Difference Between Correlation and Regression (With Table)

Correlation vs Regression

The two most common terms used in the world of statistics are Correlation followed by Regression. The two terms are described as ‘Analysis’ as they are based on the dissemination of numerous variables.

This phenomenon is commonly known as multivariate distribution. They are most commonly used when the association between two quantitative variables needs to be examined. 

Interviewees are most likely to be quizzed upon the distinguishing characteristics of Correlation as well as Regression. However, many people suffer doubtfulness in understanding the two above phrases. 

The key difference between Correlation and Regression lies in the fact how they are associated with the variables and their impact on statistics.

The meaning of Correlation is the measure of association or absence between the two variables, for instance, ‘x,’ and ‘y.’ ‘x,’ and ‘y’ are not independent or dependent variables here.

Whereas, in Regression, the value of the contingent variable is calculated using the value of the independent variable.

The relationship between the two different variables initially assessed. Regression has countless instinctive applications in the day to day life. 

Here is a thorough comparison table that can successfully explain the differences between the two terms.


 

Comparison Table Between Correlation and Regression (in Tabular Form)

Parameter of ComparisonCorrelationRegression
MeaningIt determines the co-relationship, which is the association between two variables. Largely depends on statistics-based procedures. Justifies the arithmetic relation between the two, an autonomous value and a dependent one.
ObjectiveIt enables to identify the numerical value that expresses the relationship in between two or more variables. In Regression, the values of a fixed variable help us pinpoint and approximate the values of the random variable.
UsageThe linear association between two variables is shown. Mostly based on an estimation based on one variable to predict the value of the other variable. 
Independent Variable & Dependent variableBoth dependent as well as independent variables are similar to each other. Independent and dependent variables are not the same. 
IndicationIt is the measure of the degree to which the two variables change simultaneously. Regression signifies how the switch in the value of a variable (x) is determined by the variable (y).

 

What is the Correlation?

Correlation is derived from two words, namely, ‘Co’ which means together, and ‘relation,’ meaning link or a connection, which is between a couple of quantities.

It merely means the degree of change occurring in one of the variables and is reacted by a corresponding change in the other variable. This could be an explicit change or an implicit one.

It successfully depicts the degree of association between two of the variables taken into consideration, it is based on the principles of statistics. The value determined can either be a positive one or negative.

When both the variables are moving in an identical direction, it is a positive correlation, and the results are corresponding to one another, leading to investment and gain.

Contrarily, a negative correlation occurs when the variables are moving in opposite directions, this results in the decline in the other variable. For instance, the value and requirement of an item are interrelated. 

An example where correlation can be successfully implemented is when a company wishes to compare the cumulative number of sales made to the number of salespersons employed. 

Types of Correlation
Types of Correlation
 

What is Regression?

Regression is an attempt that is used to determine the relationship of one variable with the other significant variable. The two types of variables used is a dependent one and an independent one. Regression makes one step ahead of correlation as it adds the prediction capabilities. 

Regression is applied on an intuitive level by the people on a daily basis. It holds a significant place in human actions, as it is a potent tool that is used to predict the events that occurred prior to these times, in the present, and future based on the previous or current events and occurrences.

For instance, past business records can estimate its future profits. It can be explained with a simple example of how we wake up in the morning. If you go to bed early, you can wake up early in the morning with greater ease.

We can understand linear regression using two variables ‘x’ and ‘y’. Here, both the variables ‘x’ and ‘y’ depend on another, i.e., ‘y’ depends or is affected by ‘x,’ which is an independent variable.

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The mentioned factors are indicated on a statistical graph, which is a mathematical representation. 

Quantitative Regression is more accurate as it creates an arithmetic interpretation of an equation. This equation or formulae can be used for analyzing and predicting in the future. 

For instance, a doctor estimates the appropriate drug dosage (independent variable) for a patient based on their body weight, which is a dependent variable.

