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# C O R R E L A T I O N

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### C O R R E L A T I O N

1. 1. STATISTICS FOR MANAGEMENT – 05MBA13 <ul><li>Topic Of Discussion: Correlation </li></ul><ul><li>Faculty: Ms. Prathima Bhat K. </li></ul><ul><li> Department of Management Studies </li></ul><ul><li> Acharya Institute of Technology; B’lore </li></ul><ul><li>Contact: 9242187131 </li></ul><ul><li>or mail me: [email_address] </li></ul>
2. 2. CORRELATION <ul><li>Correlation analysis is used as a statistical tool to ascertain the association between two variables. The problem in analyzing the association between two variables can be broken down into three steps: </li></ul>
3. 3. <ul><li>Try to know whether the two variables are related or independent of each other. </li></ul><ul><li>If there is a relationship between the two variables, then know its nature & strength. (i.e., positive/negative; how close is that relationship) </li></ul><ul><li>Know if there is a causal relationship between them. i.e., variation in one variable causes variation in another. </li></ul>
4. 4. CORRELATION & CAUSATION <ul><li>Correlation may be due to chance particularly when the data pertain to a small sample. </li></ul><ul><li>It is possible that both the variables are influenced by one or more other variables. </li></ul><ul><li>It may be that case, where both the variables may be influencing each other - we cannot say which is the cause and which is the effect. </li></ul>
5. 5. TYPES OF CORRELATION <ul><li>Positive and negative </li></ul><ul><li>Linear and non - linear </li></ul><ul><li>Simple, partial and multiple </li></ul>
6. 6. DIFFERENT METHODS OF CORRELATION METHODS OF CORRELATION GRAPHIC ALGEBRAIC SCATTER DIAGRAM RANK METHOD COVARIANCE METHOD CONCURRENT DEVIATION METHOD
7. 7. ALGEBRAIC METHOD (COVARIENCE METHOD) r = б x . б y Cov (x,y) Cov (x,y) = 1 Σ (x-x) (y-y) n
8. 8. PROCESS OF CALCULATION <ul><li>Calculate the means of the two series, X & Y. </li></ul><ul><li>Take deviations - from their respective means, indicated as x and y . The deviation should be taken in each case as the value of the individual item minus ( – ) the arithmetic mean. </li></ul><ul><li>Square the deviations in both the series and obtain the sum of the deviation. This would give Σ x 2 and Σ y 2 . </li></ul>
9. 9. PROCESS (Contd…..) <ul><li>Take the product of the deviations, that is, Σ xy . This means individual deviations are to be multiplied by the corresponding deviations in the other series and then their sum is obtained. </li></ul><ul><li>The values thus obtained in the preceding steps Σ xy , Σ x 2 and Σ y 2 are to be used in the formula for correlation. </li></ul>
10. 10. SHORT-CUT METHOD <ul><li>Choose convenient values as assumed means of the two series, X and Y . </li></ul><ul><li>Deviations (now dx and dy instead of x and y ) are obtained from the assumed means in the same manner as in the earlier. </li></ul><ul><li>Obtain the sum of the dx and dy columns, that is, Σ dx and Σ dy . </li></ul>
11. 11. SHORT-CUT METHOD (Contd…) <ul><li>Deviations dx and dy are squared up and their totals Σ dx 2 and Σ dy 2 are obtained. </li></ul><ul><li>Finally, obtain Σ dxdy , which is the sum of the products of deviations taken from the assumed means in the two series. </li></ul>
12. 12. IMPORTANT FORMULAS r = Σ dx.dy √ Σ dx 2 . Σ dy 2 r = n Σ xy – ( Σ x)( Σ y) √ [n Σ x 2 – ( Σ x) 2 ] [n Σ y 2 – ( Σ y) 2 ]
13. 13. IMPORTANT FORMULAS r = N Σ fuv – ( Σ fu)( Σ fv) √ [ N Σ fu 2 – ( Σ fu) 2 ] [N Σ fv 2 – ( Σ fv) 2 ] r = N Σ fxy – ( Σ fx)( Σ fy) √ [ N Σ fx 2 – ( Σ fx) 2 ] [N Σ fy 2 – ( Σ fy) 2 ]
14. 14. PROPERTIES <ul><li>Limits for Correlation Coefficient. </li></ul><ul><li>Independent of the change of origin & scale. </li></ul><ul><li>Two independent variables are uncorrelated but the converse is not true. </li></ul><ul><li>If variable x & y are connected by a linear equation: ax+by+c=0, if the correlation coefficient between x & y is (+1) if signs of a, b are different & (-1) if signs of a, b are alike. </li></ul>
15. 15. ALGEBRAIC METHOD (RANK CORRELATION METHOD) When ranks are not repeated: When ranks are repeated ρ = 1- 6 Σ D 2 n(n 2 – 1) ρ = 1- 6[ Σ D 2 +{m(m 2 -1)/12}] n(n 2 – 1)
16. 16. ALGEBRAIC METHOD (CONCURRENT DEVIATIONS) r = √ + + [(2c-n)/n]