Correlation Coefficient Formula

Correlation Coefficient Formula

In statistics, correlation is a way of establishing a relationship/association between two variables. In other words, the Correlation Coefficient Formula helps calculate correlation coefficients, which measure the dependence of one variable on another and is measured numerically using the correlation coefficient. Correlation coefficients range from -1 to 1. A negative correlation coefficient indicates an inverse relationship between the two variables. A positive correlation coefficient indicates that the value of one variable is directly dependent on the other variable. A Correlation Coefficient Formula indicates no correlation between the two variables. There are many types of correlation coefficients, but the most common is the Pearson correlation coefficient (PCC). The Correlation Coefficient Formula is calculated for a given population or sample below.


 n: the amount of information

Σx: sum of first variable values 

Σy: the sum of the values ​​of the second variable

sum of products of Σxy and the second value 

 Σx2: sum of squares of first values 

Correlation Coefficient Formula is a statistical concept. Establish the relationship between the predicted and actual values ​​obtained at the end of a statistical experiment. The Correlation Coefficient Formula is useful for calculating the relationship between two variables. The results thus obtained describe the accuracy between predicted and actual values.

There are various formulas for calculating the correlation coefficient, the formulas discussed here include Pearson’s Correlation Coefficient Formula, linear Correlation Coefficient, sample Correlation Coefficient, and population Correlation Coefficient. Before proceeding with the formulas, it is important to understand what correlation and correlation coefficients are. Below is a brief introduction to the Correlation Coefficient Formula

About Correlation Coefficient

A Correlation Coefficient Formula is a measure of the relationship between two variables. Used to find relationships between data and measures to see how strong they are. The expression returns a value between -1 and 1. Where -1 indicates a negative correlation and +1 indicates a positive correlation.

A Correlation Coefficient Formula value is positive if it indicates that there is a correlation between the two values, and negative values ​​indicate the degree of diversity between the two values.

Types of Correlation Coefficient Formula

There are many different types of Correlation Coefficient Formulas. However, one of the most commonly used formulas in statistics is the Pearson Correlation Coefficient Formula. All  Correlation Coefficient formulas are described below.

Pearson’s Correlation Coefficient Formula

Pearson’s Correlation Coefficient Formula, also known as bivariate correlation, is the most widely used correlation method in all of science and the correlation coefficient is represented by “r”.

To find r, assuming two variables x and y, the correlation coefficient r is calculated.

Linear Correlation Coefficient Formula

Use Pearson’s correlation coefficient to determine the linear relationship between two variables and Its value is between -1 and 1.

Sample Correlation Coefficient Formula

The Correlation Coefficient Formula can be learned by visiting the Extramarks website.

Population Correlation Coefficient Formula

The population correlation coefficient uses σx and σy as the population standard deviation and σxy as the population covariance. Relationship between the correlation coefficient and covariance formula.

The formulas of the Correlation Coefficient Formula can be seen on the website of Extramarks.

Relation Between Correlation Coefficient and Covariance Formulas

Relation between Correlation Coefficient and Covariance Formulas must be learned by the students. It can be accessed from the website of Extramarks.

Practice Questions from Coefficient of Correlation Formula

Exercises related to the Correlation Coefficient Formula:

Problem 1: Find the linear correlation coefficient for the following data. X = 4, 8, 12, 16 and Y = 5, 10, 15, 20. Problem 2: Compute the correlation coefficients for x = 100, 106, 112, 98, 87, 77, 67, 66, 49 and y = 28, 33, 26, 27, 24, 24, 21, 26, 22) and Y= {11,22,34,43,56}

Additional Topics Related to Correlation Coefficient Formula

Correlation analysis: Correlation analysis is used to quantify the relationship between two continuous variables, such as dependent and independent variables, or between two independent variables.

Regression analysis: Regression analysis is the evaluation of the relationship between an outcome variable and one or more variables. Outcome variables are called dependent or response variables, and risk items are called predictor or independent variables. In regression analysis, the dependent variable is denoted by ‘y’ and the independent variable by ‘x’.

Correlation analysis estimates a sample of correlation coefficients. It ranges from -1 to +1 and is represented by r and quantifies the strength and direction of the linear association between two variables. The correlation between two variables can be either positive. H. Higher levels of one variable are related to higher or negative levels of another variable. H. High levels of one variable are related to low levels of the other variable.

Correlation and regression are two important concepts in statistical studies based on variable distributions. A variable distribution is described as a classification/distribution of multiple variables. Correlation and Regression is an essential chapter for Class 12 students. It is very important for students to know and understand the difference between these two elements.

Correlation is described as an analysis that helps detect the lack of relationship between her two variables, ‘p’ and ‘q’.

Regression is also the analysis of predicting the values ​​of the dependent variable based on the known values ​​of the independent variables. The sign of the correlation coefficient indicates the direction of the association, and the size of the coefficient indicates the strength of the relationship. The Correlation Coefficient Calculator is a free online tool that displays the correlation coefficient for a given set of data values. Extramarks’ resources on correlation coefficient calculator speed up calculations and display correlation coefficient values ​​in an instant. In statistics, the linear correlation coefficient is also called Pearson’s correlation coefficient. Linear correlation coefficients are commonly used to determine the strength of the linear association between two variables in dataset values. It is marked with the letter “r”. 

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