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

Multiple Regression01:25

Multiple Regression

4.3K
Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
4.3K
Coefficient of Correlation01:12

Coefficient of Correlation

9.0K
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...
9.0K
Correlation and Regression00:53

Correlation and Regression

3.9K
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...
3.9K
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

8.4K
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:
8.4K
Residuals and Least-Squares Property01:11

Residuals and Least-Squares Property

9.7K
The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
9.7K
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

5.3K
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...
5.3K

You might also read

Related Articles

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

Sort by
Same author

Distributed Nonparametric Regression with Heterogeneity Through Prediction-Based Aggregation.

Journal of computational and graphical statistics : a joint publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America·2026
Same author

A likelihood approach to incorporating self-report data in HIV recency classification.

Biometrics·2024
Same author

Water limitation regulates positive feedback of increased ecosystem respiration.

Nature ecology & evolution·2024
Same author

A Causal Approach to Functional Mediation Analysis with Application to a Smoking Cessation Intervention.

Multivariate behavioral research·2023
Same author

Subtypes of Dual Users of Combustible and Electronic Cigarettes: Longitudinal Changes in Product Use and Dependence Symptomatology.

Nicotine & tobacco research : official journal of the Society for Research on Nicotine and Tobacco·2022
Same author

Trajectories of mortality risk among patients with cancer and associated end-of-life utilization.

NPJ digital medicine·2021
Same journal

Towards a Unified Theory for Semiparametric Data Fusion with Individual-Level Data.

Annals of statistics·2026
Same journal

One-Step Estimation of Differentiable Hilbert-Valued Parameters.

Annals of statistics·2026
Same journal

GENERALIZATION ERROR BOUNDS OF DYNAMIC TREATMENT REGIMES IN PENALIZED REGRESSION-BASED LEARNING.

Annals of statistics·2026
Same journal

EFFICIENT AND MULTIPLY ROBUST RISK ESTIMATION UNDER GENERAL FORMS OF DATASET SHIFT.

Annals of statistics·2026
Same journal

COUNTERFACTUAL INFERENCE IN SEQUENTIAL EXPERIMENTS.

Annals of statistics·2026
Same journal

A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules.

Annals of statistics·2025
See all related articles

Related Experiment Video

Updated: Mar 18, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.8K

TESTING HIGH-DIMENSIONAL REGRESSION COEFFICIENTS IN LINEAR MODELS.

Alex Zhao1, Changcheng Li2, Runze Li1

  • 1Department of Statistics, Pennsylvania State University at University Park.

Annals of Statistics
|March 16, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical test for high-dimensional linear regression models. The proposed method offers improved power and efficiency for testing regression coefficients compared to existing approaches.

Keywords:
Hotelling T2-testpower enhancementtest of high-dimensional means

More Related Videos

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

6.8K
Probing the Limits of Egg Recognition Using Egg Rejection Experiments Along Phenotypic Gradients
07:34

Probing the Limits of Egg Recognition Using Egg Rejection Experiments Along Phenotypic Gradients

Published on: August 22, 2018

8.7K

Related Experiment Videos

Last Updated: Mar 18, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.8K
Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

6.8K
Probing the Limits of Egg Recognition Using Egg Rejection Experiments Along Phenotypic Gradients
07:34

Probing the Limits of Egg Recognition Using Egg Rejection Experiments Along Phenotypic Gradients

Published on: August 22, 2018

8.7K

Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • High-dimensional linear regression models are widely used but present statistical inference challenges.
  • Existing methods for testing regression coefficients may lack sufficient power and efficiency.

Purpose of the Study:

  • To propose a novel statistical test for the coefficient vector in high-dimensional linear regression.
  • To establish the asymptotic properties and efficiency of the new test.
  • To demonstrate the practical utility and performance of the proposed method.

Main Methods:

  • Development of a new test statistic for the coefficient vector.
  • Asymptotic normality established using the martingale central limit theorem.
  • Asymptotic relative efficiency (ARE) derived and compared to existing methods.

Main Results:

  • The proposed test statistic exhibits asymptotic normality.
  • The ARE is shown to be greater than or equal to one under local alternatives.
  • Numerical studies indicate excellent Type I error rate control.
  • The proposed test demonstrates superior power compared to existing methods.

Conclusions:

  • The new statistical test provides a powerful and efficient tool for inference in high-dimensional linear models.
  • The method is validated through simulations and a real-data example.
  • This work advances statistical inference techniques for complex regression settings.