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C O R R E L A T I O N
 

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 C O R R E L A T I O N Presentation Transcript

    • STATISTICS FOR MANAGEMENT – 05MBA13
      • Topic Of Discussion: Correlation
      • Faculty: Ms. Prathima Bhat K.
      • Department of Management Studies
      • Acharya Institute of Technology; B’lore
      • Contact: 9242187131
      • or mail me: [email_address]
    • CORRELATION
      • 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:
      • Try to know whether the two variables are related or independent of each other.
      • If there is a relationship between the two variables, then know its nature & strength. (i.e., positive/negative; how close is that relationship)
      • Know if there is a causal relationship between them. i.e., variation in one variable causes variation in another.
    • CORRELATION & CAUSATION
      • Correlation may be due to chance particularly when the data pertain to a small sample.
      • It is possible that both the variables are influenced by one or more other variables.
      • 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.
    • TYPES OF CORRELATION
      • Positive and negative
      • Linear and non - linear
      • Simple, partial and multiple
    • DIFFERENT METHODS OF CORRELATION METHODS OF CORRELATION GRAPHIC ALGEBRAIC SCATTER DIAGRAM RANK METHOD COVARIANCE METHOD CONCURRENT DEVIATION METHOD
    • ALGEBRAIC METHOD (COVARIENCE METHOD) r = б x . б y Cov (x,y) Cov (x,y) = 1 Σ (x-x) (y-y) n
    • PROCESS OF CALCULATION
      • Calculate the means of the two series, X & Y.
      • 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.
      • Square the deviations in both the series and obtain the sum of the deviation. This would give Σ x 2 and Σ y 2 .
    • PROCESS (Contd…..)
      • 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.
      • 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.
    • SHORT-CUT METHOD
      • Choose convenient values as assumed means of the two series, X and Y .
      • Deviations (now dx and dy instead of x and y ) are obtained from the assumed means in the same manner as in the earlier.
      • Obtain the sum of the dx and dy columns, that is, Σ dx and Σ dy .
    • SHORT-CUT METHOD (Contd…)
      • Deviations dx and dy are squared up and their totals Σ dx 2 and Σ dy 2 are obtained.
      • Finally, obtain Σ dxdy , which is the sum of the products of deviations taken from the assumed means in the two series.
    • 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 ]
    • 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 ]
    • PROPERTIES
      • Limits for Correlation Coefficient.
      • Independent of the change of origin & scale.
      • Two independent variables are uncorrelated but the converse is not true.
      • 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.
    • 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)
    • ALGEBRAIC METHOD (CONCURRENT DEVIATIONS) r = √ + + [(2c-n)/n]