Chapter 17
17.1
a
321 x378.x679.x700.39.51y
ˆ−++=
b The standard error of estimate is
s
= 40.24. It is an estimate of the standard deviation of the
error variable.
c The coefficient of determination is
2
R
= .2425; 24.25% of the variation in prices is explained by
the model.
b
2
b
= .679; for each addition tree the price on average increases by .679 thousand dollars provided
that the other variables remain constant.
3
b
= –.378; for each addition foot from the lake the price on average decreases by .378 thousand
h
We predict that the lot in question will sell for between $35,500 and $172,240
i
17.2
a
21 x11.1x194.01.13y
ˆ++=
b The standard error of estimate is
s
= 3.75. It is an estimate of the standard deviation of the error
variable.
c The coefficient of determination is
2
R
= .7629; 76.29% of the variation in final exam marks is
explained by the model.
b
:H0
:H1
t = .97, p-value = .3417. There is not enough evidence to infer that assignment marks and final
exam marks are linearly related.
g
:H0
=2
0
:H1
2
0
h.
17.3a
b The standard error of estimate is
s
= 40.13. It is an estimate of the standard deviation of the
d H0: β1 = β2 = β3 = β4 = 0
H1: At least one
i
is not equal to zero
2
b
4
b
= 1.31; for each one percentage point increase in the office vacancy rate monthly sales increase
on average by 1.31 hundred sheets provided that the other variables remain constant.
f
:H0
=i
0
:H1
i
0
g
17.4a
b
1
b
= .666; for each additional minor league home run the number of major league home runs
increases on average by .666 provided that the other variables remain constant.
b
s
d H0: β1 = β2 = β3 = 0
H1: At least one
i
is not equal to zero
F = 22.01, p-value = 0. There is enough evidence to conclude that the model is valid.
e
:H0
=i
0
f
g
17.5
a The regression equation is
y
ˆ
= 6.06 –.00781x
1
+ .603x
2
–.0702x
3
b
s
= 1.92,
=
2
R
.7020, F = 36.12, p-value = 0. The model is valid and the fit is reasonably good.
c
:H0
=i
0
:H1
i
0
d.
95% prediction interval: Lower prediction limit = 5.64, upper prediction limit = 13.50. The offer
of 5 weeks severance pay falls below the prediction interval and thus Bill is correct.
17.6
b The coefficient of determination is
2
R
= .2882; 28.82% of the variation in university GPAs is
explained by the model.
c H0: β1 = β2 = β3 = 0
H1: At least one
i
is not equal to zero
e
We predict that the student’s GPA will fall between 4.45 and 12.00 (12 is the maximum).
f
17.7
a The regression equation is
y
ˆ
= 12.31 + .570x
1
+ 3.32x
2
+ .732x
3
b The coefficient of determination is
2
R
= .1953; 19.53% of the variation in sales is explained by
the model. The coefficient of determination adjusted for degrees of freedom is .0803. The model
fits poorly.
c The standard error of estimate is
s
= 2.59. It is an estimate of the standard deviation of the error
variable
f & g
17.8 a
b H0: β1 = β2 = β3 = 0
H1: At least one
i
is not equal to zero
17.9a
a
y
ˆ
= 35.68 + .247x
1
+ .245x
2
+ .133x
3
b H0: β1 = β2 = β3 = 0
H1: At least one
i
is not equal to zero
i
Proportion of teachers with at least one mathematics degree: t = 3.54, p-value = .0011
Age: t = 1.32, p-value = .1945
Income: t = .87, p-value = .3889.
17.10a
b H0: β1 = β2 = β3 = β4 = 0
H1: At least one
i
is not equal to zero
F = 67.97, p-value = 0. There is enough evidence to conclude that the model is valid.
c
1
b
= .451; for each one year increase in the mother’s age the customer’s age increases on average
b
on average by .0869 provided the other variables are constant.
:H0
=i
0
:H1
i
0
The ages of mothers and fathers are linearly related to the ages of their children. The other two
variables are not.
d
The man is predicted to live to an age between 65.54 and 77.31
e
17.11
Assessing the Model:
s
= 7.01 and
2
R
= .7209; the model fits well.
Testing the validity of the model:
H0: β1 = β2 = 0
17.12
a
y
ˆ
= –28.43 + .604x
1
+ .374x
2
b
s
= 7.07 and
2
R
= .8072; the model fits well.
c
1
b
= .604; for each one additional box, the amount of time to unload increases on average by
d & e
17.13
b H0: β1 = β2 = β3 = β4 = 0
H1: At least one
i
is not equal to zero
F = 18.17, p-value = 0. There is enough evidence to conclude that the model is valid.
e
:H0
=i
0
:H1
i
< 0 (for beliefs 1 and 4)
:H1
i
17.14 a
b H0: β1 = β2 = β3 = 0
H1: At least one
i
is not equal to zero
:H0
:H1