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Math Help - Calculate the correlation coefficient of the following table

  1. #1
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    Calculate the correlation coefficient of the following table

    Question :

    Calculate the correlation coefficient of the following heights(in inches) of fathers and their sons:

    X: 65 66 67 67 68 69 70 72
    Y: 67 68 65 68 72 72 69 71
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by zorro View Post
    Question :

    Calculate the correlation coefficient of the following heights(in inches) of fathers and their sons:

    X: 65 66 67 67 68 69 70 72
    Y: 67 68 65 68 72 72 69 71
    Look up you notes (or look at Wikipedia or Google for it) for the correlation coefficient. Then its just arithmetic.

    If you have any problems let us know what they are and we will help with those specific problems.

    CB
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  3. #3
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    Is this correct?

    Quote Originally Posted by CaptainBlack View Post
    Look up you notes (or look at Wikipedia or Google for it) for the correlation coefficient. Then its just arithmetic.

    If you have any problems let us know what they are and we will help with those specific problems.

    CB


    Correlation Coefficient \rho= \frac{cov(X,Y)}{\sigma_x \sigma_y}

    \mu_x = \sum_{i} \frac{x_i}{n_1} = 68

    \mu_y = \sum_{i} \frac{y_i}{n_2} = 69

    \sigma_x ^2 = \sum_{i} \frac{(x_i - \mu_x)^2}{n_1} = \frac{9}{2}

    \sigma_y ^2 = \sum_{i} \frac{(y_i - \mu_y)^2}{n_1} = \frac{11}{2}

    cov(X,Y) \ = \ E(X,Y) ......I am stuck at this protion now ....

    I dont know how to calculate the cov of x,y from the table provided ....please advice
    Also please check if am i doing it correctly or no ....
    Last edited by CaptainBlack; December 13th 2009 at 07:36 PM.
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  4. #4
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    Captain Black please check if the answer which i have done is correct or no ?

    Quote Originally Posted by CaptainBlack View Post
    Look up you notes (or look at Wikipedia or Google for it) for the correlation coefficient. Then its just arithmetic.

    If you have any problems let us know what they are and we will help with those specific problems.

    CB

    This is what i have done

    Sample Correlation coeff

    r_{xy} = \sum_{i=0}^{n} \frac{(x_i - \bar x)(y_i - \bar y)}{(n-1) S_x S_y}

    where
    \bar x , \bar y : Sample mean x,y
    S_x , S_y : Standard deviation for x , y

    Is this the right formula that i am using???

    then
    r_{xy} = \frac{4}{33} Is this answer correct ???
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by zorro View Post
    This is what i have done

    Sample Correlation coeff

    r_{xy} = \sum_{i=0}^{n} \frac{(x_i - \bar x)(y_i - \bar y)}{(n-1) S_x S_y}

    where
    \bar x , \bar y : Sample mean x,y
    S_x , S_y : Standard deviation for x , y

    Is this the right formula that i am using???




    Yes, except the lower limit of summation should be 1, there should ne n terms in the sum if you divide by (n-1)

    then r_{xy} = \frac{4}{33} Is this answer correct ???
    I don't think so, something closser to 0.6 would be right.

    CB
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  6. #6
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    Thank you Captain Black

    Quote Originally Posted by CaptainBlack View Post
    [/color]



    Yes, except the lower limit of summation should be 1, there should ne n terms in the sum if you divide by (n-1)



    I don't think so, something closser to 0.6 would be right.

    CB

    Thank you Captain Black for helping me , You dont know how much
    But thanks mate for everything
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  7. #7
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    Is this correct?

    Quote Originally Posted by CaptainBlack View Post
    [/color]



    Yes, except the lower limit of summation should be 1, there should ne n terms in the sum if you divide by (n-1)



    I don't think so, something closser to 0.6 would be right.

    CB

    I am using another formulae

    X = x - \mu_x
    Y = y - \mu_y

    r = \frac{ \sum XY}{ \sqrt{ (\sum X^2)( \sum Y^2)}}.............Is this formulae right

    r= 0.64
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  8. #8
    Grand Panjandrum
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    Quote Originally Posted by zorro View Post
    I am using another formulae

    X = x - \mu_x
    Y = y - \mu_y

    r = \frac{ \sum XY}{ \sqrt{ (\sum X^2)( \sum Y^2)}}.............Is this formulae right

    r= 0.64
    That looks about right.

    CB
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