Question 1 - A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Data from a portion of this study follow. Risk is interpreted as the probability (times 100) that a person will have a stroke over the next 10-years period. For the smoker variable, 1 indicates a smoker and 0 indicates a nonsmoker.
|
Risk
|
Age
|
Blood Pressure
|
Smoker
|
|
12
|
57
|
152
|
0
|
|
24
|
67
|
163
|
0
|
|
13
|
58
|
155
|
0
|
|
56
|
86
|
177
|
1
|
|
28
|
59
|
196
|
0
|
|
51
|
76
|
189
|
1
|
|
18
|
56
|
155
|
1
|
|
31
|
78
|
120
|
0
|
|
37
|
80
|
135
|
1
|
|
15
|
78
|
98
|
0
|
|
22
|
71
|
152
|
0
|
|
36
|
70
|
173
|
1
|
|
15
|
67
|
135
|
1
|
|
48
|
77
|
209
|
1
|
|
15
|
60
|
199
|
0
|
|
36
|
82
|
119
|
1
|
|
8
|
66
|
166
|
0
|
|
34
|
80
|
125
|
1
|
|
3
|
62
|
117
|
0
|
|
37
|
59
|
207
|
1
|
a. Develop an estimated regression equation that can be used to predict the risk of stroke given the age and blood-pressure level.
b. Consider adding two independent variables to the model developed in part (a), one for (the interaction between age and blood-pressure level and the other for whether the person is a smoker. Develop an estimated regression equation using these four independent variables.
c. At a .05 level of significance, test to see whether the addition of the interaction term and the smoker variable contribute significantly to the estimated regression equation developed in part (a).
Question 2 - The National Football League rates prospects by position on a scale that ranges from 5 to 9. The ratings are interpreted as follows: 8-9 should start the first year; 7.0-7.9 should start; 6.0-6.9 will make the team as backup; and 5.0-5.9 can make the club and contribute. The following table shows the position, weight, time in seconds to run 40 yards, and ratings for 40 NFL prospects (USA Today, April 14, 2000).
|
Observation
|
Name
|
Position
|
Weight
|
Time
|
Rating
|
|
1
|
Peter Warrick
|
Wide receiver
|
194
|
4.53
|
9.0
|
|
2
|
Plaxico Burress
|
Wide receiver
|
231
|
4.52
|
8.8
|
|
3
|
Sylvester Morris
|
Wide receiver
|
216
|
4.59
|
8.3
|
|
4
|
Travis Taylor
|
Wide receiver
|
199
|
4.36
|
8.1
|
|
5
|
Laveranues Coles
|
Wide receiver
|
192
|
4.29
|
8.0
|
|
6
|
Dez White
|
Wide receiver
|
218
|
4.49
|
7.9
|
|
7
|
Jerry Porter
|
Wide receiver
|
221
|
4.55
|
7.4
|
|
8
|
Ron Dugans
|
Wide receiver
|
206
|
4.47
|
7.1
|
|
9
|
Todd Pinkston
|
Wide receiver
|
169
|
4.37
|
7.0
|
|
10
|
Dennis Northcutt
|
Wide receiver
|
175
|
4.43
|
7.0
|
|
11
|
Anthony Lucas
|
Wide receiver
|
194
|
4.51
|
6.9
|
|
12
|
Darrell Jackson
|
Wide receiver
|
197
|
4.56
|
6.6
|
|
13
|
Danny Farmer
|
Wide receiver
|
217
|
4.60
|
6.5
|
|
14
|
Sherrod Gideon
|
Wide receiver
|
173
|
4.57
|
6.4
|
|
15
|
Trevor Gaylor
|
Wide receiver
|
199
|
4.57
|
6.2
|
|
16
|
Cosey Coleman
|
Guard
|
322
|
5.38
|
7.4
|
|
17
|
Travis Claridge
|
Guard
|
303
|
5.18
|
7.0
|
|
18
|
Kaulana Noa
|
Guard
|
317
|
5.34
|
6.8
|
|
19
|
Leander Jordan
|
Guard
|
330
|
5.46
|
6.7
|
|
20
|
Chad Clifton
|
Guard
|
334
|
5.18
|
6.3
|
|
21
|
Manula Savea
|
Guard
|
308
|
5.32
|
6.1
|
|
22
|
