Formula for correlation coefficient along with its explanation is given here for all its types. There are many formulas for correlation coefficient and the ones covered here include Pearson's Correlation Coefficient Formula, Linear Correlation Coefficient Formula, Sample Correlation Coefficient Formula, and Population Correlation Coefficient Formula. But before dealing with the formulas related to correlation, it would be great to have some basic knowledge of what correlation and correlation coefficient is.

About the Correlation Coefficient

The correlation coefficient is a value that measures the relationship between two variables. It is used to find how strong the relationship is and between what data and measure this relationship exists. The return of the formula value ranges from -1 to 1; -1 indicates that variables have a negative correlation, and +1 shows a positive correlation.

The value of the correlation coefficient is positive if it shows that there exists correlation between these two values, and the negative value shows the amount of diversity among the two values.

Formula

Pearson Correlation Coefficient Formula

Also known as bivariate correlation, the Pearson's correlation coefficient formula is perhaps the most widely used correlation method among all the sciences. The correlation coefficient is represented by "r".

To determine r, let's assume the two variables as x & y, then the correlation coefficient r is given as:

Linear Correlation Coefficient Formula

The linear correlation coefficient formula is stated as follows

Sample Correlation Coefficient Formula

Sx and Sy : Sample Standard Deviations,

Sxy : Sample Covariance.

Population Correlation Coefficient Formula

σx and σy : Population Standard Deviations,

σxy : Population Covariance.

Relation Between Correlation Coefficient and Covariance Formulas

Here, Cov(x, y) is the covariance between x and y, and σx and σy are the standard deviations of x and y respectively.

Other Related Sections

Admissions Open for

Correlation Coefficient Formula

About the Correlation Coefficient

The value of the correlation coefficient is positive if it shows that there exists correlation between these two values, and the negative value shows the amount of diversity among the two values.

Formula

Pearson Correlation Coefficient Formula

To determine r, let's assume the two variables as x & y, then the correlation coefficient r is given as:

Linear Correlation Coefficient Formula

The linear correlation coefficient formula is stated as follows

Sample Correlation Coefficient Formula

Sx and Sy : Sample Standard Deviations,

Sxy : Sample Covariance.

Population Correlation Coefficient Formula

σx and σy : Population Standard Deviations,

σxy : Population Covariance.

Relation Between Correlation Coefficient and Covariance Formulas

Here, Cov(x, y) is the covariance between x and y, and σx and σy are the standard deviations of x and y respectively.

Other Related Sections

Admissions Open for

Frequently Asked Questions

What is an integral formula?

An integral formula provides a method to evaluate the integral of a function, representing the area under the curve of that function or the accumulation of quantities.

What is the purpose of integral tables?

Integral tables offer precomputed antiderivatives for various functions, simplifying the process of finding integrals for complex or unfamiliar functions.

CBSE Schools In Popular Cities

We are also listed in

ORCHIDS - The International School |

Terms|

Cancellation