What is the Difference Between Correlation and Regression?

Introduction

Statistical analysis is used as a powerful tool in the marketing industry. It helps companies determine the price and sales of a product. Correlation and regression are the most vital statistical analysis techniques that define the qualitative and quantitative relationship between two or more variables. This post will describe in detail the concepts of correlation and regression and the differences between the two.

What is Correlation?

The term correlation comprises two parts — co, which means to be together, and relation, which explains the connection between two variables. It measures the degree of association between two variables when one variable changes. 

A classic example of correlation can be seen between demand and price. As the price of a product goes up, its demand decreases. Similarly, if the price of a product goes down, its demand increases. This inverse relationship is called a negative correlation.

The degree of relationship between two or more variables is tested through correlation analysis. It helps us figure out the presence or absence of a connection between the variables. In case the variables are related, we can find the degree of the association through correlation analysis. Correlation helps a great deal during market research. It helps us predict the performance of a campaign and the sale of a product or service based on factors such as consumer behavior, culture, weather, and advertisements.

Correlation is divided into various categories. There are primarily two types of correlation: positive and negative. If a variable moves in the same direction as the other changed variable, it is termed positive correlation. Similarly, if the other variable moves in the opposite direction to the variable that has changed, it is called a negative correlation.

The other types of correlations are simple, partial and multiple. When correlation determines the degree of relationship between two variables, it is called simple correlation. For instance, the relationship between the marks of a student and the classes attended during a session will be treated as a simple correlation. In partial correlation, the relationship between three or four variables is considered. However, two of those variables are kept constant, and the effect of the other two is considered.

If we take the above example, the marks of a student are associated with attendance and the method of teaching. The other two variables, such as using technology for teaching students and real-world learning, are constant. Last is the multiple correlations that determine the relationship between three or more variables. The difference between partial and multiple correlations is that partial correlation determines the relationship only between two variables, and the remaining variables are treated as constants. On the other hand, various correlations help find the degree and direction of a relationship between three or four variables simultaneously.

The last category is a linear and non-linear correlation. They can be described as the ratio of change between two variables. In a linear correlation, there is a direct relationship between two variables. For example, there is a direct relation between raw material available and finished goods produced. If the raw material is 5kg, the production of finished goods is 1kg.

Similarly, if the raw material available is 10kg, the production of finished goods will be 2kg, and so on. In non-linear correlation, there is no constant ratio between two variables. For instance, if variable A changes x times in an environment, variable B will change 2x times in a different environment. Again, if variable A changes x times, B will change 5x times.

There are two methods of finding out the correlation between two or more variables. First is the graphic method that uses scatter diagrams and graphs to determine the correlation. In a scatter diagram, the variables are mentioned on the X and Y axis of a graph, and the values are plotted on the graph as dots. If the dots move upward in a straight line, there is a perfect positive correlation. However, if the points move downward in a straight line, there is a perfect negative correlation.

The other method of determining the correlation between variables is the algebraic method that uses correlation coefficients.

What is Regression?

While correlation determines whether there is a relationship between two variables, regression tells us about the effect two variables have on each other. It tells us how one variable is dependent on another independent variable. In regression, there are two variables: one independent and one dependent. The independent variable acts as a base or standard for predicting another variable called the dependent variable.

For instance, the amount of rainfall in a particular year affects the growth of crops in the country. In this case, regression will help us determine the extent to which the amount of rainfall will affect the development of crops. Here, the amount of rainfall is the independent variable whereas the growth of crops is the dependent variable. Another example of regression can be the amount of tax levied on the product and the price of that commodity. Again, the amount of tax imposed is an independent variable, and the commodity’s price is the dependent variable.

The extent of the relationship between two variables is found out through regression analysis. It is done with the help of lines and algebraic equations.

What is the Difference Between Correlation and Regression?

Primarily, correlation and regression might appear to be the same concepts. However, there are several differences between the two that have been discussed below.

• Correlation helps us determine the degree of relationship between two variables, whether or not they are related to each other. On the other hand, regression determines the extent to which two variables are related.
• While correlation is a relative measure between two or more variables, regression is an absolute measure between variables.
• We cannot treat correlation as a forecasting device. On the other hand, regression helps in predicting possible outcomes. Through regression, we can forecast the value of the dependent variable if the value of the independent variable is available.
• The coefficient of correlation is independent of both origin and scale in a graph whereas, the coefficient of regression is independent only of change of origin and not the scale.
• In correlation, the variables do not have units of measurement. However, in regression, the variables’ units of measurement have to be considered.
• The value of a correlation lies between -1 to +1. However, the value of regression should be determined using algebraic equations. The value of correlation can be zero, but regression cannot be null.
• Correlation is used at the time of explaining a direct relationship between two or more variables. On the other hand, regression is used to predict outcomes with the help of numeric responses.
• In correlation, we do not require mathematical equations whereas an algebraic equation is a must in regression.
• In correlation, you can change the values of X and Y on a graph because both variables are independent. However, in regression, X and Y values cannot be interchanged as one of them is a dependent variable.

 Why Use  Correlation and Regression in Business?

Even though correlation and regression might appear to be theoretical concepts, they are valuable for businesses. Here are some ways how correlation and regression are beneficial for businesses:

• The most crucial importance in using regression analysis is to forecast consumer response. Regression allows businesses to predict possible opportunities and potential risks in the market and helps in analyzing demand in the market and calculating possible purchases of products. This also allows companies to plan their budget and forecast revenues.
• Regression also helps in improving the efficiency of operations or services. Businesses can find out the factors that hamper productivity and efficiency.
• Since regression is based on cause and effect, it enables businesses to make informed decisions. For example, a company might consider increasing the production of particular goods, but it has limited raw materials. In this case, the company might not generate revenues if another product also requires the same raw material. Thus, the company must figure out which product they should manufacture to maximize their revenues.
• Correlation helps in market research as it allows businesses to determine whether two variables are related. This makes it easier for companies to consider only those factors that directly affect sales or revenues.

Conclusion

Correlation and regression also play a crucial role in machine learning, deep learning and AI to predict continuous values within a large dataset. If you have a keen interest in ML or deep learning and want to build a career in the same field, it will be beneficial for you to know in-depth about correlation and regression. upGrad’s Advanced Certificate Program in Machine Learning and Deep Learning will help you understand the concept of regression in-depth and its practical usage in machine learning. More than 40,000 people from more than 85 countries have enrolled in various programs at upGrad. Along with peer learning, upGrad also offers 360-degree career support to all of its students.