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product moment correlation

when data is coded correlation constant is same but does sxx or syy change. values of sxx is 3535237.5 and coded h=x/1000 how to find shh. thanx in advance.
(edited 11 years ago)
Reply 1
Shh = Sxx / 1000^2.
Reply 2
why is it 1000^2
Reply 3
Sxx=(xixˉ)2\displaystyle S_{xx}= \sum (x_i-\bar{x})^2

Shh=(hihˉ)2\displaystyle S_{hh}= \sum (h_i-\bar{h})^2

Shh=(xi1000xˉ1000)2\displaystyle S_{hh}= \sum \left(\frac{x_i}{1000}-\frac{\bar{x}}{1000}\right)^2

Shh=(xixˉ1000)2\displaystyle S_{hh}= \sum \left(\frac{x_i-\bar{x}}{1000}\right)^2

Shh=110002(xixˉ)2\displaystyle S_{hh}=\frac{1}{1000^2}\sum (x_i-\bar{x})^2
Reply 4
I don't mean by the above that you should work it out that way.


You just need to know that if h=axh=ax then Shh=a2SxxS_{hh}=a^2 S_{xx}.


You can compare this to Var(aX)=a2Var(X)Var(aX)=a^2Var(X).

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