38
3
3.1 (a) Time spent studying is explanatory; the grade is the response variable. (b) Explore the rela
tionship; there is no reason to view one or the other as explanatory. (c) Rainfall is explanatory; crop
yield is the response variable. (d) Explore the relationship. (e) The father’s class is explanatory; the
son’s class is the response variable.
3.2 Height at age six is explanatory, and height at age 16 is the response variable. Both are quan
titative.
3.3 Sex is explanatory, and political preference in the last election is the response. Both are cate
gorical.
3.4 “Treatment”—old or new—is the (categorical) explanatory variable. Survival time is the (quan
titative) response variable.
3.5 The variables are: SAT math score; SAT verbal score. There is no explanatory/response rela
tionship. Both variables are quantitative.
3.6 (a) Explanatory variable
5
number of powerboat registrations.
(b)
50
40
30
20
10
0
Manatees killed
400
450
500
550
600
650
700
Boats (thousands)
3.7 (a) Explanatory variable: number of jet skis in use.
(b)
The plot shows a moderately strong linear
relationship. As registrations increase, the
number of manatee deaths also tends to
increase.
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Page 38
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View Full DocumentExamining Relationships
39
The horizontal axis is “Jet skis in use,” and the vertical axis is “Accidents.” There is a strong
explanatoryresponse relationship between the number of jet skis in use (explanatory) and the
number of accidents (response).
3.8 Answers will vary.
3.9 (a) The variables are positively associated.
(b) The association is moderately linear.
(c) The association is relatively strong. The number of manatees killed can be predicted
accurately from the number of powerboat registrations. If the number of registrations
remains constant at 719,000, we would expect between 45 and 50 manatees to be killed per
year.
3.10 (a) The variables are positively associated; that is, as the number of jet skis in use increases,
the number of accidents also increases.
(b) The association is linear.
3.11 (a) Speed is the explanatory variable.
0
20
40
60
80
100
120
140
Speed (km/hr)
20
10
“Mileage” (liters/100 km)
(b) The relationship is curved—low in the middle, higher at the extremes. Since low
“mileage” is actually
good
(it means that we use less fuel to travel 100 km), this makes sense:
moderate speeds yield the best performance. Note that 60 km/hr is about 37 mph.
(c) Aboveaverage values of “mileage” are found with both low and high values of “speed.”
(d) The relationship is very strong—there is little scatter around the curve, and it is very use
ful for prediction.
3.12 (a) See plot on next page. Body mass is the explanatory variable.
(b) Positive association, linear, moderately strong.
(c) The male subjects’ plot can be described in much the same way, though the scatter appears
to be greater. The males typically have larger values for both variables.
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 Linear Regression, Regression Analysis, Errors and residuals in statistics

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