Statistics - Correlation Co-efficient

Statistics – Correlation Co-efficient

Correlation Co-efficient

A correlation coefficient is a statistical measure of the diploma to which modifications to the worth of 1 variable predict change to the worth of one other. In positively correlated variables, the worth will increase or decreases in tandem. In negatively correlated variables, the worth of 1 will increase as the worth of the opposite decreases.

Correlation coefficients are expressed as values between +1 and -1.

A coefficient of +1 signifies an ideal optimistic correlation: A change within the worth of 1 variable will predict a change in the identical route within the second variable.

A coefficient of -1 signifies an ideal adverse: A change within the worth of 1 variable predicts a change in the wrong way within the second variable. Lesser levels of correlation are expressed as non-zero decimals. A coefficient of zero signifies there isn’t any discernable relationship between fluctuations of the variables.

Method

r=Nâˆ‘xyâˆ’(âˆ‘x)(âˆ‘y)[Nâˆ‘x2âˆ’(âˆ‘x)2][Nâˆ‘y2âˆ’(âˆ‘y)2]âˆšr=Nâˆ‘xyâˆ’(âˆ‘x)(âˆ‘y)[Nâˆ‘x2âˆ’(âˆ‘x)2][Nâˆ‘y2âˆ’(âˆ‘y)2]

The place âˆ’

• NNÂ = Variety of pairs of scores
• âˆ‘xyâˆ‘xyÂ = Sum of merchandise of paired scores.
• âˆ‘xâˆ‘xÂ = Sum of x scores.
• âˆ‘yâˆ‘yÂ = Sum of y scores.
• âˆ‘x2âˆ‘x2Â = Sum of squared x scores.
• âˆ‘y2âˆ‘y2Â = Sum of squared y scores.

Instance

Drawback Assertion:

Calculate the correlation co-efficient of the next:

X Y
1 2
3 5
4 5
4 8

Resolution:

âˆ‘xy=(1)(2)+(3)(5)+(4)(5)+(4)(8)=69âˆ‘x=1+3+4+4=12âˆ‘y=2+5+5+8=20âˆ‘x2=12+32+42+42=42âˆ‘y2=22+52+52+82=118r=69âˆ’(12)(20)4(42âˆ’(12)24)(118âˆ’(20)24âˆš=.866