Correlation coefficient example

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Correlation coefficient is used to derive a relationship between two or more variables in a given dataset. Apart from that, correlation coefficient can also defines how strong the relationship is.

In this article we will see an example of correlation coefficient and how it can be calculated:

Correlation coefficient formula:

Where,

n=Quantity of information
Σx=Total of all values for first variable
Σy=Total of all values for second variable
Σxy=Sum of product of first and second value
Σx2=Sum of squares of the first value
Σy2=Sum of squares of the second value

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Steps to perform correlation coefficient:

Step 1: Make a table of the given data. In our case, given below is a table that shows students’ marks before (x) and marks after (y) special training in the subject English.

Step 2: Now add three columns for xy, x2, and y2.

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Step 3: Now add all the columns to find each of their SUM (Σ)

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Step 4: Next, use the correlation coefficient formula and substitute the values in the formula from the table.

n = 6
Σx = 247
Σy = 474
Σxy = 20522
Σx2 = 11409
Σy2 = 38648

Substituting in the formula;

r = 6(20522) – (247) (474) / √ [6(11409) – (247)2] [6(38648) – (474)2]

r = 123132 – 117078 / √ [68454 – 61009] [231888 – 224676]

r = 6054 / √ (7445) (7212)

r = 6054 / √ 53693340

r = 6054 / 7327.57

r = 0.826

Step 5: Analyse the results

In our example, we got a correlation coefficient of 0.826. Which is 82%.

+1 indicates a strong positive relationship.
-1 indicates a strong negative relationship.
A result of zero indicates no relationship at all.

Since our coefficient is more than 0 and slightly less than +1 that is, we can say that the variables have a positive correlation.

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