Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Correlation and Regression00:53

Correlation and Regression

4.1K
In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is mathematically expressed by the correlation coefficient, which describes the strength and direction of the relationship between two variables. The coefficient is symbolically represented by 'r' and ranges from -1 to +1. A positive value indicates a positive correlation where the two variables move in the same direction. A negative value suggests a...
4.1K
Coefficient of Correlation01:12

Coefficient of Correlation

9.1K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
9.1K
Correlation01:09

Correlation

15.9K
In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
Two variables, for example, a and b, are said to be positively correlated if both variables move in the same direction. In other words, a positive correlation exists between two variables, a and b, if:
15.9K
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

8.5K
The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
8.5K
Correlations02:20

Correlations

37.0K
Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
37.0K
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

5.6K
In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
5.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

BRIEF REPORT: THE DISTRIBUTION OF PARTIAL CORRELATIONS AND GENERALIZATIONS.

Multivariate behavioral research·2016
Same author

Regions of Significance in Multiple Regression Analysis.

Multivariate behavioral research·2016
Same author

The Relation Between Rao's Paradox in Discriminate Analysis and Regression Analysis.

Multivariate behavioral research·2016
Same author

BRIEF REPORT: THE USE OF HIGHLY CORRELATED PREDICTORS IN REGRESSION ANALYSIS.

Multivariate behavioral research·2016
Same author

The Anti-aggregating Peptide KRDS Impairs a-granule Release, Whereas RGDS Does Not.

Platelets·2010
Same author

Redistribution of granulophysin and SRC protein in normal and gray platelets after activation.

Platelets·2010
Same journal

Bayesian Machine Learning Tools for Alcohol Use Disorder Research: The bpaup R Package.

Multivariate behavioral research·2026
Same journal

A Unified Framework for Jointly modelling Response Times and Item Position Effects in Computer-Based Learning Assessments.

Multivariate behavioral research·2026
Same journal

Generalizability Theory Applied to Daily Relationship Quality: Substantive and Statistical Directions.

Multivariate behavioral research·2026
Same journal

A Modularized Higher-Order Diagnostic Classification Model for Clustered Attribute Hierarchies.

Multivariate behavioral research·2026
Same journal

Generalizing Causal Effects to a Target Population Without Individual-Level Data from the Target Population.

Multivariate behavioral research·2026
Same journal

betaselectr: Selective (and Proper) Standardization in Structural Equation Models.

Multivariate behavioral research·2026
See all related articles

Related Experiment Video

Updated: Mar 26, 2026

Basics of Multivariate Analysis in Neuroimaging Data
06:35

Basics of Multivariate Analysis in Neuroimaging Data

Published on: July 24, 2010

17.4K

A GENERALIZATION OF VECTOR CORRELATION AND ITS RELATION TO CANONICAL CORRELATION.

E M Cramer

    Multivariate Behavioral Research
    |January 26, 2016
    PubMed
    Summary
    This summary is machine-generated.

    This study links multivariate linear regression and canonical correlation. It shows vector correlation is the product of canonical correlations, offering a significance test for relationships between variable sets.

    More Related Videos

    Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
    14:27

    Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

    Published on: June 26, 2013

    16.5K
    Author Spotlight: Emerging Technologies and Advanced Tools for Decoding Metabolomics Data Analysis
    07:11

    Author Spotlight: Emerging Technologies and Advanced Tools for Decoding Metabolomics Data Analysis

    Published on: November 10, 2023

    3.5K

    Related Experiment Videos

    Last Updated: Mar 26, 2026

    Basics of Multivariate Analysis in Neuroimaging Data
    06:35

    Basics of Multivariate Analysis in Neuroimaging Data

    Published on: July 24, 2010

    17.4K
    Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data
    14:27

    Identification of Disease-related Spatial Covariance Patterns using Neuroimaging Data

    Published on: June 26, 2013

    16.5K
    Author Spotlight: Emerging Technologies and Advanced Tools for Decoding Metabolomics Data Analysis
    07:11

    Author Spotlight: Emerging Technologies and Advanced Tools for Decoding Metabolomics Data Analysis

    Published on: November 10, 2023

    3.5K

    Area of Science:

    • Multivariate statistics
    • Linear regression analysis
    • Correlation analysis

    Background:

    • Chow (1966) established that least-squares estimates in multivariate linear regression maximize squared vector correlation.
    • Existing methods for assessing relationships between sets of variables have limitations.

    Purpose of the Study:

    • To demonstrate the close relationship between multivariate linear regression, vector correlation, and canonical correlation.
    • To introduce a symmetric generalization of vector correlation applicable to matrices with varying numbers of variables and linear dependencies.
    • To provide a significance test for vector correlation and related measures.

    Main Methods:

    • Analysis of the relationship between least-squares estimates in multivariate linear regression and vector correlation.
    • Derivation of vector correlation as a product of canonical correlations.
    • Development of a symmetric generalization of vector correlation.

    Main Results:

    • The vector correlation is shown to be the product of canonical correlations between independent and dependent variables.
    • A symmetric generalization of vector correlation is presented, handling matrices with different variable counts and linear dependencies.
    • This generalization is linked to canonical correlation and Rozeboom's (1965) measure of correlation between variable sets.

    Conclusions:

    • Vector correlation is fundamentally linked to canonical correlation.
    • The proposed generalization provides a unified framework for understanding correlations between sets of variables.
    • The findings offer a significance test for vector correlation, enhancing its utility in assessing linear relationships between variable sets.