Understanding What is Regression Analysis in Statistics?

So, what is regression analysis, and why is it useful? While many are familiar with the term regression analysis, understanding it fully requires exploring how it reveals relationships within data. We explain what you need to know about this popular method of analysis. If you’re moving your business decisions or making predictions about the market based on data, you can’t just hoover up data and think you can make decisions or anticipate what might happen based on what you’ve found.

However, the challenge is that so many variables can influence business data: even the weather, market conditions, and economic disruption! Thus, you must understand the variables affecting your data and forecasts and which data you can throw away. One of the best ways of finding data value and monitoring running trends—including relations among the variables—is through regression analysis, a set of statistical methods for estimating the relationship between dependent and independent variables.

In this guide, we’ll cover the basics of regression analysis, including what it is, how it works, its benefits, and even practical applications.

Also Read: Linear Regression in Machine Learning

Understanding the Basics of Regression Analysis

Regression analysis is a simple statistical method of understanding and describing how changing one or more variables will influence another variable. It allows a business to calculate one dependent variable from the values of one or more independent variables.

In particular, regression analysis is used to figure out…how much a change in one variable relates to another. This is similar to uncovering a mathematical formula that fits the data perfectly and allows one to make a prediction or understand the effect of any given factor on an outcome.

Moreover, regression analysis answers questions such as ‘How does one variable influence the other?’ or ‘Is one variable predictable from other variables’. The most important stages of regression analysis are – Data Collection, Data Preprocessing and Regression Model selection.

However, regression analysis is not limited only to one independent variable. A more complex analysis known as multiple regression allows us to have multiple independent variables. Thus, this can be used in real-world scenarios where multiple factors impact the outcome.

Also Read: Regression Testing – Meaning, Types and Tools

Simple Linear Regression

This method models the relationship between two variables: Most simply, one predictor and one outcome, one independent (predictor) and one dependent (outcome). For instance, it is capable of predicting sales by advertising spend. Simple linear regression can predict the prospective increase in sales if a company’s advertising budget is increased.

Multiple Linear Regression

This model is an extension of simple linear regression, in which we use multiple independent variables to predict a dependent variable. For example, predicting home prices could include square footage, number of bedrooms, or neighbourhood. Multiple linear regression lets you determine how each factor contributes to the final price.

Logistic Regression

In logistic regression, the goal is to calculate the probability of a result when the dependent variable has just two possible outcomes. This is a common example where we want to predict customer opinion—will a customer leave a service or not? Logistic regression can also predict the probability that a loan applicant will default.

Polynomial Regression

The method models a relationship between variables when the relationship isn’t a simple straight line but more the characteristics of a curve. For instance, forecasting plant growth in time as seasons change with temperature and humidity. Polynomial regression removes the assumption that they have a linear relationship.

Non-linear Regression

Simple regression, such as non-linear regression, is used when the real relation between variables is unrelated to the straight line. In the case of a business, and for instance, predicting customer satisfaction, there are many factors interacting ({product quality}, {customer service}, …, {delivery time}) in non-linear ways on the outcome.

Linear Regression in Multivariate Format

Multivariate analysis extends multiple linear regression that takes multiple dependent variables and correlates several independent variables. For example, a company may analyse different marketing methods and their impacts on sales, customer engagement, and brand awareness in different regions. This allows the business to understand how each strategy impacts these outcomes in these various contexts.

How is Regression Analysis Used?

For this, regression analysis is very useful for finding meaningful relations between different variables so businesses can make data-based decisions. For example, by analysing the correlation between GDP, consumer confidence, or industry trends, companies can determine whether or not it is time to invest, reshuffle their strategies, or forecast future results.

How Regression Analysis Works

To understand these relationships, here’s a simple breakdown of how regression analysis is conducted:

• Data Collection: Collect data on the dependent variable and one or multiple independent variables that might affect it, in this case, sales and advertisement dollars.

