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c. −3.67
d. 2.66
4-33 Refer to the following computer output from estimating the parameters of the nonlinear model
Y=aRbScTd
The computer output from the regression analysis is:
DEPENDENT VARIABLE:
LNY
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
32
0.7766
32.44
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
−0.6931
0.32
−2.17
0.0390
LNR
4.66
1.36
3.43
0.0019
LNS
−0.44
0.24
−1.83
0.0774
LNT
8.28
4.6
1.80
0.0826
Based on the info above, which of the parameter estimates are statistically significant at the 90%
level of confidence?
a. All the parameter estimates are statistically significant.
b. All parameter estimates except
ˆ
a
and
ˆ
b
are statistically significant.
c.
ˆ
a
is not statistically significant, but all the rest of the parameter estimates are significant.
d.
ˆ
c
is not statistically significant, but all the rest of the parameter estimates are significant.
4-34 Refer to the following computer output from estimating the parameters of the nonlinear model
Y=aRbScTd
The computer output from the regression analysis is:
DEPENDENT VARIABLE:
LNY
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
32
0.7766
32.44
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
−0.6931
0.32
−2.17
0.0390
LNR
4.66
1.36
3.43
0.0019
LNS
−0.44
0.24
−1.83
0.0774
LNT
8.28
4.6
1.80
0.0826
Based on the info above, if R = 1, S = 2, and T = 3, what value do you expect Y will have?
a. 143
b. 1,345
c. 3,289
d. 6,578
e. −4,559
4-35 Refer to the following computer output from estimating the parameters of the nonlinear model
Y=aRbScTd
The computer output from the regression analysis is:
DEPENDENT VARIABLE:
LNY
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
32
0.7766
32.44
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
−0.6931
0.32
−2.17
0.0390
LNR
4.66
1.36
3.43
0.0019
LNS
−0.44
0.24
−1.83
0.0774
LNT
8.28
4.6
1.80
0.0826
Based on the info above, if R decreases by 10% (all other things constant), Y will
a. increase by 4.66%.
b. increase by 46.6%.
c. decrease by 4.66%.
d. decrease by 46.6%.
4-36 Refer to the following computer output from estimating the parameters of the nonlinear model
Y=aRbScTd
The computer output from the regression analysis is:
DEPENDENT VARIABLE:
LNY
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
32
0.7766
32.44
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
−0.6931
0.32
−2.17
0.0390
LNR
4.66
1.36
3.43
0.0019
LNS
−0.44
0.24
−1.83
0.0774
LNT
8.28
4.6
1.80
0.0826
Based on the info above, if S increases by 8% (all other things constant), Y will
a. decrease by 3.52%.
b. decrease by 0.44%.
c. decrease by 4.4%.
d. increase by 0.44%.
4-37 Refer to the following nonlinear model which relates W to P, Q, and R:
W=aPbQcRd
The computer output form the regression analysis is:
DEPENDENT VARIABLE:
LNW
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
18
0.9023
43.12
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
2.50
0.45
5.56
0.0001
LNP
−5.10
1.75
−2.91
0.0113
LNQ
12.4
3.2
3.88
0.0017
LNR
−6.00
1.5
−4.00
0.0010
Based on the info above, the nonlinear relation can be transformed into the following linear
regression model:
a.
W=ln(aPbQcRd)
b.
lnW=ln(aPbQcRd)
c.
lnW=ln a×ln P×lnQ×ln R
d.
lnW=ln a+bln P+clnQ+dln R
4-38 Refer to the following nonlinear model which relates W to P, Q, and R:
W=aPbQcRd
The computer output form the regression analysis is:
DEPENDENT VARIABLE:
LNW
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
18
0.9023
43.12
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
2.50
0.45
5.56
0.0001
LNP
−5.10
1.75
−2.91
0.0113
LNQ
12.4
3.2
3.88
0.0017
LNR
−6.00
1.5
−4.00
0.0010
Based on the info above, which of the parameter estimates are statistically significant at the 5%
level of significance?
a. All the parameter estimates are statistically significant.
b. All parameter estimates except
ˆ
a
and
ˆ
b
are statistically significant.
c.
ˆ
a
is not statistically significant, but all the rest of the parameter estimates are significant.
d.
ˆ
c
is not statistically significant, but all the rest of the parameter estimates are significant.
4-39 Refer to the following nonlinear model which relates W to P, Q, and R:
W=aPbQcRd
The computer output form the regression analysis is:
DEPENDENT VARIABLE:
LNW
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
18
0.9023
43.12
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
2.50
0.45
5.56
0.0001
LNP
−5.10
1.75
−2.91
0.0113
LNQ
12.4
3.2
3.88
0.0017
LNR
−6.00
1.5
−4.00
0.0010
Based on the info above, the estimated value of a is
a. 0.916
b. 12.182
c. 2.50
d. 2.66
4-40 Refer to the following nonlinear model which relates W to P, Q, and R:
W=aPbQcRd
The computer output form the regression analysis is:
DEPENDENT VARIABLE:
LNW
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
18
0.9023
43.12
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
2.50
0.45
5.56
0.0001
LNP
−5.10
1.75
−2.91
0.0113
LNQ
12.4
3.2
3.88
0.0017
LNR
−6.00
1.5
−4.00
0.0010
Based on the info above, if P = 0.5, Q = 1.5, and R = 0.8, what value do you expect W will have?
a. 16,712
b. 243,200
c. 1,345
d. 3,289
4-41 Refer to the following nonlinear model which relates W to P, Q, and R:
W=aPbQcRd
The computer output form the regression analysis is:
DEPENDENT VARIABLE:
LNW
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
18
0.9023
43.12
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
2.50
0.45
5.56
0.0001
LNP
−5.10
1.75
−2.91
0.0113
LNQ
12.4
3.2
3.88
0.0017
LNR
−6.00
1.5
−4.00
0.0010
Based on the info above, if R decreases by 12% (all other things constant), W will
a. decrease by 72%.
b. decrease by 6%.
c. increase by 6%.
d. increase by 72%.
