What is Regression Analysis? Definition, Types, and Examples

If you want to find data trends or predict sales based on certain variables, then regression analysis is the way to go.

In this article, we will learn about regression analysis, types of regression analysis, business applications, and its use cases. Feel free to jump to a section that’s relevant to you.

• What is the definition of regression analysis?
• Regression analysis: FAQs
• Why is regression analysis important?
• Types of regression analysis and when to use them
• How is regression analysis used by businesses
• Use cases of regression analysis

What is Regression Analysis?

Need a quick regression definition? In simple terms, regression analysis identifies the variables that have an impact on another variable.

The regression model is primarily used in finance, investing, and other areas to determine the strength and character of the relationship between one dependent variable and a series of other variables.

Regression Analysis: FAQs

Let us look at some of the most commonly asked questions about regression analysis before we head deep into understanding everything about the regression method.

1. What is multiple regression analysis meaning?

Multiple regression analysis is a statistical method that is used to predict the value of a dependent variable based on the values of two or more independent variables.

2. In regression analysis, what is the predictor variable called?

The predictor variable is the name given to an independent variable that we use in regression analysis.

The predictor variable provides information about an associated dependent variable regarding a certain outcome. At their core, predictor variables are those that are linked with particular outcomes.

3. What is a residual plot in a regression analysis?

A residual plot is a graph that shows the residuals on the vertical axis and the independent variable on the horizontal axis.

Moreover, the residual plot is a representation of how close each data point is (vertically) from the graph of the prediction equation of the regression model. If the data point is above or below the graph of the prediction equation of the model, then it is supposed to fit the data.

4. What is linear regression analysis?

Linear regression analysis is used to predict the value of a variable based on the value of another variable. The variable that you want to predict is referred to as the dependent variable. The variable that you are using to predict the other value is called the independent variable.

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Why is Regression Analysis Important?

There are many business applications of regression analysis.

• For any machine learning problem which involves continuous numbers, regression analysis is essential. Some of those instances could be:

1. Testing automobiles
2. Weather analysis, and prediction
3. Sales and promotions forecasting
4. Financial forecasting
5. Time series forecasting

• Regression analysis data also helps you understand whether the relationship between two different variables can give way to potential business opportunities.
• For example, if you change one variable (say delivery speed), regression analysis will tell you the kind of effect that it has on other variables (such as customer satisfaction, small value orders, etc).
• One of the best ways to solve regression issues in machine learning using a data model is through regression analysis. Plotting points on a chart, and running the best fit line, helps predict the possibility of errors.
• The insights from these patterns help businesses to see the kind of difference that it makes to their bottom line.

5 Types of Regression Analysis and When to Use Them

1. Linear Regression Analysis

• This type of regression analysis is one of the most basic types of regression and is used extensively in machine learning.
• Linear regression has a predictor variable and a dependent variable which is related to each linearly.
• Moreover, linear regression is used in cases where the relationship between the variables is related in a linear fashion.

Let’s say you are looking to measure the impact of email marketing on your sales. The linear analysis can be wrong as there will be aberrations. So, you should not use big data sets (big data services) for linear regression.

2. Logistic Regression Analysis

• If your dependent variable has discrete values, that is, if they can have only one or two values, then logistic regression SPSS is the way to go.
• The two values could be either 0 or 1, black or white, true or false, proceed or not proceed, and so on.
• To show the relationship between the target and independent variables, logistic regression uses a sigmoid curve.

This type of regression is best used when there are large data sets that have a chance of equal occurrence of values in target variables. There should not be a huge correlation between the independent variables in the dataset.

3. Lasso Regression Analysis

• Lasso regression is a regularization technique that reduces the model’s complexity.
• How does it do that? By limiting the absolute size of the regression coefficient.
• When doing so, the coefficient value becomes closer to zero. This does not happen with ridge regression.

Lass regression is advantageous as it uses feature selection – where it lets you select a set of features from the database to build your model. Since it uses only the required features, lasso regression manages to avoid overfitting.

4. Ridge Regression Analysis

• If there is a high correlation between independent variables, ridge regression is the recommended tool.
• It is also a regularization technique that reduces the complexity of the model.

Ridge regression manages to make the model less prone to overfitting by introducing a small amount of bias known as the ridge regression penalty, with the help of a bias matrix.

5. Polynomial Regression Analysis

• Polynomial regression models a non-linear dataset with the help of a linear model.
• Its working is similar to that of multiple linear regression. But it uses a non-linear curve and is mainly employed when data points are available in a non-linear fashion.
• It transforms the data points into polynomial features of a given degree and manages to model them in the form of a linear model.

Polynomial regression involves fitting the data points using a polynomial line. Since this model is susceptible to overfitting, businesses are advised to analyze the curve during the end so that they get accurate results.

While there are many more regression analysis techniques, these are the most popular ones.

How is regression analysis used by businesses?

Regression stats help businesses understand what their data points represent and how to use them with the help of business analytics techniques.

Using this regression model, you will understand how the typical value of the dependent variable changes based on how the other independent variables are held fixed.

Data professionals use this incredibly powerful statistical tool to remove unwanted variables and select the ones that are more important for the business.

Here are some uses of regression analysis:

1. Business Optimization

• The whole objective of regression analysis is to make use of the collected data and turn it into actionable insights.
• With the help of regression analysis, there won’t be any guesswork or hunches based on which decisions need to be made.
• Data-driven decision-making improves the output that the organization provides.
• Also, regression charts help organizations experiment with inputs that might not have been earlier thought of, but now that it is backed with data, the chances of success are also incredibly high.
• When there is a lot of data available, the accuracy of the insights will also be high.

