Introduction to the Practice of Statistics
Fifth Edition
Moore, McCabe
Section 2.1 Homework Answers
2.21 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 data on prices paid to
coffee growers in Indonesia and the rate of deforestation in a national, park that lies in a
coffee-producing region for five years.
Price (cents Deforestation
per pound)
(percent)
29
0.49
40
1.59
54
1.69
55
1.82
72
3.1
The explanatory variable should be the price of
the coffee, and the variable of interest is the
percent of deforested land.
The relationship seems to be positive. As the
price of coffee goes up the percent of
deforestation increases.
Deforestation (percent)
(a) Make a scatterplot. Which is the explanatory variable? What kind of pattern does your plot
show?
3.5
3
2.5
2
1.5
1
0.5
0
0
20
40
60
Price (cents per lb)
(b) Find the correlation r step-by-step. That is, find the mean and standard deviation of the
two variables. Then find the five standardized values for each variable and use the formula for
r. Explain how your value for r matches your graph in (a).
Price (cents Deforestation
per pound)
(percent)
Zx
Zy
(Zx)(Zy)
29
0.49
-1.28638 -1.34507 1.73028
40
1.59
-0.61256 -0.15951 0.097711
54
1.69
0.245026 -0.05173 -0.01268
55
1.82
0.306282 0.088378 0.027069
72
3.1
1.34764 1.46794 1.978255
3.820639
50
1.738
mean
0.95516
16.3248277 0.927830804
s
SUM
r
I automated all the calculations by using the copy feature of Excel.
80
(c) Now enter these data into your calculator or software and use the correlation function to
find r. Check that you get the same result as in (b).
On Excel I used the command “=correl(enter explanatory data, enter response data), and I got
the same answers as in b.
2.22 Figure 2.4 (page 109) displays the positive association between number of prey (perch)
present in an area and the proportion eaten by predators (bass).
(a) Do you think the correlation between these variables is closest to r = 0.1, r = 0.6,
or r = 0.9-? Explain the reason for your guess.
(b) Calculate the correlation. Was your guess correct?
2.23 Figure 2.6 (page 113) displays the positive association between the IQ scores of fifthgrade students and their reading scores. Do you think the correlation between these variables
is closest to r = 0.1, r = 0.6, or r == 0.9? Explain the reason for your guess.
I would guess that the value is r = 0.6, since the
association is pronounced but not overtly strong.
The value r = 0.9 suggests a very strong relationship which does
not seem to be the case here. While r = 0.1 suggest a very weak
association, which is not the case here also.
2.25 Coffee is currently priced in dollars. If it were priced in euros, and the dollar prices in
Exercise 2.21 were translated into the equivalent prices in euros, would the correlation
between coffee price and percent deforestation change? Explain your answer.
No, the measurement r is a unit less value. When we calculate r we are using standardized
scores so the units are “cancelled”. Thus, it would not make any difference if we changed to
euros since the transformation used to exchange money is a linear one.