# Statistics – Correlation

In Statistics Correlation denotes the relation between to variables. If change in one variable is initiating change in the other variable then it is said that there is a correlation between them. There are two kinds of correlation. One is Positive Correlation and the other is Negative Correlation.

Positive Correlation is said to exist when a change in one variable is causing a positive change in the other variable as well then it is called Positive Correlation. For example, there is said to be a Positive Correlation between Income and spending. As income increases so is the purchasing power and spending.

Negative Correlation on the other hand is a positive change in one variable causes a negative change in the other variable. The best example for this is the demand theory in Economics. We all know that when price of a product increases then the demand of that product decreases and when the price of the product decreases then the demand increases.

The result of Correlation can only range between -1.00 and +1.00. If the answer is -1.00 then it is called perfect Negative Correlation and +1.00 denotes a perfect Positive Correlation. 0.00 denotes that there is no correlation at all.

Let us understand the process of Correlation with a good example.

The Mean of X and Y are calculated to be 4.7 and 79.9 respectively. The Standard Deviation of X and Y are calculated to be 2.1628 and 11.5706 respectively.

Now, the formula for Correlation Coefficient or Karl Pearsson Correlation (r) is

Here, we can observe that the ∑XY = 3939; N¯X ¯Y is the means of X and Y, calculated to be 4.7 and 79.9 respectively. Standard Deviation is denoted by Sx and Sy which are calculated to be 2.1628 and 11.5706. When we apply the values we get

r = (1/(10-1 ) (3939-10(4.7)(79.9) ))/((2.1628)(11.5706))

r = (1/(9 ) (3939-3755.3))/25.0249 = (1/(9 ) (183.7))/25.0249 = 20.4111/25.0249 =

0.8156 = 0.82

The Coefficient Determination = r2 = 0.822 = 0.67 or 67%.

Therefore, we can conclude that the score in exams is directly related to the number of hours studied to a significant extent. And we can say that there is a positive correlation between the Number of hours Studied and the Scores obtained in Exams.

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