• Choosing a Model: Having understood your data, choose the right regression model. They identified simple linear regression, for example, as suitable for determining the relationship of two variables with a straight line.

• Finding the Best-Fit Line: Regression analysis provides the method for finding out the line that is the most appropriate for such data. In simple linear regression, this line follows the formula:

Y = mX + b

Here:

• Y is the variable under study; in other words, it is the variable to be explained and labelled as a dependent variable, for example, sales.
• X stands for the predictor or, in some cases, often referred to as the independent variable (m = media ad spend).
• m or slope is the coefficient of X, and we can better understand how much Y changes for each movement in X.
• b is the intercept, which is the value of Y when all values of Xi = 0.

• Making Predictions: With the equation, you can plug in values of X to predict Y.

Example in Practice

Suppose you have realised that while $1,000 is spent on advertising, $5,000 is received in sales. If:

• m=5 (Because, going by the information given on the spreadsheet, if sales increase by $5,000 for every $1,000 spent).
• b = 10. The company must achieve a benchmark of $10,000 even without placing a single advertisement.

The equation becomes:

Y = 5X + 10

If the business spends $3,000 on ads, substitute X = 3 into the formula:

Y = 5(3) + 10

Y = 15 + 10

Y = 25

Therefore, for $3,000 spent on the ads, the projected sales would be $25,000.

This lets businesses determine which factors affect them and then change accordingly rather than guessing decisions based on trial and error.

Also Read: Difference Between Correlation and Regression

Benefits of Regression Analysis

Regression analysis offers numerous advantages, making it a widely used tool in various fields:

• Ability to forecast future trends: Regression gives accurate forecasts by analysing historical data and correlational variables with each other. Using regression models, for example, businesses can predict future sales depending on factors like advertising spend or market trends.
• Simplicity: Although incorporating complex data is quite possible, regression analysis is based on simple concepts that are easy to apply. This is very accessible for the true beginner and someone with more experience. Intuition is one of the basic premises that one predicts to get an output based on input parameters.
• Model Interpretation: Regression models can provide many insights into the relationship between variables. Businesses can interpret the coefficients and overall fit to see what factors most strongly correlate with decision-making and strategy development outcomes.
• Efficiency in Data Use: With regression, we maximise the use of available data by finding relationships within it, thus decreasing the amount of data required for collecting massive amounts of extra data. This helps businesses make informed decisions with what they already have data.

Limitations of Regression Analysis

While regression is a powerful tool, it has certain limitations that need careful consideration:

• Assumptions: Several key assumptions are built on regression analysis linearity (the relationship function variable is a straight line), the independence of errors, and the normality of the error distribution. If these assumptions are violated, the results may be unreliable. For example, predicting using linear regression for no longer linear data would result in incorrect predictions.
• Outliers: Excessive values, called outliers, are major factors affecting regression analysis results. Outliers can lure the regression line into a misleading slope. Outliers must be identified and handled with robust regression methods that minimise or remove their effect.
• Overfitting: A regression model with too many variables is said to be overfitting. While it may be good for the training data, it is naive when applied to new, unseen data. However, this decreases the predictive accuracy of the model in real-world conditions. In general, we want to keep the model simple or those models simple, plus use regularisation to control how complex the model gets.
• Limited by Available Data: The quality and quantity of available data are very important to the effectiveness of regression analysis. If the data is incomplete, biased, or insufficient, the results will be skewed, and the model will not achieve accurate prediction.

Conclusion

In conclusion, regression analysis is a good statistical idea for understanding and forecasting the relationship between variables. When we study how one variable affects another, we can make informed decisions and predictions in fields as varied as business, healthcare, and economics. Simple linear regression and speech or ridge regression give us valuable life insight. Though crude and with its limitations, regression is one of the most important tools we have for analysing and understanding data. To learn professionally about this topic, you should join the Accelerator Program in Business Analytics and Data Science powered by Hero Vired in collaboration with edX and Harvard University.