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Prove linear function of a variable

  1. Sep 30, 2009 #1
    1. The problem statement, all variables and given/known data

    In the data table they are noon-hour temperatures of a certain week.

    datatable.jpg


    I calculated the mean which is 25 and l also calculated the standard deviation which is 3.74. Now they want me to show that :

    if [tex]y=ax+b[/tex] then [tex]\bar{y}=a\bar{x}+b[/tex] and [tex]s_{y}= \left| a\right|s_{x}[/tex]






    3. The attempt at a solution


    I don't know where they get this y from. Can you give me hints on how to solve this question ?
     
  2. jcsd
  3. Sep 30, 2009 #2

    tiny-tim

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    Hi Nyasha! :smile:
    For example, x could be in degrees Celsius, while y could be (9/5)x + 32, which is degrees Fahrenheit.

    It's just a change in scale. :wink:
     
  4. Sep 30, 2009 #3

    HallsofIvy

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    They are not "getting" y from anywhere. They are defining y to be this linear function of x. The point is to show that if y is a linear function of x then the mean of y is that same linear function of the mean of x and the standard deviation of y is a multiple of the standard deviation of x.
     
  5. Sep 30, 2009 #4
    Okay guys is this correct for the other part which says show that :
    [tex]s_{y}= \left| a\right|s_{x}[/tex]

    Attempt to solution:

    [tex]s^2_{y}=(a^2)\cdot(s^2_{x})[/tex]
    [tex]\sqrt{(s^2_{y})}=\sqrt{(a^2)\cdot(s^2_{x})[/tex]
    [tex]s_{y}= \left| a\right|s_{x}[/tex]
     
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