Chapter 4 Solutions
4.1. (a)
Time spent studying is explanatory; the grade is the response variable.
(b)
Explore
the relationship; there is no reason to view one or the other as explanatory.
(c)
Time spent
on extracurricular activities is explanatory, GPA is the response variable.
(d)
Explore the
relationship.
4.2.
Water temperature is explanatory, and weight change (growth) is the response variable.
Both are quantitative.
4.3.
For example: Weight, gender, other food eaten by the students, type of beer (light,
imported,
...
).
4.4.
Check that students understand that the
explanatory variable (returning birds) goes on
the horizontal axis.
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35
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60
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Count of new birds
Percent of returning birds
4.5.
The scatterplot (see the previous exercise) shows a linear, negative, fairly weak
relationship. (Note: form = linear, direction = negative, strength = weak.) Because this
association is negative, we conclude that the sparrowhawk is a longlived territorial species.
4.6. (a)
At right; speed is explanatory.
(b)
The
relationship is curved—low in the middle,
higher at the extremes. Because low
“mileage” is actually
good
(it means that
we use less fuel to travel 100 km), this makes
sense: moderate speeds yield the best perfor
mance. Note that 60 km
/
hr is about 37 mph.
(c)
Aboveaverage (that is, bad) values of
“fuel used” are found with both low and high
values of “speed.”
(d)
The relationship is
very strong—there is little scatter around the
curve, so the curve is very useful for prediction.
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Fuel used (liters/100 km)
Speed (km/hr)
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Chapter 4
Scatterplots and Correlation
4.7. (a)
In the scatterplot on the right, the open
circles represent Run 8905, the higher ﬂow
rate.
(b)
Icicles seem to grow faster when
the water runs more slowly. (Note that there
is no guarantee that the pattern we observe
with these two ﬂow rates applies to rates
much faster than 29.6 mg
/
s, or slower than
11.9 mg
/
s.)
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100
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Icicle length (cm)
Time (minutes)
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Run 8903
o
Run 8905
4.8. (a)
Price is explanatory (and so is on the horizontal axis). The plot shows a positive linear
association.
(b)
x
=
50 cents
/
lb and
s
x
.
=
16
.
3248 cents
/
lb;
y
=
1
.
738% and
s
y
.
=
0
.
9278%.
The standardized values are below; the correlation is
r
=
3
.
8206
/
4
=
0
.
955.
(c)
Obviously,
the calculator value should be the same.
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 Fall '09
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 Correlation, Treasury bill, treasury bills, Correlation and dependence, gas usage, Professor McDaniel

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