Pearson Correlation Formula with Problem Solution & Solved Example

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Correlation Coefficient is a popular term in mathematics that is used to measure the relationship between two variables. One of the popular categories of Correlation Coefficient is Pearson Correlation Coefficient that is denoted by the symbol R and commonly used in linear regression. If you wanted to start with statistics then Pearson Correlation Coefficient is the first thing you need to learn.

It would help in measuring the strength between two variables and their relationship. It is also named as Pearson Test in mathematics. When you conduct a statistical test among two variables, this would be an excellent choice using Pearson correlation coefficient formula to check how strong is the relationship between two variables.

You must be wondering what is the meaning of coefficient values here. The coefficient value lies between -1.00 and 1.00 in statistics. If the value is negative then it signifies that there is negative relation between two variables. At the same time, if value is positive then relationship is also positive. Greater the value of variable, stronger the relationship would be.

\[\large r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}\]

r = Pearson correlation coefficient
x = Values in the first set of data
y = Values in the second set of data
n = Total number of values.

For example, if you wanted to check the relationship between age and reported income of participants then you should use Pearson correlation coefficient formula here. It will give you either positive or negative values as mentioned earlier.

Mostly, the relationship between two variables is stronger because as the age will grow, the income will also increase in the same ration. If you are interested in learning more about relationship strength then don’t stop here but practice more problems to get a better understanding of the concept.