2. Predictive Analytics

• For businesses that want to stay ahead of the competition, they need to be able to predict future trends. Organizations use regression analysis to understand what the future holds for them.
• To forecast trends, the data analysts predict how the dependent variables change based on the specific values given to them.
• You can use multivariate linear regression for tasks such as charting growth plans, forecasting sales volumes, predicting inventory required, and so on.
• To make good predictions, the procedure for regression is mentioned below:
  • Find out more about the area so that you can gather data from different sources
  • Collect the data required for the relevant variables
  • Specify and measure your regression model
  • If you have a model which fits the data, then use it to come up with predictions

3. Decision-making

• For businesses to run effectively, they need to make better decisions and be aware of how each of their decisions will affect them. If they do not understand the consequences of their decisions, it can be difficult for their smooth functioning.
• Businesses need to collect information about each of their departments – sales, operations, marketing, finance, HR, expenditures, budgetary allocation, and so on. Using relevant parameters and analyzing them helps businesses improve their outcomes.
• Regression analysis helps businesses understand their data and gain insights into their operations. Business analysts use regression analysis extensively to make strategic business decisions.

4. Understanding failures

• One of the most important things that most businesses miss doing is not reflecting on their failures.
• Without contemplating why they met with failure for a marketing campaign or why their churn rate increased in the last two years, they will never find ways to make it right.
• Regression analysis provides quantitative support to enable this kind decision-making.

5. Predicting Success

• You can use regression analysis to predict the probability of success of an organization in various aspects.
• Additionally, regression in stats analyses the data point of various sales data, including current sales data, to understand and predict the success rate in the future.

6. Risk Analysis

• When analyzing data, data analysts, sometimes, make the mistake of considering correlation and causation as the same. However, businesses should know that correlation is not causation.
• Financial organizations use regression data to assess their risk and guide them to make sound business decisions.

7. Provides New Insights

• Looking at a huge set of data will help you get new insights. But data, without analysis, is meaningless.
• With the help of regression analysis, you can find the relationship between a variety of variables to uncover patterns.
• For example, regression models might indicate that there are more returns from a particular seller. So the eCommerce company can get in touch with the seller to understand how they send their products.

Each of these issues has different solutions to them. Without regression analysis, it might have been difficult to understand exactly what was the issue in the first place.

8. Analyze marketing effectiveness

• When the company wants to know if the funds they have invested in marketing campaigns for a particular brand will give them enough ROI, then regression analysis is the way to go.
• It is possible to check the isolated impact of each of the campaigns by controlling the factors that will have an impact on the sales.
• Businesses invest in a number of marketing channels – email marketing, paid ads, Instagram influencers, etc. Regression statistics is capable of capturing the isolated ROI as well as the combined ROI of each of these companies.

7 Use Cases of Regression Analysis

1. Credit Card

• Credit card companies use regression analysis to understand various user factors such as the consumer’s future behavior, prediction of credit balance, risk of customer’s credit default, etc.
• All of these data points help the company implement specific EMI options based on the results.
• This will help credit card companies take note of the risky customers.

2. Finance

• Simple linear regression (also called Ordinary Least Squares (OLS)) gives an overall rationale for the placing of the line of the best fit among the data points.
• One of the most common applications using the statistical model is the Capital Asset Pricing Model (CAPM) which describes the relationship between the returns and risks of investing in a security.

3. Pharmaceuticals

• Pharmaceutical companies use the process to analyze the quantitative stability data to estimate the shelf life of a product. This is because it finds the nature of the relationship between an attribute and time.
• Medical researchers use regression analysis to understand if changes in drug dosage will have an impact on the blood pressure of patients. Pharma companies leveraging best engagement platforms of HCP to increase brand awareness in the virtual space.

For example, researchers will administer different dosages of a certain drug to patients and observe changes in their blood pressure. They will fit a simple regression model where they use dosage as the predictor variable and blood pressure as the response variable.

4. Text Editing

• Logistic regression is a popular choice in a number of natural language processing (NLP) tasks such as text preprocessing.
• After this, you can use logistic regression to make claims about the text fragment.
• Email sorting, toxic speech detection, topic classification for questions, etc, are some of the areas where logistic regression shows great results.

5. Hospitality

• You can use regression analysis to predict the intention of users and recognize them. For example, like where do the customers want to go? What they are planning to do?
• It can even predict if the customer hasn’t typed anything in the search bar, based on how they started.
• It is not possible to build such a huge and complex system from scratch. There are already several machine learning algorithms that have accumulated data and have simple models that make such predictions possible.

6. Professional sports

• Data scientists working with professional sports teams use regression analysis to understand the effect that training regiments will have on the performance of players.
• They will find out how different types of exercises, like weightlifting sessions or Zumba sessions, affect the number of points that player scores for their team (let’s say basketball).
• Using Zumba and weightlifting as the predictor variables, and the total points scored as the response variable, they will fit the regression model.

Depending on the final values, the analysts will recommend that a player participates in more or less weightlifting or Zumba sessions to maximize their performance.

7. Agriculture

• Agricultural scientists use regression analysis to understand the effect of different fertilizers and how it affects the yield of the crops.
• For example, the analysts might use different types of fertilizers and water on fields to understand if there is an impact on the crop’s yield.
• Based on the final results, the agriculture analysts will change the number of fertilizers and water to maximize the crop output.

Wrapping Up

Using regression analysis helps you separate the effects that involve complicated research questions. It will allow you to make informed decisions, guide you with resource allocation, and increase your bottom line by a huge margin if you use the statistical method effectively.

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