functionality. These languages are for complex mathematical operations, including regression analysis. Its tools for computation and visualization have made it very popular in academia, engineering, and industry for calculating regression and displaying the results. MATLAB integrates with other toolboxes so developers can extend its functionality and allow for application-specific solutions.

Python

Python is a more general programming language than the previous examples, but many libraries are available that extend its functionality. For regression analysis, packages like Scikit-Learn and StatsModels provide the computational tools necessary for the job. In contrast, packages like Pandas and Matplotlib can handle large amounts of data and display the results. Python is a simple-to-learn, easy-to-read programming language, which can give it a leg up over the more dedicated math and statistics languages. 

SAS

SAS (Statistical Analysis System) is a commercial software suite for advanced analytics, multivariate analysis, business intelligence, and data management. It includes a procedure called PROC REG that allows users to efficiently perform regression analysis on their data. The software is well-known for its data-handling capabilities, extensive documentation, and technical support. These factors make it a common choice for large-scale enterprise use and industries requiring rigorous statistical analysis. 

Stata

Stata is another statistical software package. It provides an integrated data analysis, management, and graphics environment. The tool includes tools for performing a range of regression analysis tasks. This tool's popularity is due to its ease of use, reproducibility, and ability to handle complex datasets intuitively. The 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 can perform basic linear regression and visualize the results. Excel is not an excellent choice for more complex regression or very large datasets. But for those with basic needs who only want to analyze smaller datasets quickly, it's a convenient option already in many tech stacks. 

SPSS

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

Regression analysis is a statistical method used to estimate and quantify the relationship between a dependent variable and one or more independent variables. It helps determine the strength and direction of these relationships, allowing predictions about the dependent variable based on the independent variables and providing insights into how each independent variable impacts the dependent variable.

Dependent variables: typically continuous (e.g., house price) or binary (e.g., yes/no outcomes).

Independent variables: can be continuous, categorical, binary, or ordinal.

Regression analysis identifies the relationships between a dependent variable and one or more independent variables. It quantifies the strength and direction of these relationships, allowing you to predict the dependent variable based on the independent variables and understand the impact of each independent variable on the dependent variable.