12 Difference Between Correlation And Regression

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What Is Correlation?

Correlation is a statistical method that is used to establish relationship between two variables/datasets and how strong that relationship may be. The measure is best used in variables that demonstrate a linear relationship between each other. The fit of the data can be visually represented in a scatterplot. Using a scatterplot, we can generally analyze and establish the relationship between the variables and determine whether they are correlated or not. Typically, correlation analysis is used for spotting patterns within datasets. A positive correlation means that both variables increase in relation to each other while a negative correlation means that as one variable decreases, the other increases.

The correlation coefficient is a value that indicates the strength of the relationship between the variables. The coefficient can take any values from -1 to 1. The interpretations of the values are:

  • -1: Perfect negative correlation. The variables tend to move in opposite direction (i.e when one variable increases, the other variable decreases).
  • 0: No correlation. The variables do not have a relationship with each other.
  • 1: Perfect positive correlation. The variables tend to move in the same direction (i.e when one variable increases, the other variable also increases).

What You Need To Know About Correlation

  • Correlation is the relationship between two or more variables, which vary with the other in the same or the opposite direction. In other words, it determines the interconnection or a co-relationship between the variables.
  • Correlation is a single statistic or data point.
  • It finds out the degree of relationship between two variables and not the cause and effect relationship.
  • Correlation between two variables can be expressed through a single point on a graph visually.
  • It has limited application because it is confined only to linear relationship between the variables.
  • The coefficient of correlation is a relative measure. The range of relationship lies between -1 and +1.
  • In correlation, both variables x and y are random variables.
  • In correlation, both the independent and dependent values have no difference.
  • The objective of correlation is to find a numerical value expressing the relationship between variables.
  • Correlation is used for testing and verifying the relationship between two variables and gives limited information.
  • Its coefficient serves to be independent of any change of Scale or shift in Origin.
  • Its coefficient is mutual and symmetrical.

What Is Regression?

Regression is a set of statistical methods used for the estimation of relationship between a dependent variable (usually denoted as Y) and one or more independent variables (usually denoted as X). It can be utilized to assess the strength of the relationship between variables and for modeling the future relationship between them.

Regression includes several variations such as linear, multiple linear and nonlinear. Most common models are simple linear and multiple linear. Non-linear regression is commonly used for more complicated data sets in which the dependent and independent variables show a nonlinear relationship. Regression as a statistical method, finds application in finance, investing and other disciplines that attempts to determine the strength and character of the relationship between one dependent variable and a series of other variables.

What You Need To Know About Regression

  • Regression means going back and it is a mathematical measure showing the average relationship between two variables.  In other words, it explains how an independent variable is numerically associated with the dependent variable.  
  • Regression is the entire equation with all of the data points that are represented with a line.
  • It indicates the cause and effect relationship between the variables and establishes functional relationship.
  • A line or a curve is fitted to the given data and the line or the curve is extrapolated to predict the data and make sure the line or the curve fits the data on the graph.
  • It has wider application as it studies linear and nonlinear relationship between the variables.
  • Regression coefficient is an absolute figure. If we know the value of independent variable, we can find the value of the dependent variable.  
  • In regression, x is a random variable while y is a fixed variable. At times, both variables may be like random variables.
  • In regression, both the dependent and independent variable are different.  
  • The objective of regression is to estimate values of random variable on the basis of the values of fixed variable.
  • Other than verifying relation between two variables, Regression is used to fit the best line and estimate or predict one variable on the basis of another (predict one value, in relation to the other given value).
  • Its coefficient shows dependency on the change of Scale but is independent of its shift in origin.
  • Its coefficient is not symmetrical.

Also Read: Difference Between Logistic And Linear Regression

Difference Between Correlation And Regression In Tabular Form

BASIS OF COMPARISON CORRELATION REGRESSION
Description Correlation is the relationship between two or more variables, which vary with the other in the same or the opposite direction. Regression means going back and it is a mathematical measure showing the average relationship between two variables.  
Nature Correlation is a single statistic or data point.   Regression is the entire equation with all of the data points that are represented with a line.  
Cause-Effect Relationship It finds out the degree of relationship between two variables and not the cause and effect relationship.   It indicates the cause and effect relationship between the variables and establishes functional relationship.  
Expression Correlation between two variables can be expressed through a single point on a graph visually.   A line or a curve is fitted to the given data and the line or the curve is extrapolated to predict the data and make sure the line or the curve fits the data on the graph.  
Application It has limited application because it is confined only to linear relationship between the variables.   It has wider application as it studies linear and nonlinear relationship between the variables.  
Coefficient The coefficient of correlation is a relative measure. The range of relationship lies between -1 and +1.   Regression coefficient is an absolute figure. If we know the value of independent variable, we can find the value of the dependent variable.    
Variable In correlation, both variables x and y are random variables.   In regression, x is a random variable while y is a fixed variable. At times, both variables may be like random variables.  
Difference In Variables In correlation, both the independent and dependent values have no difference.   In regression, both the dependent and independent variable are different.    
Objective The objective of correlation is to find a numerical value expressing the relationship between variables.   The objective of regression is to estimate values of random variable on the basis of the values of fixed variable.  
Use Correlation is used for testing and verifying the relationship between two variables and gives limited information.   Other than verifying relation between two variables, Regression is used to fit the best line and estimate or predict one variable on the basis of another.
Change Of Scale Its coefficient serves to be independent of any change of Scale or shift in Origin.   Its coefficient shows dependency on the change of Scale but is independent of its shift in origin.  
Coefficient Symmetry Its coefficient is mutual and symmetrical.   Its coefficient is not symmetrical.  

Similarities Between Correlation And Regression

  • Both are used to quantify the direction and strength of the relationship between two numeric variables.
  • When the correlation is negative, the regression slope (line within the graph) will be negative.
  • When the correlation is positive, the regression slope (line within the graph) will be positive.

Advantage of Correlation

  • Correlation is a more concise (single value) summary of the relationship between two variables than regression. In result, many pairwise correlations can be viewed together at the same time in one graph.

Advantage Of Regression

  • Regression provides a more detailed analysis which includes an equation which can be used for prediction and/or optimization.