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http//cc.jlu.edu.cn/ms.html http//cc.jlu.edu.cn/
ss.html
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?10-1 ??????????,?????14?4060??????,?????????(
kJ /day)???(kg)??,??11-1???????????????????
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????????????(scatter plot),?????????????????
?????????13-1?
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????(linear correlation)?????????????????
?????????????(simple correlation)???????????(linea
r correlation coefficient)????????????????????????
??????????(Bivariate normal distribution)?
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????????????,??Pearson????,?r
???????????????????,???????????????????r
?????????,?r ????????????????
???????,??????-1r1?r
????????,???????,????????r 1??????,r -1????
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???????r ????????? ?
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????????????
??(10-4)
??(10-3)
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You may use Excels functions CORREL() or
PEARSON() to get r easily.
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????????r ???????,??????????
???????????X?Y??????????,?????????,??????r
????????????????r ??????,????X?Y?????????????t
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??(10-5,6)
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• Let's see two stories firstly

• Story1 Correlation between height of son and
  tree.

A correlation coefficient was calculated at the
first anniversary. r 0.97, Plt0.05 .

• Question The tree made his son growing

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up quickly, or his son made the tree growing up
quickly !?

• Story2 Correlation between swimming and ice
  cream.

They calculated a correlation coefficient at the
end of observation. r 0.92, Plt0.05 .
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• Question Swimming people must like ice ream, or
  buying ice ream must go to swimming ?!

• Question if Plt0.001, very small, can we say the
  correlation is very strong?

• Question If r0.90, can you claim the two
  variables are correlated each other?

So many questions !
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1) Dont put any two variables together for
correlation -- They must have some
relation in subject matter. 2) Simple
correlation Direct association indirect
association Simple correlation does not
necessary mean a direct association.
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Son
Tree
Swimming
Ice ream
Time
Temperature
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Correlation ? Direct association
Correlation ? Causation
3) After calculating a sample correlation coeffic
ient(r), it is necessary to have a test for
H0 ? 0, H1 ? ? 0 Rejecting
H0 just means ? ? 0 . 4) Before correlation,
you should draw a Scatter plot to judge linear
tendency or not.
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Pearsons Correlation Coefficient (r) is just
for linear relationship between two variables.
5) Linear Correlation requires two variables
that should follow bivariate normal distri-
bution .
You should know the Scatter plot is very
important for Linear Correlation regression!
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???(rank correlation),???????????????????
????????????????????????????????????????
????????Spearman?????rS,?????????
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