Correlation vs. Regression — What's the Difference?
By Tayyaba Rehman & Fiza Rafique — Updated on May 14, 2024
Correlation quantifies the degree to which two variables move in relation to each other, whereas regression determines the relationship by predicting one variable based on the other.
Difference Between Correlation and Regression
Table of Contents
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Key Differences
Correlation is a statistical measure that expresses the extent to which two variables are linearly related, indicating how changes in one variable mirror changes in the other. On the other hand, regression is used to predict the value of a dependent variable based on the value of one or more independent variables, explaining the direction of the relationship.
While correlation coefficients range from -1 to 1, indicating the strength and direction of the relationship, regression provides an equation that models the relationship. This equation can predict outcomes based on varying input values.
In correlation, the relationship is described in terms of strength and type (positive or negative), whereas regression not only describes but also quantifies the relationship in the form of a predictive equation.
Correlation does not imply causation and is generally used to identify a possible association. Regression, however, often aims to establish a cause-and-effect relationship, although this interpretation requires careful validation beyond the statistical analysis.
Comparison Chart
Purpose
To measure the strength of association between variables
To predict values of one variable based on another
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Output
Correlation coefficient (e.g., Pearson’s r)
Equation of the regression line (e.g., y = mx + b)
Interpretation
Strength and direction of linear relationship
Direction and quantification of the relationship
Dependency
No variable is dependent on the other
Defines dependent and independent variables
Implication of Relationship
Does not imply causation; only association
Often used to suggest causation (with caution)
Compare with Definitions
Correlation
The degree to which two variables have a linear relationship to each other.
There is a strong negative correlation between exercise and heart disease risk.
Regression
Often used to predict the outcome of a variable based on others.
They used regression to predict college grades from high school grades.
Correlation
Typically computed as Pearson’s r, Spearman’s rho, or Kendall’s tau.
The Spearman’s rho correlation was used due to the non-parametric nature of the data.
Regression
Involves fitting a line or curve to data points.
Linear regression was applied to forecast sales growth.
Correlation
In statistics, a calculated coefficient that describes the extent and direction of a relationship.
The correlation coefficient for height and weight was 0.75.
Regression
Can include multiple independent variables in multiple regression scenarios.
Multiple regression was used to assess the impact of age, income, and education on savings.
Correlation
A statistical measure that indicates the extent to which two or more variables fluctuate together.
A high correlation between smoking and lung cancer was found in the study.
Regression
The process or an instance of regressing, as to a less perfect or less developed state.
Correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. In the broadest sense correlation is any statistical association, though it commonly refers to the degree to which a pair of variables are linearly related.
Regression
(Psychology) In psychoanalytic theory, reversion to an earlier or less mature stage of psychological development.
Correlation
A relationship or connection between two things based on co-occurrence or pattern of change
A correlation between drug abuse and crime.
Regression
(Medicine) Subsidence of the symptoms or process of a disease.
Correlation
(Statistics) The tendency for two values or variables to change together, in either the same or opposite way
As cigarette smoking increases, so does the incidence of lung cancer, indicating a positive correlation.
Regression
(Statistics) A technique for predicting the value of a dependent variable as a function of one or more independent variables in the presence of random error.
Correlation
An act of correlating or the condition of being correlated.
Regression
(Astronomy) Retrograde motion of a celestial body.
Correlation
A reciprocal, parallel or complementary relationship between two or more comparable objects.
Regression
(Geology) A relative fall in sea level resulting in deposition of terrestrial strata over marine strata.
Correlation
(statistics) One of the several measures of the linear statistical relationship between two random variables, indicating both the strength and direction of the relationship.
Regression
An action of regressing, a return to a previous state.
Correlation
(algebra) An isomorphism from a projective space to the dual of a projective space, often to the dual of itself.
Regression
An action of travelling mentally back in time.
