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Covariance between data stats problem

  1. Jul 30, 2007 #1

    danago

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    Gold Member

    Hi. At the moment in class we are going over statistics :yuck:

    Anyway, the formula ive been using for covariance between two sets of data is:

    [tex]
    s_{xy} = \frac{1}{n}\sum\limits_{i = 1}^n {x_i y_i } - \overline x \overline y
    [/tex]


    Now, if i was to get a question such as:

    "If all the elements of set 'x' are multiplied by 'a', what is the new covariance"

    Would this be a valid in mathematical terms:

    [tex]
    \begin{array}{c}
    s_{xy} = \frac{1}{n}(ax_1 y_1 + ax_2 y_2 + ... + ax_n y_n ) - a\overline x \overline y \\
    = a[\frac{1}{n}(x_1 y_1 + x_2 y_2 + ... + x_n y_n ) - \overline x \overline y ] \\
    = a[\frac{1}{n}\sum\limits_{i = 1}^n {x_i y_i } - \overline x \overline y ] \\
    \end{array}
    [/tex]

    Therefore, if the elements of the set of data are multiplied by a constant, the covariance is also changed by that same factor? Has my working been valid in terms of the summation notation. The reason i ask is because we've never worked much with summations, so im not 100% sure how to deal with them.

    Thanks,
    Dan.
     
  2. jcsd
  3. Jul 30, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    Your reasoning is fine. Summations are just sums.
     
  4. Jul 30, 2007 #3

    danago

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    Gold Member

    Alright thanks for the confirmation. I just thought that maybe i was overlooking something, and had possibly made a mathematical error.

    Thanks again.
    Dan.
     
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