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Math Help - Stats

  1. #1
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    Stats

    Could someone please help me with the following question.

    The ages and salaries (in thousands of $) of 10 employees in a firm are given below.

    Age - Salary
    28 - 17
    31 - 22
    31 - 28
    35 - 20
    40 - 26
    44 - 30
    45 - 32
    48 - 18
    53 - 33
    67 - 42

    What is the correlation coefficient between age and salary? (Giving enough detail to understand the proceedings)

    Comment on its value (referring maybe back to the data, to note any individuals who figures make a particular contribution to the value of the coefficient)
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  2. #2
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    Quote Originally Posted by Natasha1
    Could someone please help me with the following question.

    The ages and salaries (in thousands of $) of 10 employees in a firm are given below.

    Age - Salary
    28 - 17
    31 - 22
    31 - 28
    35 - 20
    40 - 26
    44 - 30
    45 - 32
    48 - 18
    53 - 33
    67 - 42

    What is the correlation coefficient between age and salary? (Giving enough detail to understand the proceedings)

    Comment on its value (referring maybe back to the data, to note any individuals who figures make a particular contribution to the value of the coefficient)
    I think it is,
    r=.761
    Attached Thumbnails Attached Thumbnails Stats-picture8.gif  
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Natasha1
    Could someone please help me with the following question.

    The ages and salaries (in thousands of $) of 10 employees in a firm are given below.

    Age - Salary
    28 - 17
    31 - 22
    31 - 28
    35 - 20
    40 - 26
    44 - 30
    45 - 32
    48 - 18
    53 - 33
    67 - 42

    What is the correlation coefficient between age and salary? (Giving enough detail to understand the proceedings)

    Comment on its value (referring maybe back to the data, to note any individuals who figures make a particular contribution to the value of the coefficient)
    There are a number of ways of expressing this but the one I usually use
    is:

    <br />
R=\frac{\sum_{i=1}^N (x_i-\bar x)(y_i-\bar y)}<br />
{\sum_{i=1}^N \sqrt{(x_i-\bar x)^2}<br />
 \sum_{i=1}^N \sqrt{(y_i-\bar y)^2}}<br />

    Attached are figures from an Excel spread sheet evaluating this.

    RonL
    Attached Thumbnails Attached Thumbnails Stats-xl-data.jpg   Stats-xl-plot.jpg  
    Last edited by CaptainBlack; May 11th 2006 at 06:00 AM. Reason: correct error using R^2 rather than R
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  4. #4
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    Thanks RoL.

    What does R = 0.76404 actually mean? (referring back to the last question)
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by Natasha1
    Thanks RoL.

    What does R = 0.76404 actually mean? (referring back to the last question)
    Get ready for this-

    R is the cosine of the angle between the N-vectors [x_1,..,x_N] and [y_1,..,y_N].

    If the points fall on a line of positive slope R=1 of negative
    slope R=-1. It is a measure of how well the regression line
    fits the data.

    RonL
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  6. #6
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    Quote Originally Posted by CaptainBlack
    Get ready for this-

    R is the cosine of the angle between the N-vectors [x_1,..,x_N] and [y_1,..,y_N].

    If the points fall on a line of positive slope R=1 of negative
    slope R=-1. It is a measure of how well the regression line
    fits the data.

    RonL
    Mmm not sure I get that. So how does this answer the last part of the question?

    Comment on its value...
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by Natasha1
    Mmm not sure I get that. So how does this answer the last part of the question?

    Comment on its value...
    The value of R indicates a strong positive correlation between age and salary.

    The (48,18) point is clearly far from the line and is reducing the value of R
    that would be obtained with the remaining data.

    Of the other points the first and last contribute the most to the correlation
    coefficient (look at column F of the table)

    RonL
    Last edited by CaptainBlack; May 11th 2006 at 08:04 AM.
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  8. #8
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    thanks Ron
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