Solution manual for a second course in statistics regression analysis 7th edition by mendenhall

Case Study 3

CS3-1

Case Study

Deregulation of the Intrastate Trucking
Industry
1.

3

Deregulated for x3 = 1

yˆ = 12.192 − .598 x1 − .00598 x2 − .01078 x1 x2 + .086 x12 + .00014 x22 + .677 x4 − .275 x1 x4 − .026 x2 x4
+.013x1 x2 x4 − .782 + .0399 x1 − .021x2 − .00331 x2
⇒= 11.41− .5581x1 − .02698 x2 − .01408 x1 x2 + .086 x12 + .0014 x22 + .677 x4 − .275 x1 x4
−.026 x2 x4 + .013x1 x2 x4
Regulated for x3 = 0
yˆ = 12.192 − .598 x1 − .00598 x2 − .01078 x1 x2 + .086 x12 + .00014 x22 + .677 x4 − .275 x1 x4 − .026 x2 x4
+.013x1 x2 x4

yˆ regulated − yˆ deregulated = .782 − .0399 x1 + .021x2 + .0033x1 x2 .
For x4 = 0, x2 = 15, yˆ regulated − yˆderegulated = 1.097 + .0096 x1 .
Deregulated yˆ = 12.5632 − .086 x12
yˆ = 11.5712 − .8439 x1 + .086 x12

Regulated

The difference between the regulated and deregulated prices is given by
yˆ regulated − yˆ deregulated = −.992 + .0069 x1

Scatterplot of Predicted Value of LNPRICE vs DISTANCE
12.5

Predicted Value of LNPRICE

2.

Regulation
0
1

12.0
11.5
11.0
10.5
10.0
9.5
0

1

Regulated = 1

2

3
DISTANCE

4

5

6

Deregulated = 0

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.


Deregulation of the Intrastate Trucking Industry
a.

The interval plot for lnprice with carriers shows that carrier B is significantly different from
the other carriers.
Interval Plot of y-LNPRICE
95% CI for the Mean
11.2
11.1
11.0
y-LNPRICE

CS3-2

10.9
10.8
10.7
10.6
10.5
10.4

CARRIER_D
CARRIER_C
CARRIER_B
CARRIER_A

0

1

0

0

1

0 1
0

1
0

0 1
1

0 1
0

1

0 1

1

0

1

0

0 1
1

0

0

1
1

MINTAB results shown below indicate that there is a difference in the carriers.
The regression equation is
LNPRICE = 11.9 - 0.287 DISTANCE - 0.0326 WEIGHT + 0.180 ORIGIN_MIA
Predictor
Constant
DISTANCE
WEIGHT
ORIGIN_MIA

Coef
11.8980
-0.28700

-0.032593
0.17980

S = 0.489209

SE Coef
0.0608
0.01674
0.002660
0.04651

R-Sq = 51.0%

PRESS = 108.478

T
195.79
-17.14
-12.25
3.87

P
0.000
0.000
0.000
0.000

R-Sq(adj) = 50.7%

R-Sq(pred) = 49.99%

Analysis of Variance
Source
Regression
Residual Error
Total

DF
3
444
447

SS
110.635
106.261
216.895

MS
36.878
0.239

F
154.09

P
0.000

⎧1 if Carrier A
x5 = ⎨
else

⎩0
⎧1 if Carrier C
If we let x6 = ⎨
and add interaction terms for each of these dummy variables
else
⎩0
⎧1 if Carrier D
x7 = ⎨
else
⎩0
(except with x12 and x22 ), the model becomes

E ( y ) = β 0 + β1 x1 + β 2 x2 + β 3 x1 x2 + β 4 x12 + β 5 x22 + β 6 x3 + β 7 x4 + β 9 x1 x3 + β10 x1 x4
+ β12 x2 x3 + β13 x2 x4 + β15 x1 x2 x3 + β16 x1 x2 x4
+ β17 x5 + β18 x1 x5 + β19 x2 x5 + β 20 x1 x2 x5 + β 21 x3 x5 + β 22 x4 x5 + β 23 x1 x3 x5
+ β 24 x1 x4 x5 + β 25 x2 x3 x5 + β 26 x2 x4 x5 + β 27 x1 x2 x3 x5 + β 28 x1 x2 x4 x5
+ β 29 x6 + … β 40 x1 x2 x4 x6 + β 41 x7 + … + β 52 x1 x2 x4 x7

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.


Case Study 3

CS3-3

In running a partial least squares procedure in MINITAB with the above model, the optimal model
obtained had the same variables as in Model 7.
y_LNPRICE = 12.2 - 0.567 x1_DISTANCE - 0.0167 x2_WEIGHT - 0.373 x3_dereg
+ 0.600 x4_origin + 0.0748 x1_Sq + 0.000349 x2_Sq - 0.00754 x1x2
+ 0.0077 x1x3 - 0.224 x1x4 - 0.0093 x2x3 - 0.0263 x2x4

+ 0.00111 x1x2x3 + 0.00864 x1x2x4

However, if variable x5 is defined as a dummy variable for Carrier B, with x5 = x6 = x7 = 0
denoting Carrier A, then the added terms in the model for Carrier B are significant.

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall.