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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 NPresentation 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
• 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]