Coffee is a leading export from several developing countries. When coffee prices
ID: 3157385 • Letter: C
Question
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 and the percent of forest area lost in a national park that lies in a coffee-producing region:
What is (±0.001) the least-squares slope and its standard error?
Because there are only 5 observations, the observed slope b may not be an accurate estimate of the population slope . Give a 99% confidence interval (±0.001) for :
Price (cents per pound) 29 39 55 57 72 Forest lost (percent) 0.5 1.68 1.71 1.86 3.18Explanation / Answer
The least-squares slope and its standard error are given by
b = 0.0527
SEb =0.4129
The 99% confidence interval for the observed slope is given by(-0.0194,0.1248)
The summary of the Regression output is
SUMMARY OUTPUT Regression Statistics Multiple R 0.9266 R Square 0.8587 Adjusted R Square 0.8115 Standard Error 0.4129 Observations 5 ANOVA df SS MS F Significance F Regression 1 3.1079 3.1079 18.2255 0.0236 Residual 3 0.5116 0.1705 Total 4 3.6195 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept -0.8699 0.6490 -1.3405 0.2726 -2.9352 1.1953 -4.6604 2.9206 Price 0.0527 0.0123 4.2691 0.0236 0.0134 0.0920 -0.0194 0.1248