# correlation formula

# Define correlation

**Correlation** is very helpful to investigate the **dependence** between two or more variables. As an example we are interested to know whether there is an association between the weights of fathers and son. **correlation coefficient** can be calculated to answer this question.

If there is no relationship between the two variables (father and son weights), the average weight of son should be the same regardless of the weight of the fathers and vice versa.

There are different methods to perform **correlation analysis** : **Pearson**, **Kendall** and **Spearman** correlation tests.

The most commonly used is **Pearson correlation**. The aim of this article is to describe Pearson **correlation formula**.

# Pearson correlation

**Pearson correlation** measures a linear dependence between two variables (x and y). It’s also known as a **parametric correlation** test because it depends to the distribution of the data. The plot of y = f(x) is named **linear regression** curve.

The **pearson correlation** formula is :

\[ r = \frac{\sum{(x-m_x)(y-m_y)}}{\sqrt{\sum{(x-mx)^2}\sum{(y-my)^2}}} \]

\(m_x\) and \(m_y\) are the means of x and y variables.

the p-value (significance level) of the correlation can be determined :

by using the correlation coefficient table for the degrees of freedom : \(df = n-2\)

or by calculating the

**t value**: \[ t=\frac{r}{\sqrt{1-r^2}}\sqrt{n-2} \]

In this case the corresponding p-value is determined using **t distribution table** for \(df = n-2\)

If the p-value is less than 5%, then the correlation is significant.

# Interpretation of correlation coefficient

Correlation coefficient is between -1 (strong **negative correlation**) and 1 (strong **positive correlation**)

# Correlation coefficient calculator

**correlation coefficient calculator**is also available by following this links :

**Correlation coefficient calculator**.

Show me some love with the like buttons below... Thank you and please don't forget to share and comment below!!

Montrez-moi un peu d'amour avec les like ci-dessous ... Merci et n'oubliez pas, s'il vous plaît, de partager et de commenter ci-dessous!

## Recommended for You!

## Recommended for you

This section contains best data science and self-development resources to help you on your path.

### Coursera - Online Courses and Specialization

#### Data science

- Course: Machine Learning: Master the Fundamentals by Standford
- Specialization: Data Science by Johns Hopkins University
- Specialization: Python for Everybody by University of Michigan
- Courses: Build Skills for a Top Job in any Industry by Coursera
- Specialization: Master Machine Learning Fundamentals by University of Washington
- Specialization: Statistics with R by Duke University
- Specialization: Software Development in R by Johns Hopkins University
- Specialization: Genomic Data Science by Johns Hopkins University

#### Popular Courses Launched in 2020

- Google IT Automation with Python by Google
- AI for Medicine by deeplearning.ai
- Epidemiology in Public Health Practice by Johns Hopkins University
- AWS Fundamentals by Amazon Web Services

#### Trending Courses

- The Science of Well-Being by Yale University
- Google IT Support Professional by Google
- Python for Everybody by University of Michigan
- IBM Data Science Professional Certificate by IBM
- Business Foundations by University of Pennsylvania
- Introduction to Psychology by Yale University
- Excel Skills for Business by Macquarie University
- Psychological First Aid by Johns Hopkins University
- Graphic Design by Cal Arts

### Books - Data Science

#### Our Books

- Practical Guide to Cluster Analysis in R by A. Kassambara (Datanovia)
- Practical Guide To Principal Component Methods in R by A. Kassambara (Datanovia)
- Machine Learning Essentials: Practical Guide in R by A. Kassambara (Datanovia)
- R Graphics Essentials for Great Data Visualization by A. Kassambara (Datanovia)
- GGPlot2 Essentials for Great Data Visualization in R by A. Kassambara (Datanovia)
- Network Analysis and Visualization in R by A. Kassambara (Datanovia)
- Practical Statistics in R for Comparing Groups: Numerical Variables by A. Kassambara (Datanovia)
- Inter-Rater Reliability Essentials: Practical Guide in R by A. Kassambara (Datanovia)

#### Others

- R for Data Science: Import, Tidy, Transform, Visualize, and Model Data by Hadley Wickham & Garrett Grolemund
- Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow: Concepts, Tools, and Techniques to Build Intelligent Systems by Aurelien Géron
- Practical Statistics for Data Scientists: 50 Essential Concepts by Peter Bruce & Andrew Bruce
- Hands-On Programming with R: Write Your Own Functions And Simulations by Garrett Grolemund & Hadley Wickham
- An Introduction to Statistical Learning: with Applications in R by Gareth James et al.
- Deep Learning with R by François Chollet & J.J. Allaire
- Deep Learning with Python by François Chollet