4.27

Coffee and deforestation. 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 of 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:

\begin{array}{|c|r|r|r|r|r|} \hline \text{Coffee Price (cents per pound)} & 29 & 40 &54 &55 &72 \\ \hline \text{Forest Lost (percentage)} & 0.49 & 1.59 & 1.69 & 1.82 & 3.10 \\ \hline\end{array}

  1. Make a scatterplot.  Which is the explanatory variable?  What kind of pattern does your plot show?
  2. Find the correlation r between coffee price and forest loss.  Do your scatterplot and correlation support the idea that higher coffee prices increase the loss of forest?
  3. The price of coffee in international trade is given in dollars and cents.  If the prices in the data were translated into the equivalent prices in euros, would the correlation between coffee price and percent of forest loss change?  Explain your answer.

Solution

A scatterplot shows that the data is almost in line; we can expect then that the correlation is almost one in absolute value.  Since the “line” increases from left to right, the correlation should be positive.  The explanatory variable in this case is the price of the coffee.

These are the partial values I obtained (rounding to two or three decimal places).

\begin{array}{|r|r|r|r|}\hline &&&\\ x & x-\overline{x} & (x-\overline{x})^2 & \displaystyle{\frac{x-\overline{x}}{s_x}}\\ &&& \\ \hline 29 & -21 & 441 & -1.29 \\40 & -10 & 100 & -0.61 \\54 & 4 & 16 & 0.24 \\55 & 5 & 25 & 0.31 \\72 & 22 & 484 & 1.35\\ \hline \end{array}\hfill\begin{array}{|r|r|r|r|}\hline &&&\\ y & y-\overline{y} & (y-\overline{y})^2 & \displaystyle{\frac{y-\overline{y}}{s_y}}\\ &&& \\ \hline 0.49 & -1.248 & 1.56 & -1.34 \\1.59 & -0.148 & 0.02 & -0.16 \\1.69 & -0.048 & 0.00 & -0.05 \\1.82 & 0.082 & 0.01 & 0.09 \\3.10 & 1.362 & 1.85 & 1.46\\ \hline \end{array}

The mean and standard deviation for the x values are respectively \overline{x} = 50 and s_x = 16.32. The mean and standard deviation for the y values are respectively \overline{y} = 1.738 and s_y = 0.93.

The computation of the correlation using the values indicated above give an approximated value of r = 0.95. We can then claim with confidence that there is indeed a relationship between coffee prices and deforestation.

Notice that the correlation is a unitless (or dimensionless) quantity; it does not matter in what units we measure the price of the coffee, it will always amount to roughly r=0.95.

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