4-42 Refer to the following nonlinear model which relates W to P, Q, and R:
W=aPbQcRd
The computer output form the regression analysis is:
DEPENDENT VARIABLE:
LNW
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
18
0.9023
43.12
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
2.50
0.45
5.56
0.0001
LNP
−5.10
1.75
−2.91
0.0113
LNQ
12.4
3.2
3.88
0.0017
LNR
−6.00
1.5
−4.00
0.0010
Based on the info above, if Q increases by 8% (all other things constant), W will
a. decrease by 99.2%.
b. decrease by 12.5%.
c. increase by 0.99%.
d. increase by 99.2%.
4-43 Refer to the following nonlinear model which relates W to P, Q, and R:
W=aPbQcRd
The computer output form the regression analysis is:
DEPENDENT VARIABLE:
LNW
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
18
0.9023
43.12
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
2.50
0.45
5.56
0.0001
LNP
−5.10
1.75
−2.91
0.0113
LNQ
12.4
3.2
3.88
0.0017
LNR
−6.00
1.5
−4.00
0.0010
Based on the info above, if P = Q = R = 1, what value do you expect W will have?
a. 0
b. 1
c. 12.182
d. 2.50
4-44 Refer to the following nonlinear model which relates W to P, Q, and R:
W=aPbQcRd
The computer output form the regression analysis is:
DEPENDENT VARIABLE:
LNW
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
18
0.9023
43.12
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
2.50
0.45
5.56
0.0001
LNP
−5.10
1.75
−2.91
0.0113
LNQ
12.4
3.2
3.88
0.0017
LNR
−6.00
1.5
−4.00
0.0010
Based on the info above, the value of R2 tells us that
a. 0.9023% of the total variation in ln W is explained by the regression equation.
b. 90.23% of the total variation in ln W is explained by the regression equation.
c. 0.9023% of the total variation in P, W, and R is explained by the regression equation.
d. 0.9023% of the total variation in ln P, ln Q, and ln R is explained by the regression
4-45 In a multiple regression model, the coefficients on the independent variables measure
a. the percent of the variation in the dependent variable explained by a change in that
independent variable, all other influences held constant.
b. the change in the dependent variable from a one-unit change in that independent variable,
all other influences held constant.
c. the change in that independent variable from a one-unit change in the dependent variable,
all other influences held constant.
d. the change in the dependent variable explained by the random error, all other influences
held constant.
4-46 The quadratic equation Y = a + bX +cX 2 can be estimated using linear regression by estimating
a. Y = a + bX + ZX where Z = c2
b. Y = a + ZX where Z = (b + c)
c. Y = a + bZ where Z = X 2
d. Y = a + ZX where Z = (b + c)2
e. none of the above will work
4-47 A manager wishes to estimate an average cost equation of the following form:
C=a+bQ +cQ2
where Q is the level of output. Letting Z = Q2 and using least-squares estimation, the manager
obtains the following computer output:
DEPENDENT VARIABLE:
C
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
28
0.7679
26.47
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
200
38.00
5.26
0.0001
Q
−12.00
4.36
−2.75
0.0111
Z
0.50
0.16
3.13
0.0046
Given the above information, which of the parameter estimates are statistically significant at the
1% significance level?
a. All parameter estimates are statistically significant.
b. All parameter estimates except
ˆ
b
are statistically significant.
c.
ˆ
a
is not statistically significant, but all the rest of the parameter estimates are significant.
d.
ˆ
c
is not statistically significant, but all the rest of the parameter estimates are significant.
4-48 A manager wishes to estimate an average cost equation of the following form:
C=a+bQ +cQ2
where Q is the level of output. Letting Z = Q2 and using least-squares estimation, the manager
obtains the following computer output:
DEPENDENT VARIABLE:
C
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
28
0.7679
26.47
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
200
38.00
5.26
0.0001
Q
−12.00
4.36
−2.75
0.0111
Z
0.50
0.16
3.13
0.0046
Given the above information, the value of R2 indicates that _______ of the total variation in C is
explained by the regression equation.
a. 0.7679%
b. 76.79%
c. 7.679%
d. 7679%
4-49 A manager wishes to estimate an average cost equation of the following form:
C=a+bQ +cQ2
where Q is the level of output. Letting Z = Q2 and using least-squares estimation, the manager
obtains the following computer output:
DEPENDENT VARIABLE:
C
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
28
0.7679
26.47
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
200
38.00
5.26
0.0001
Q
−12.00
4.36
−2.75
0.0111
Z
0.50
0.16
3.13
0.0046
Given the above information, when output is 40 units, what is average cost?
a. $200
b. $280
c. $360
d. $480
e. $520
4-50 A manager wishes to estimate an average cost equation of the following form:
C=a+bQ +cQ2
where Q is the level of output. Letting Z = Q2 and using least-squares estimation, the manager
obtains the following computer output:
DEPENDENT VARIABLE:
C
R−SQUARE
F−RATIO
P−VALUE ON F
OBSERVATIONS:
28
0.7679
26.47
0.0001
VARIABLE
PARAMETER
ESTIMATE
STANDARD
ERROR
T−RATIO
P−VALUE
INTERCEPT
200
38.00
5.26
0.0001
Q
−12.00
4.36
−2.75
0.0111
Z
0.50
0.16
3.13
0.0046
Given the above information, when output is 20 units, what is average cost?
a. $160
b. $200
c. $280
d. $340
e. $360
