quant for managers

1. Exercise 12.1
Worked­Out Answers to Self­Check Exercise
SC 12-1 (a) We want to see whether absences (ABS) depend on temperature (TEMP).
(b)
(c) Curvilinear.
(d) Quadratic curve (parabola).
(e) When it is very cold and when it is very hot there are many absences. For moderate
temperatures, there are not as many absences.
Exercise 12.2
Worked­Out Answers to Self­Check Exercises
SC 12-2 (a)
(b)
X
Y
XY
X 2
13
6.2
80.6
169
16
8.6
137.6
256
14
7.2
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2. 100.8
196
11
4.5
49.5
121
17
9.0
153.0
289
9
3.5
31.5
81
13
6.5
84.5
169
17
9.3
158.1
289
18
9.5
171.0
324
12
5.7
68.4
144
 X 140
 Y 70.0
 XY 1,035.0
 X 2
 2,038
X 140 /10 14
  Y 70.0 /10 7.0
 
b
XY nXY
X nX
2 2

 -
 - 
1,035.0 10(14)(7.0)
2,038 10(14)
0.7051
2
-
-

a Y bX 7.0 (0.7051)(14) 2.8714
 -  - -
Thus, Y
ˆ  –2.8714 + 0.7051X. If you used a computer regression package to do your
computation, you probably got
Ŷ  –2.8718 + 0.7051X.
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3. This slight difference occurs because most computer packages carry their calculations to
more than ten decimal places, but we rounded b to only four places before finding a. For most
practical purposes, this slight difference (i.e., a  –2.8714 instead of –2.8718) is
inconsequential.
(c) X  10, Ŷ = –2.8714 + 0.7051(10) = 4.1796
X  15, Ŷ  –2.8714 + 0.7051(15)  7.7051
X  20, Ŷ  –2.8714 + 0.7051(20)  11.2306
SC 12-3 In this problem, Y  overhead and X  units produced.
(a)
X
Y
XY
X 2
Y 2
40
191
7,640
1,600
36,481
42
170
7,140
1,764
28,900
53
272
14,416
2,809
73,984
35
155
5,425
1,225
24,025
56
280
15,680
3,136
78,400
39
173
6,747
1,521
29,929
48
234
11,232
2,304
54,756
30
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4. 116
3,480
900
13,456
37
153
5,661
1,369
23,409
40
178
7,120
1,600
31,684
 X  420
 Y  1,922
 XY  84,541
 X 2
 18,228
 Y 2
 395,024
X
420
10
42
  Y
1,922
10
192.2
 
b
XY nXY
X nX
2 2

 -
 -
84,541 10(42)(192.2)
18,228 10(42)
6.4915
2

-
-

a Y bX 192.2 6.4915(42) 80.4430
 -  - -
Thus, Y
ˆ  –80.4430 + 6.4915X (Computer packages: Ŷ  –80.4428 + 6.4915 X ).
(b) Y
ˆ  –80.4430 + 6.4915(50)  244.1320
(c)
s
Y a Y b XY
n 2
e
2

 -  - 
-
395,024 ( 80.4430)(1,922) 6.4915(84,541)
8

- - -
 10.2320
Exercise 12.3
Worked­Out Answers to Self­Check Exercises
SC 12-4 In this problem, Y  sales and X  number of sections.
(a)
X
Y
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5. XY
X 2
Y 2
3
33
99
9
1.089
7
38
266
49
1,444
6
24
144
36
576
6
61
366
36
3,721
10
52
520
100
2,704
12
45
540
144
2,025
12
65
780
144
4,225
13
82
1,066
169
6,724
12
29
348
144
841
13
63
819
169
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6. 3,969
14
50
700
196
2,500
15
79
1,185
225
6,241
X  123
Y  621
XY  6,833
X 2
 1,421
Y 2
 36,059
X  123/12 = 10.25 X  621/12 = 51.75
b
XY nXY
X nX
6,883 12(10.25)(51.75)
1,421 12(10.25)
2.9189
2 2 2

 -
 -

-
-

a  Y bX
-  51.75-2.9189(10.25)  21.8313.
Thus, Y
ˆ  21.8313 + 2.9189X (Computer packages: Ŷ  21.8315 + 2.9189X).
(b)
r
a Y b XY nY
Y nY
2
2
2 2

 +  -
 -
21.8313(621) 2.9189(6,833) 12(51.75)
36,059 12(51.75)
0.3481
2
2

+ -
-

r 0.3481 0.5900
 
SC 12-5 From the solution to Exercise SC 12-3 on page 637, we have n  10, Y  1,922, Y 
192.2, XY  84,541, Y 2
 395,024, a  –80.4430, and b  6.4915. Hence
r
a Y b XY nY
Y nY
2
2
2 2

 +  -
 -
80.4430(1,922) 6.4915(84,541) 10(192.2)
395,024 10(192.2)
2
2

- + -
-
 0.9673
r 0.9673 0.9835
 
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7. Exercise 12.4
Worked­Out Answers to Self­Check Exercises
SC 12-6
X
Y
XY
X 2
Y 2
11
10
110
121
100
15
12
180
225
144
3
8
24
9
64
18
15
270
324
225
10
9
90
100
81
12
11
132
144
121
6
8
48
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8. 36
64
7
10
70
49
100
18
13
234
324
169
13
11
143
169
121
X  113
Y  107
XY  1,301
X 2
 1,501
Y 2
 1,189
X
113
10
11.3
 
Y
107
10
10.7
 
b
XY nXY
X nX
1,301 10(11.3)(10.7)
1,501 10(11.3)
0.4101
2 2 2

 -
 -

-
-

a  Y bX 10.7 0.4101(11.3) 6.0659
-  - 
(Computer packages: 6.0660)
s
Y a Y b XY
n 2
e
2

 -  - 
-
1,189 6.0659(107) 0.4101(1,301)
8
0.8950

- -

(Computer packages: 0.8953)
s
s
X nX
0.8950
224.1
0.060
b
e
2 2

 -
 
H0: B  1 H
1: B < 1   0.05
The standardized statistic is
t
b B
s
0.4101 1
0.06
9.83.
b
H0

-

-
-
Because the critical value
of t(–1.860) is greater than –9.83, we reject H0. Stock is insensitive to changes in the market
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9. (the slope is significantly <1).
SC 12-7 (a)
s
s
X nX
28.654
871.56
0.9706
b
e
2 2

 -
 
(b) The 98 percent confidence interval is
b ± t(sb) 3.73 ± 2.602(0.9706)  3.73 ± 2.53  (1.20, 6.26).
(c) In repeated sampling, 98 out of 100 intervals constructed as above would contain the
true, unknown population slope B. For our single sample, we can say that we are 98 percent
confident that our computed interval contains B.
Chapter 12
1. F 16. F 31. b
2. F 17. F 32. d
3. F 18. F 33. d
4. F 19. T 34. b
5. T 20. T 35. d
6. T 21. F 36. e
7. T 22. d 37. inverse
8. T 23. a 38. curvilinear
9. F 24. a 39. slope
10. T 25. e 40. standard error of estimate
11. F 26. b 41. r2
, the coefficient of determination
12. T 27. c 42.  0.866
13. T 28. d 43. Correlation analysis
14. T 29. a 44. direction (direct or inverse)
15. F 30. c 45. minimizes
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