What Is Regression Analysis? Its Role in Data-Driven Decision Making

In cloud environments, regression is among the most common examples of data analytics and is frequently used in finance and investment. What is regression? It is an analysis designed to interpret the relationship between a dependent variable and one or more independent variables. How is it analyzed, what are its types, and what role does it play in data-driven decision-making processes? We break down all the details in this article. Continue reading to find out exactly what regression analysis is—and what it is not.

As briefly mentioned above, regression is a method used to understand how changes in a set of independent variables are related to a dependent variable. Regression analysis includes a wide range of approaches, including linear, nonlinear, and regularized models. Linear regression, which is less complex than others, is commonly preferred. When it assumes a linear relationship between two variables, it is called simple linear regression. Interpreting regression analysis results is much more practical in linear models compared to nonlinear ones.

Types of Regression

• Linear Regression: The most basic form of regression, which models the relationship between a dependent variable and one or more independent variables as a straight line. For example, it answers the question: “How does a home’s price change as its square footage increases?”
• Stepwise Regression: A variable selection method in which variables are added or removed step by step based on statistical criteria. The goal is to eliminate unnecessary variables and find the best explanatory model.
• Polynomial Regression: When data exhibits a curved rather than a linear relationship, polynomial terms (such as x² or x³) are added to model that relationship. For example, the relationship between age and income often follows a curved pattern.
• Logistic Regression: Used when the dependent variable is categorical (e.g., “yes-no”, “diseased-healthy”). It estimates the probability of an event occurring.
• Ridge Regression: An enhanced version of linear regression used when there is high correlation among variables—known as multicollinearity. It reduces coefficient values to prevent overfitting.
• Lasso Regression: Similar to ridge regression, but it can shrink some coefficients to zero, effectively performing variable selection.
• Elastic Net Regression: A combination of ridge and lasso regression. It shrinks coefficients and can eliminate some entirely, balancing flexibility and model accuracy.
• Ordinal Logistic Regression: Used when the dependent variable consists of naturally ordered categories. It works with categorical variables that follow a logical sequence.

Like any analysis, regression analysis follows certain basic steps. Here is the detailed answer to the question how to conduct regression analysis!

• Hypothesis Formulation: To begin, you must identify your dependent variable and at least one independent variable. Gather as much data as possible regarding these variables. For instance, if you are examining the relationship between advertising and sales, considering at least one year of financial data will allow you to run a more accurate analysis.
• Visualization: Once you have two data sets, it is time to visualize the data. You can plot your information on a chart—placing one variable on the X-axis and the other on the Y-axis. In a spreadsheet, it becomes much easier to observe relationships between variables, including whether the linear correlation is positive or negative.
• Interpreting the Results: By examining the chart within the scope of linear regression, you can clearly identify the intersection, the coefficient, and the relationship structure between the variables. These figures reveal the historical relationship between variables while also enabling future predictions.

You can also find the linear regression analysis formula below. In the formula, “β” represents parameter estimates, while “ϵ” refers to error terms.

Y=β0+∑ βiXi+ϵi

Simple Regression Equation

In the simple regression formula, “Y” represents the dependent variable, “X” the independent variable, “a” the intercept, “b” the slope, and “u” the residual value representing the difference between predicted and observed values.

Y = a+bX+u

Multiple Regression Equation

In the multiple regression formula, “Y” is the dependent variable, “X1, X2, X3, X4” are the independent variables, “a” is the intercept, “b, c, d” are slopes, and “u” is the residual.

Y = a+bX1+cX2+dX3+eX4+…….+tXt+u

What Is Multiple Regression Analysis?

So, what is multiple regression analysis? Multiple linear regression is a method that measures the impact of multiple independent variables on a dependent variable. For example, multiple linear regression may be highly suitable to measure how a person’s weight, age, and stress level affect their blood pressure. Here, the number of independent variables must be more than one, the relationships must be assumed linear, multicollinearity must be low, and the Durbin-Watson statistic should be around 2.

For businesses, the question "Why conduct regression analysis?" is crucial for understanding all patterns in the data, correcting flawed assumptions, and improving processes. By selecting a model aligned with your business, you can better identify emerging patterns, gain quantitative insights, and optimize workflows.

• Understanding patterns within data
• Correcting flawed assumptions
• Improving processes
• Identifying emerging data patterns more effectively
• Providing quantitative support by observing various factors
• Optimizing business operations

So, how do you determine the right type of regression model for your business? Follow the steps below to make choosing between regression models easier.

• First, define the purpose of the analysis. Clarify whether the goal is prediction, relationship analysis, or classification. This directly affects the type of regression model to be used.
• Next, examine the type of dependent variable. If the dependent variable is continuous (such as income or sales volume), linear or polynomial models are suitable. If it is categorical, logistic or ordinal regression should be preferred.
• Analyze the structure of your data to guide your decision. If the relationship appears linear, a simple model is sufficient; however, if it is curved or complex, more advanced approaches like polynomial or elastic net regression may be required.
• Consider the relationships between variables. If independent variables are highly correlated, you should utilize regularization methods such as ridge or lasso regression.
• Then, evaluate the size of your dataset. Smaller datasets benefit from simpler models, while larger datasets can support more complex techniques.
• Do not forget to assess model performance. Compare model metrics using regression-appropriate criteria such as MSE, RMSE, MAE, and R-squared (R²).
• Avoid overfitting. Ensure the model generalizes well to new data rather than fitting only the current dataset.

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What is regression analysis used for?

It is used to understand the relationship between variables and measure the impact of one variable on others.

When should regression analysis be performed?

It is performed when you want to determine whether a relationship exists between variables or when you want to predict future values.

Where is regression analysis used?

It is widely used in finance, marketing, economics, engineering, healthcare, and social sciences.

How are regression analysis results interpreted?

The direction and magnitude of coefficients indicate the strength and direction of the relationship between variables and are supported by statistical significance tests.

What does R-squared (R²) represent in regression analysis?

It indicates how well the independent variables explain the dependent variable. The closer it is to 1, the stronger the model’s explanatory power.

Which software is used for regression analysis?

It can be performed using statistical software such as Excel, SPSS, R, Python, SAS, and Minitab. For more details, feel free to contact us.