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Note : r is also known as product-moment coefficient of correlation.

OR r =

OR r =

Now covariance of x and y is defined as

Example Calculate the coefficient of correlation between the heights of father and his son for the following data.

Height of father (cm):

165

166

167

168

167

169

170

172

Height of son (cm):

167

168

165

172

168

172

169

171



Solution: n = 8 ( pairs of observations )

Height of

father

xi

Height of

son

yi

x = xi-x

y = yi-y

xy

x2

y2

165

167

-3

-2

6

9

4

166

168

-2

-1

2

4

1

167

165

-1

-4

4

1

16

167

168

-1

-1

1

1

1

168

172

0

3

0

0

9

169

172

1

3

3

1

9

170

169

2

0

0

4

0

172

171

4

2

8

16

4

Sxi=1344

Syi=1352

0

0

Sxy=24

Sx2=36

Sy2=44

Calculation:

Index

6. 1 Introduction
6. 2 Correlation
6. 3 Types of Correlation
6. 4 Degrees of Correlation
6. 5 Methods of determining correlation

6. 6 Coefficients of Correlation for Bivariate Grouped Data
6. 7 Probable Error
6. 8 Rank Correlation Coefficient
6. 9 Linear Regression

Chapter 7





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