T3.13 Long-term records from the Serengeti National Park in Tanzania show interesting ecological relationships. When wildebeest are more abundant, they graze the grass more heavily, so there are fewer fires and more trees grow. Lions feed more successfully when there are more trees, so SO

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T3.13 Long-term records from the Serengeti National
Park in Tanzania show interesting ecological relationships.
When wildebeest are more abundant, they graze the
more heavily, so there are fewer fires and more trees grow.
Lions feed more successfully when there are more trees, so
the lion population increases. Researchers collected data
on one part of this cycle, wildebeest abundance (in thou-
sands of animals) and the percent of the grass area burned
in the same year. The results of a least-squares regression
on the data are shown here.27
grass
06
80-
70
60
50-
40-
30-
20-
10-
1500
1000
Wildebeest (1000s)
500
750
1250
Percent burned
Transcribed Image Text:T3.13 Long-term records from the Serengeti National Park in Tanzania show interesting ecological relationships. When wildebeest are more abundant, they graze the more heavily, so there are fewer fires and more trees grow. Lions feed more successfully when there are more trees, so the lion population increases. Researchers collected data on one part of this cycle, wildebeest abundance (in thou- sands of animals) and the percent of the grass area burned in the same year. The results of a least-squares regression on the data are shown here.27 grass 06 80- 70 60 50- 40- 30- 20- 10- 1500 1000 Wildebeest (1000s) 500 750 1250 Percent burned
Residuals Versus Wildebeest (1000s)
(response is Percent burned)
40-
30-
20-
10-
-10-
-20
-30-
500
750
wildebeest (1000s)
1000
1250
1500
Predictor
Coef
SE Coef
Constant
92.29
10.06
9.17
0.000
Wildebeest (1000s) -0.05762 0.01035
-5.56
0.000
S = 15.9880 R-Sq = 64.6% R-Sq(adj) = 62.5%
%3D
%3D
(a) Give the equation of the least-squares regression line.
Be sure to define any variables you use.
(b) Explain what the slope of the regression line means in
this setting.
(c) Find the correlation. Interpret this value in context.
(d) Is a linear model appropriate for describing the relation-
ship between wildebeest abundance and percent of grass area
burned? Support your answer with appropriate evidence.
Rasidnl
Transcribed Image Text:Residuals Versus Wildebeest (1000s) (response is Percent burned) 40- 30- 20- 10- -10- -20 -30- 500 750 wildebeest (1000s) 1000 1250 1500 Predictor Coef SE Coef Constant 92.29 10.06 9.17 0.000 Wildebeest (1000s) -0.05762 0.01035 -5.56 0.000 S = 15.9880 R-Sq = 64.6% R-Sq(adj) = 62.5% %3D %3D (a) Give the equation of the least-squares regression line. Be sure to define any variables you use. (b) Explain what the slope of the regression line means in this setting. (c) Find the correlation. Interpret this value in context. (d) Is a linear model appropriate for describing the relation- ship between wildebeest abundance and percent of grass area burned? Support your answer with appropriate evidence. Rasidnl
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