Correlation

Correlation

So far we have studied problems relating to one variable only i.e. mean of the distribution of height, SD of weight etc.But many situations arise in which we may have to study two variables simultaneously, say x and y. For example, the variable may be:i)The amount of rainfall and yield of a certain crop. ii)Income and expenditure of certain families. iii)Price of commodities and amount demanded. iv)Age and sick days. Age

20

30

32

35

40

46

52

55

58

62

Sick days

11

12

10

13

14

16

15

17

18

19

There are two main problems involved in such studies:Firstly, the data may reveal some association between x and y, and we may be interested to measure numerically the strength of association between the variables. The statistical tool with the help of which these relationship between the two variables is studied is called correlation.

Correlation The word “correlation” is used to denote the degree of association between two variables. If two variables x and y are so related that variations in the magnitude of one variable tend to be accompanied by variations in the magnitude of the other variable are said to be correlated.

Types of correlation 1) Positive. 2) Negative. 3) Uncorrelated. Whether correlation is positive or negative would depend upon the direction of change of the variable. If both the variables are varying in the same direction i.e. if one variable is increasing the other on an average is also increasing or if one variable is decreasing the other on an average is also decreasing, correlation is said to be positive.

If, on the other hand, the variables are varying in opposite directions i.e. as one variable is increasing the other is decreasing or vice versa, correlation is said to be negative.  Positive Correlation X

Y

80 70 60 40 30

50 45 30 20 10

 Negative Correlation X

Y

100 90 60 40 30

10 20 30 40 50

If the values of y are not affected by changes in the values of x, the values are said to be uncorrelated. Correlation analysis helps us in determining the degree of relationship between two or more variables- it does not tell us anything about cause and effect relationship. Even a high degree of correlation does not necessarily mean that a relationship of cause and effect exists between variables or simply stated, correlation does not necessarily imply causation relationship though the existence of causation always implies correlation.

Regression After having established the fact that