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    Partial and Multiple Correlation

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    Bharghav Roy
    This document discusses partial and multiple correlation analysis. Partial correlation provides a measure of the relationship between two variables while removing the effect of other variables. Multiple correlation determines the relationship between one dependent variable and multiple independent variables together. Equations for calculating partial and multiple correlation coefficients are provided. An example calculation is shown for a trivariate distribution with given correlation coefficients.

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    Partial and Multiple Correlation

    Uploaded by

    Bharghav Roy
    7K views2 pages
    This document discusses partial and multiple correlation analysis. Partial correlation provides a measure of the relationship between two variables while removing the effect of other variables. Multiple correlation determines the relationship between one dependent variable and multiple independent variables together. Equations for calculating partial and multiple correlation coefficients are provided. An example calculation is shown for a trivariate distribution with given correlation coefficients.

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    This document discusses partial and multiple correlation analysis. Partial correlation provides a measure of the relationship between two variables while removing the effect of other variables. Multiple correlation determines the relationship between one dependent variable and multiple independent variables together. Equations for calculating partial and multiple correlation coefficients are provided. An example calculation is shown for a trivariate distribution with given correlation coefficients.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    7K views2 pages

    Partial and Multiple Correlation

    Uploaded by

    Bharghav Roy
    This document discusses partial and multiple correlation analysis. Partial correlation provides a measure of the relationship between two variables while removing the effect of other variables. Multiple correlation determines the relationship between one dependent variable and multiple independent variables together. Equations for calculating partial and multiple correlation coefficients are provided. An example calculation is shown for a trivariate distribution with given correlation coefficients.

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    of 2

    MAT 2001-Statistics for Engineers

    Partial and Multiple Correlation:

    Let us consider the example of yield of rice in a firm. It may be affected by the type
    of soil, temperature, amount of rainfall, usage of fertilizers etc.,. It will be useful to determine
    how yield of rice is influenced by one factor or how yield of rice is affected by several other
    factors. This is done with the help of partial and multiple correlation analysis.

    The basic distinction between multiple and partial correlation Analysis is that in the
    former, the degree of relationship between the variable Y and all the other variables
    X 1 , X 2 ,..., X n taken together is measured, whereas, in the latter, the degree of relationship
    between Y and one of the variables X 1 , X 2 ,..., X n is measured by removing the effect of all
    the other variables.

    Partial correlation:

    Partial correlation coefficient provides a measure of the relationship between the


    dependent variable and other variable, with the effect of the rest of the variables eliminated.

    If there are three variables X 1 , X 2 and X 3 , there will be three coefficients of


    partial correlation, each studying the relationship between two variables when the third is
    held constant. If we denote by r12.3, that is, the coefficient of partial correlation
    X1 and X 2 keeping X 3 constant, it is calculated as
    r12  r13 r23 r13  r12 r23 r23  r12 r13
    r12.3  , r13.2  , r23.1 
    1  r132 1  r23
    2
    1  r122 1  r23
    2
    1  r122 1  r132

    In a trivariate distribution, it is found that r12  0.7 , r13  0.61 and r23  0.4 . Find the partial
    correlation coefficients.

    Solution:

    r12  r13 r23 0.7  (0.61  0.4)


    r12.3  =  0.628
    1  r132 1  r23
    2
    1  (0.61) 2
    1  (0.4) 2

    r13  r12 r23 0.61  (0.7  0.4)


    r13.2  =  0.504
    1  r122 1  r23
    2
    1  (0.7) 2
    1  (0.4) 2

    r23  r12 r13 0.4  (0.7  0.61)


    r23.1  =  0.048
    1  r122 1  r132 1  (0.7) 2
    1  (0.61) 2

    Dr.Mokesh Rayalu,M.Sc,Ph.D.
    MAT 2001-Statistics for Engineers

    Multiple corelation:

    In multiple correlation, we are trying to make estimates of the value of one of the variable
    based on the values of all the others. The variable whose value we are trying to estimate is
    called the dependent variable and the other variables on which our estimates are based are
    known as independent variables.

    The coefficient of multiple correlation with three variables X 1 , X 2 and X 3 are


    R1.23, R2.13 and R3.21 . R1.23, is the coefficient of multiple correlation related to X1 as a
    dependent variable and X 2 , X 3 as two independent variables and it can be expressed interms
    of r12, r23 and r13 as
    r122  r132  2r12 r23 r13 r122  r23
    2
     2r12 r23 r13
    R1.23  , R2.13  ,
    1  r23
    2
    1  r132
    r132  r23
    2
     2r12 r23 r13
    R3.12 
    1  r122

    The following zero-order correlation coefficients are given: r12  0.98, r13  0.44 and r23 =
    0.54. Calculate multiple correlation coefficient treating first variable as dependent and second
    and third variables as independent.

    Solution:
    r122  r132  2r12 r23 r13
    R1.23 
    1  r23
    2

    (0.98) 2  (0.44) 2  2(0.98)(0.54)(0.44)


    =  0.986
    1  (0.54) 2

    Dr.Mokesh Rayalu,M.Sc,Ph.D.

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