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Available in LSE Learning Resources Online: May 2012
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R.13 Let HT be the correlation between humidity, H, andtemperature measured in degrees Fahrenheit, F.Demonstrate that the correlation coefficient is unaffectedif temperature is instead measured in degrees Celsius, C.
Note: C = 5/9(F – 32).
1
EXERCISE R.13
R.13 Let HT be the correlation between humidity, H, andtemperature measured in degrees Fahrenheit, F.Demonstrate that the correlation coefficient is unaffectedif temperature is instead measured in degrees Celsius, C.
Note: C = 5/9(F – 32).
We start by noting that
2
FFCC ii 95
HF
ii
ii
ii
ii
ii
iiHC
FFHH
FFHH
FFHH
FFHH
CCHH
CCHH
22
22
2
22
9595
EXERCISE R.13
3
FFCC ii 95
We start with the definition of the correlation between H and C and substitute for Ci – C.
EXERCISE R.13
4
HF
ii
ii
ii
ii
ii
iiHC
FFHH
FFHH
FFHH
FFHH
CCHH
CCHH
22
22
2
22
9595
FFCC ii 95
The 5/9 terms cancel and we are left with the definition of the correlation between H and F.
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