Lesson 11 Homework Solutions
12.1
Car mileage and weight
:
a)
The response variable is mileage, and the explanatory variable is weight.
b)
x
y
0052
.
6
.
45
ˆ

=
; the
y
intercept is 45.6 and the slope is  0.0052.
c)
For each 1000 pound increase in the vehicle, the predicted mileage will decrease by 5.2
miles per gallon.
d) The
y
intercept is the predicted miles per gallon for a car that weighs 0 pounds. This is far
outside the range of the car weights in this database and, therefore, does not have
contextual meaning for these data.
12.3 Children of working females
:
a)
(
29
968
.
3
28
044
.
2
.
5
ˆ
=

=
y
(rounds to 4.0)
b)
(
29
196
.
1
91
044
.
2
.
5
ˆ
=

=
y
(rounds to 1.2)
c)
104
.
1
196
.
1
3
.
2
ˆ
=

=

y
y
(rounds to 1.1)
d)
The
y
intercept indicates that for nations with no female economic activity, the predicted
fertility rate is 5.2. As
x
increases from 0 to 100, the predicted fertility rate decreases
from 5.2 to 0.8.
12.11 Dollars and thousands of dollars
:
Slope when income is in dollars: 1.50/1000 = 0.0015
12.13 When can you compare slopes?
:
a)
For a $1000 increase in GDP, the predicted percentage using cell phones increases by
2.62, and the predicted percentage using the Internet increases by 1.55.
b)
Because the slope of GDP to cell phone use is larger than is the relation of GDP to
Internet use, an increase in GDP would have a slightly greater impact on the percentage
using cell phones than on the percentage using the Internet.
12.16 Weight, height, and fat
:
a)
(i) Percentage of body fat and body mass index have the strongest association.
(ii) Height and body mass index have the weakest association.
b)
There is a fairly strong, positive association between height and weight. As one goes up,
the other tends to go up.
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 Spring '11
 Thomas
 Statistics, Regression Analysis, Standard Deviation, Statistical hypothesis testing, squared errors

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