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Correlation Co-efficient Tutorial

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Correlation Co-efficient Tutorial

Correlation Co-efficient Definition:
A measure of the strength of linear association between two variables. Correlation will always between -1.0 and +1.0. If the correlation is positive, we have a positive relationship. If it is negative, the relationship is negative.

Formula:

Correlation Co-efficient :
Correlation(r) = NΣXY - (ΣX)(ΣY) / Sqrt([NΣX² - (ΣX)²][NΣY² - (ΣY)²])
where
N = Number of values or elements
X = First Score
Y = Second Score
ΣXY = Sum of the product of first and Second Scores
ΣX = Sum of First Scores
ΣY = Sum of Second Scores
ΣX² = Sum of square First Scores
ΣY² = Sum of square Second Scores

Correlation Co-efficient Example: To find the Correlation of

X Values	Y Values
60	3.1
61	3.6
62	3.8
63	4
65	4.1

Step 1: Count the number of values.
N = 5

Step 2: Find XY, X², Y²
See the below table

X Value	Y Value	X*Y	X*X	Y*Y
60	3.1	60 * 3.1 = 186	60 * 60 = 3600	3.1 * 3.1 = 9.61
61	3.6	61 * 3.6 = 219.6	61 * 61 = 3721	3.6 * 3.6 = 12.96
62	3.8	62 * 3.8 = 235.6	62 * 62 = 3844	3.8 * 3.8 = 14.44
63	4	63 * 4 = 252	63 * 63 = 3969	4 * 4 = 16
65	4.1	65 * 4.1 = 266.5	65 * 65 = 4225	4.1 * 4.1 = 16.81

Step 3: Find ΣX, ΣY, ΣXY, ΣX², ΣY².
ΣX = 311
ΣY = 18.6
ΣXY = 1159.7
ΣX² = 19359
ΣY² = 69.82

Step 4: Now, Substitute in the above formula given.
Correlation(r) = NΣXY - (ΣX)(ΣY) / Sqrt([NΣX² - (ΣX)²][NΣY² - (ΣY)²])
= ((5)*(1159.7)-(311)*(18.6))/sqrt([(5)*(19359)-(311)²]*[(5)*(69.82)-(18.6)²])
= (5798.5 - 5784.6)/sqrt([96795 - 96721]*[349.1 - 345.96])
= 13.9/sqrt(74*3.14)
= 13.9/sqrt(232.36)
= 13.9/15.24336
= 0.9119

This example will guide you to find the relationship between two variables by calculating the Correlation Co-efficient from the above steps.

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This tutorial will help you dynamically to find the Correlation Co-efficient problems.