Correlation
Reciprocal relation; corresponding similarity or parallelism of relation or law; capacity of being converted into, or of giving place to, one another, under certain conditions; as, the correlation of forces, or of zymotic diseases.
Regression
(psychotherapy) A psychotherapeutic method whereby healing is facilitated by inducing the patient to act out behaviour typical of an earlier developmental stage.
Correlation
A reciprocal relation between two or more things
Regression
(statistics) An analytic method to measure the association of one or more independent variables with a dependent variable.
Correlation
A statistic representing how closely two variables co-vary; it can vary from -1 (perfect negative correlation) through 0 (no correlation) to +1 (perfect positive correlation);
What is the correlation between those two variables?
Regression
(statistics) An equation using specified and associated data for two or more variables such that one variable can be estimated from the remaining variable(s). Category:en:Functions
Correlation
A statistical relation between two or more variables such that systematic changes in the value of one variable are accompanied by systematic changes in the other
Regression
(programming) The reappearance of a bug in a piece of software that had previously been fixed.
Correlation
A mutual relationship or connection between two or more things.
Researchers are investigating the correlation between sleep patterns and stress.
Regression
(medicine) The diminishing of a cellular mass like a tumor, or of an organ size.
Regression
(exercise) The making an exercise less straining to perform by manipulating the details of its performance like loaded weight, range of motion, angle, speed.
Regression
The act of passing back or returning; retrogression; retrogradation.
Regression
An abnormal state in which development has stopped prematurely
Regression
(psychiatry) a defense mechanism in which you flee from reality by assuming a more infantile state
Regression
The relation between selected values of x and observed values of y (from which the most probable value of y can be predicted for any value of x)
Regression
Returning to a former state
Regression
A statistical process for estimating the relationships among variables.
Regression analysis showed that income predicts spending habits.
Regression
Used for both prediction and to infer causal relationships in data.
The regression model suggests a strong causal link between diet and health outcomes.
Common Curiosities
What is the main difference between correlation and regression?
Correlation measures the strength of a relationship between variables, while regression models the relationship to predict outcomes.
How do correlation and regression relate in statistical analysis?
Correlation is often a preliminary step to regression, identifying whether a relationship exists to justify further analysis.
What is the purpose of using regression?
The purpose of regression is to predict outcomes and sometimes to infer causation.
What types of data are suitable for correlation analysis?
Numeric data where linear relationships are suspected are suitable for correlation.
Can correlation indicate causality?
No, correlation does not imply causation; it only indicates association.
What does a correlation coefficient of 0 imply?
A coefficient of 0 implies no linear correlation between the variables.
Why is regression considered more informative than correlation?
Because regression provides a predictive model, not just the strength of the relationship.
How can one validate the results of regression analysis?
Validation involves checking assumptions, using residual plots, and cross-validation techniques.
Can regression be used on categorical data?
Yes, logistic regression is used to handle categorical dependent variables.
How does one choose between correlation and regression analysis?
Choose correlation to understand the relationship, regression to predict based on the relationship.
Can both positive and negative correlations be strong?
Yes, both can be equally strong, indicating a strong linear relationship, either positive or negative.
What mathematical skills are required to perform these analyses?
Basic algebra for correlation and calculus for understanding regression analysis.
What is the best way to visualize correlation and regression?
Scatter plots are ideal for visualizing both correlation and regression.
How do outliers affect correlation and regression?
Outliers can significantly skew the results of both analyses, leading to misleading conclusions.
Is regression applicable in all research scenarios?
Regression is not suitable when the relationship between variables is not clear or when data are non-linear without transformation.
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Written by
Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.
Co-written by
Fiza RafiqueFiza Rafique is a skilled content writer at AskDifference.com, where she meticulously refines and enhances written pieces. Drawing from her vast editorial expertise, Fiza ensures clarity, accuracy, and precision in every article. Passionate about language, she continually seeks to elevate the quality of content for readers worldwide.
