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# Select a vector of temperatures in Centigrade call it X, and convert it to a vector Y representing those temperatures in Fahrenheit: Then show that the correlation ...

## Question

###### Select a vector of temperatures in Centigrade call it X, and convert it to a vector Y representing those temperatures in Fahrenheit: Then show that the correlation between their mean-centered values is 1. (Note that both data sets carry the same information; just in different units ) Note also that their angular separation in data space is Zero.10. Generalize the previous. Pick some numerical values for a data vector X. Show that if Y = mX + bU (so that the entries of Y are all linearly related

Select a vector of temperatures in Centigrade call it X, and convert it to a vector Y representing those temperatures in Fahrenheit: Then show that the correlation between their mean-centered values is 1. (Note that both data sets carry the same information; just in different units ) Note also that their angular separation in data space is Zero. 10. Generalize the previous. Pick some numerical values for a data vector X. Show that if Y = mX + bU (so that the entries of Y are all linearly related to the entries of X) then their mean- centered values satisfy p(AX,AY) = +l. If p = 1 they are called perfectly correlated and if p = ~1 they are perfectly anti-correlated: If p = 0 they they would be called perfectly uncorrelated: Hints First check that AY = mAX How does the sign of m affect the correlation constant?

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