# Correlation Co-efficient Tutorial

## 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 ValuesY Values
603.1
613.6
623.8
634
654.1
###### Step 1:

Count the number of values. N = 5

###### Step 2:

Find XY, X2, Y2 See the below table

X ValueY ValueX*YX*XY*Y
603.160 * 3.1 = 18660 * 60 = 36003.1 * 3.1 = 9.61
613.661 * 3.6 = 219.661 * 61 = 37213.6 * 3.6 = 12.96
623.862 * 3.8 = 235.662 * 62 = 38443.8 * 3.8 = 14.44
63463 * 4 = 25263 * 63 = 39694 * 4 = 16
654.165 * 4.1 = 266.565 * 65 = 42254.1 * 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.

#### Related Calculator:

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