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Relation between two or more variables is known as correlation, type of correlation

(i) Positive correlation

(ii) Negative correlation

(iii) No correlation or Zero correlation

(iv) Spurious correlation

(i) Positive correlation In the case of Positive correlation both variables moves in the same direction either upwards or downwards.
In this case curve moves from lower left to upper right.
for example.   demand and supply.

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(ii) Negative correlation In the case of negative correlation both variables move in the opposite direction if one variable moves in upward then another variable moves in downward and vice verse.
In this case curve moves from upper left to lower right.
for example    price and demand.

 (iii) No correlation In this case there is no relationship between two variables

(iv)spurious correlation Some time two variables shows relationship but it has no meaning in real life.
for example    relation-ship between shoe size and IQ level.

Correlation coefficient:It gives us degree of relation ship between two or more variables. It is mathematical mesurement of relationship.

The range of Correlation coefficient is -1 to 1(both included)

If r = 1 (perfectly positevely correlated)

If r = -1(perfectly negatively correlated

If r = 0 (No correlation)

(a) Product moment correlation coefficient or Karl pearson correlation coefficient it is denoted by ,r, and it is applicable only for quantitative type data.

(b) Rank correlation coeficient or Spearman correlation coeficient it is denoted by ,R, and it is applicable only for qualitative type data.

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Formula of Product moment correlation coefficient

1 .

cov(x,y) = covariance between x and y .

s_x = standard deviation of x .

s_y = standard deviation of y.

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2 .

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3 .

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4 .

where x̅ mean of variable x and y̅ mean of variable y

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Formula of covariance and standard deviation

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Formula of rank correlation coefficient

1 . For non repetition rank



where D is difference between rank x and rank y and n is number of paired observation .

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2 . For repeated rank



where d is difference between rank of x and rank of y,n is number of paired observation , t is number of repetition of repeated rank.

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Properties of correlation coefficient