Estadisticas

Coffee is a leading export from several developing countries. When coffee prices are high, farmers often clear forest to plant more cofee trees. Here are data onprices paid to coffe growers in Indonesia and the rate of deforestation in a national park that lies in a coffee-producing region for five years:

Price (cents perpound) | Deforestation(percent) |
29 | 0,49 |
40 | 1,59 |
54 | 1,69 |
55 | 1,82 |
72 | 3,1 |

x | y | (xi-x)/Sx | (yi-y)/Sy | (xi-x)/Sx*(yi-y)/Sy |
29 |0,49 | -1,2863842 | -1,3450728 | 1,73028039 |
40 | 1,59 | -0,6125639 | -0,1595118 | 0,09771119 |
54 | 1,69 | 0,24502556 | -0,0517336 | -0,012676 |
55 | 1,82 |0,30628195 | 0,08837818 | 0,02706864 |
72 | 3,1 | 1,34764056 | 1,46794005 | 1,97825556 |
| | | Total | 3,82063974 |

r = 3,82063974/4
r= 0,95515994
yʹ= a +bx
y’= -0.9763527 + 0.05428705x

α=0.05

Ho: ρ=0
H1: ρ>0

t= r√n-2 / √1-r² ; gl= n-2
gl= 3

Si t>2.353 se rechaza Ho.Si t<2.353 no se rechaza Ho.

t= 0.95519√5-2/√1-0.95519²
t= 5.589441

t es mayor que 2.353, por lo tanto se rechaza Ho, lo que comprueba que hay evidencia queel coeficiente de correlacion poblacional es positivo.

Ho: β=0
H1: β>0

α= 0.05

t= b/SEb

SEb= s / √Σ(xi-x̃)²

S= √Σei²/n-2

e= yi-ỹ

x | y | x̃| ỹ | xi-x̃ | yi-ỹ |
29 | 0,49 | 50 | 1.738 | -21 | -1.248 |
40 | 1,59 | 50 | 1.738 | -10 | -0.148 |
54 | 1,69 | 50 | 1.738 | 4 | -0.048 |
55 | 1,82 | 50 |1.738 | 5 | 0.082 |
72 | 3,1 | 50 | 1.738 | 22 | 1.362 |
| | | total | 0 | 0 |

Si t>2.353 se rechaza Ho
Si t<2.353 no se rechaza Ho.
S=0
SE=0
t=0