Types of Regression
Types of Regression

Main Differences Between Correlation and Regression

  1. Only a single piece of data or statistics is considered in Correlation. However, Regression provides a complete mathematical equation. 
  2. Correlation pinpoints the degree to which two variables are associated with each other. On the other hand, Regression reflects the impression of a unit change in the independent variable due to the changes in the dependent variable. 
  3. Correlation can give a crisp value describing the relationship between the two variables. Regression is beneficial as it thoroughly examines and further predicts values for a variable using mathematical equations.
  4. In Correlation, the variables ‘x’ and ‘y’ are arbitrary. They can weight, blood pressure, or cholesterol level. As opposed to Regression that assumes ‘x’ as a fixed variable with no error, such as temperature setting.
  5. The term Correlation was derived during the 16th century, from the Medieval Latin, meaning a mutual relationship or connection between two or more things.
  6. On the other side, Francis Galton coined the term Regression in the 19th century. He used it to illustrate a biological occurrence. In Particular, regression means reverting to a primitive state.

 

Frequently Asked Questions (FAQ) About Correlation and Regression

What are the types of regression? 🤔

There are mainly seven types of regressions, namely:

  1. Linear regression – nature of the regression line is linear; the independent variable is either discrete or continuous, the dependent variable is continuous
  2. Logistic regression – linear relationship between the dependent and independent variable is not required, the dependent variable’s nature is binary (0/1, Yes/No, True/False)
  3. Polynomial regression – independent variable’s power exceeds 1.
  4. Stepwise regression – is used when there are multiple independent variables, the automatic process selects independent variables without human intervention
  5. Ridge regression – is used when independent variables are highly correlated, use the shrinkage parameter to solve multicollinearity problem
  6. Lasso regression – assumptions are the same as least squared regression, shrinks coefficients to zero, improve the accuracy of linear regression models
  7. ElasticNet regression – a hybrid of techniques of lasso and ridge regression, no limitation on selected variables’ numbers

What are the different types of correlation?

There are mainly six types of correlations, namely:

  1. Positive correlation – an increase in variable increases the value of other
  2. Negative correlation – an increase in a variable decreases the value of other
  3. No correlation – linear dependency does not exist between two variables
  4. Perfect correlation – functional dependency exists between two variables
  5. Strong correlation – points are located close to one another in the line
  6. Weak correlation – points are located far from each other in the line

Why is the regression used? 🚀

The main use of regression is to observe a dependent variable’s relationship with an independent one. Statistics of regression can be used to determine the value of a dependent variable when the independent variable’s value is already known.

Can you use correlation to predict? 📈

Yes, correlation can be used to predict a variable’s value, given we already of the value of another variable.

How do you interpret the correlation coefficient?

The interpretation of the correlation coefficient can be made by observing which of the below-given value is closer to the value correlation coefficient:

Negative linear relationship

  1. -1 = perfect downhill.
  2. -0.70 = strong downhill.
  3. -0.50 = moderate downhill.
  4. -0.30 = weak downhill.

No relationship
0 = no linear relationship.

Positive linear relationship

  1. +0.30 = weak uphill.
  2. +0.50 = moderate uphill.
  3. +0.70 = strong uphill.
  4. +1 = perfect uphill.

 

Infographic

Correlation vs Regression

 

Learn More With the Help of Video


 

Conclusion

It is obvious that the Correlation analysis and the Regression analysis have a major difference between each other, although these couple of mathematical concepts are calculated together.

Whilst in a Regression analysis, the researcher tries to identify the functional relationship between the two variables established to make future benefits and profits.


 

Word Cloud for Difference Between Correlation and Regression

The following is a collection of the most used terms in this article on Correlation and Regression. This should help in recalling related terms as used in this article at a later stage for you.

Correlation and Regression 1
Word Cloud for Correlation and Regression

 

References

  1. https://psycnet.apa.org/record/1960-06763-000
  2. https://link.springer.com/content/pdf/10.3758/BRM.41.4.1149.pdf
  3. https://psycnet.apa.org/record/1995-97110-002

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