# Correlation Coefficient {corr(X,Y)} Calculator

getcalc.com's **Correlation Coefficient calculator**, formula & work with steps to find the degree or magnitude of linear relationship between two or more variables in statistical experiments. Supply the values and check if two data sets or variables are positively or negatively correlated. This calculator is featured to generate the complete work with steps for any corresponding input values of correlation coefficient.

**Input Parameters**

Users may supply the values for the below input parameters to find if X & Y variables are positively or negatively correlated by using this calculator.

**Random Variable X** :

The collection random variables for X that must be number, date, time or duration. All values must be same in kind.

**Random Variable Y** :

The collection random variables for Y that must be number, date, time or duration. All values must be same in kind.

## What is Correlation Coefficient?

**Correlation Coefficient** is a method used in the context of *probability *& statistics often denoted by {Corr(X, Y)} or r(X, Y) used to find the degree or magnitude of linear relationship between two or more variables in statistical experiments. It is a ratio of co*variance* of random variables X and Y to the product of *standard deviation* of random variable X and standard deviation of random variable Y. Generally, correlation refers to the change in one variable effects the change in another variable and it is classified into three types as positive correlation, negative correlation and zero correlation.

It always lie between -1 and +1 which represented by -1 ≤ r(X, Y) ≤ 1.

if r(X, Y) = 1 then the variables X and Y are positively correlated.

if r(X, Y) = -1 then the variables X and Y are negatively correlated.

if r(X, Y) = 0 then there is no correlation between the variables X and Y.

Income & expenditure, shares & debentures, rainfall & yield, supply & demand, demand & price blood pressure & age, age & income, expenditure &age, family & number of persons, age & height, age & weight are some of the examples for correlation. It's a measure of degree of relationship between two or more variables. It's also stated that it is an analysis between covariance between two or more variables. The range of correlation is between -1 to +1. There are different types of correlation measured in statistics based on the random variables & outcome of such calculations. Positive or negative, linear or non-linear, partial or total and simple or multiple correlation are the different types of correlation.

**Formulas**

The below formula is the mathematical representation for correlation r. Users may refer this below formula to know what are all the input parameters are being used to find the correlation between two or more variables.

## Solved Example Problems with Steps

The below are some of the solved examples with solutions for for correlation r calculation. Users may refer the work with steps to learn or practice how to calculate correlation coefficient between two dataset X & Y. Use this correlation coefficient calculator to verify the results for user supplied values.

- Find the following data X & Y positively or negatively correlated?
X 81 85 96 75 65 90 82 75 Y 95 96 99 82 85 60 57 75 - The following data collected from the survey taken at 11 persons. The purpose of this survey is to estimate the height correlation between each father & son in the group. All the measurements are given in feet & inches.
**All the measurement in feet & inches**Father 6.1 6.0 5.9 5.8 5.5 5.4 5.2 5.1 5.0 4.9 4.8 Son 5.9 5.7 6.1 5.2 5.7 4.8 5.5 4.3 4.3 4.1 5.7 - Find the correlation between this below income & expense report.
Income 7000 7500 6500 5000 7500 9000 9500 12000 Expense 5200 5500 5750 4300 6000 8900 7200 8300