(4.49 S-AQ) Coffee is a leading export from several developing countries. When c

Question

(4.49 S-AQ) Coffee is a leading export from several developing countries. When coffee prices are high, farmers often clear forest to plant more coffee trees. Here are five years' data on prices paid to coffee growers in Indonesia

Price ($US per pound) 0.39 0.31 0.54 0.51 0.76

Forest lost (percent) 0.77 1.7 1.66 1.85 3.25

What is the correlation (± 0.01) between the price of coffee and the forest loss in US dollars? _______

What is the correlation (± 0.01) between the price of coffee and the forest loss in euros, if the exchange rate is 1 euros per US dollar? _______

Explanation / Answer

calculation procedure for correlation
sum of (x) = x = 2.51
sum of (y) = y = 9.23
sum of (x^2)= x^2 = 1.378
sum of (y^2)= y^2 = 20.224
sum of (x*y)= x*y = 5.137
to caluclate value of r( x,y) = covariance ( x,y ) / sd (x) * sd (y)
covariance ( x,y ) = [ x*y - N *(x/N) * (y/N) ]/n-1
= 5.137 - [ 5 * (2.51/5) * (9.23/5) ]/5- 1
= 0.101
and now to calculate r( x,y) = 0.101/ (SQRT(1/5*5.1372-(1/5*2.51)^2) ) * ( SQRT(1/5*5.1372-(1/5*9.23)^2)
=0.101 / (0.153*0.798)
=0.824
value of correlation is =0.824
coeffcient of determination = r^2 = 0.678

the correlation (± 0.01) between the price of coffee and the forest loss in US dollars = 0.824

and to caulate in euros, it is said  if the exchange rate is 1 euros per US dollar i.e. the values in Price ($US per pound) is never change since the conversion rate mentioned 1 euro per US dollor,

and the corrlation we receive would be 0.824

( X) ( Y) X^2 Y^2 X*Y 0.39 0.77 0.1521 0.5929 0.3003 0.31 1.7 0.0961 2.89 0.527 0.54 1.66 0.2916 2.7556 0.8964 0.51 1.85 0.2601 3.4225 0.9435 0.76 3.25 0.5776 10.5625 2.47

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