Christopher Dougherty

EC220 - Introduction to econometrics (review chapter)Slideshow: exercise r.13

 

 

 

 

Original citation:

Dougherty, C. (2012) EC220 - Introduction to econometrics (review chapter). [Teaching Resource]

© 2012 The Author

This version available at: http://learningresources.lse.ac.uk/141/

Available in LSE Learning Resources Online: May 2012

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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).

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.

Copyright Christopher Dougherty 1999–2006. This slideshow may be freely copied for personal use.

26.08.06