Ryan Johanningmeir
|
Guard
|
310
|
5.28
|
6.0
|
|
23
|
Mark Tauscher
|
Guard
|
318
|
5.37
|
6.0
|
|
24
|
Blaine Saipaia
|
Guard
|
321
|
5.25
|
6.0
|
|
25
|
Richard Mercier
|
Guard
|
295
|
5.34
|
5.8
|
|
26
|
Damion McIntosh
|
Guard
|
328
|
5.31
|
5.3
|
|
27
|
Jeno James
|
Guard
|
320
|
5.64
|
5.0
|
|
28
|
Al Jackson
|
Guard
|
304
|
5.20
|
5.0
|
|
29
|
Chris Samuels
|
Offensive tackle
|
325
|
4.95
|
8.5
|
|
30
|
Stockar McDougle
|
Offensive tackle
|
361
|
5.50
|
8.0
|
|
31
|
Chris McIngosh
|
Offensive tackle
|
315
|
5.39
|
7.8
|
|
32
|
Adrian Klemm
|
Offensive tackle
|
307
|
4.98
|
7.6
|
|
33
|
Todd Wade
|
Offensive tackle
|
326
|
5.20
|
7.3
|
|
34
|
Marvel Smith
|
Offensive tackle
|
320
|
5.36
|
7.1
|
|
35
|
Michael Thompson
|
Offensive tackle
|
287
|
5.05
|
6.8
|
|
36
|
Bobby Williams
|
Offensive tackle
|
332
|
5.26
|
6.8
|
|
37
|
Darnell Alford
|
Offensive tackle
|
334
|
5.55
|
6.4
|
|
38
|
Terrance Beadles
|
Offensive tackle
|
312
|
5.15
|
6.3
|
|
39
|
Tutan Reyes
|
Offensive tackle
|
299
|
5.35
|
6.1
|
|
40
|
Greg Robinson-Ran
|
Offensive tackle
|
333
|
5.59
|
6.0
|
a. Develop dummy variables that will account for the player's position.
b. Develop an estimated regression equation to show how rating is related to position, weight, and time to run 40 yards.
c. At the .05 level of significance, test whether the estimated regression equation developed in part (b) represents a significant relationship between the independent variables and the dependent variable.
d. Is position a significant factor in the player's rating? Use a = .05. Explain.
Question 3 - A study investigated the relationship between audit delay (Delay), the length of time from a company's fiscal year-end to the date of the auditor s report, and variables that describe the client and the auditor. Some of the independent variables that were included in this study follow.
Industry - A dummy variable coded 1 if the firm was an industrial company or 0 if the firm was a bank, savings and loan, or insurance company.
Public - A dummy variable coded 1 if the company was traded on an organized exchange or over the counter; otherwise coded 0.
Quality - A measure of overall quality of internal controls, as judged by the auditor, on a five-point scale ranging from "virtually none" (1) to "excellent" (5).
Finished - A measure ranging from 1 to 4, as judged by the auditor, where 1 indicates "all work performed subsequent to year-end" and 4 indicates "most work performed prior to year-end."
A sample of 40 companies provided the following data.
|
Delay
|
Industry
|
Public
|
Quality
|
Finished
|
|
62
|
0
|
0
|
3
|
1
|
|
45
|
0
|
1
|
3
|
3
|
|
54
|
0
|
0
|
2
|
2
|
|
71
|
0
|
1
|
1
|
2
|
|
91
|
0
|
0
|
1
|
1
|
|
62
|
0
|
0
|
4
|
4
|
|
61
|
0
|
0
|
3
|
2
|
|
69
|
0
|
1
|
5
|
2
|
|
80
|
0
|
0
|
1
|
1
|
|
52
|
0
|
0
|
5
|
3
|
|
47
|
0
|
0
|
3
|
2
|
|
65
|
0
|
1
|
2
|
3
|
|
60
|
0
|
0
|
1
|
3
|
|
81
|
1
|
0
|
1
|
2
|
|
73
|
1
|
0
|
2
|
2
|
|
89
|
1
|
0
|
2
|
1
|
|
71
|
1
|
0
|
5
|
4
|
|
76
|
1
|
0
|
2
|
2
|
|
68
|
1
|
0
|
1
|
2
|
|
68
|
1
|
0
|
5
|
2
|
|
86
|
1
|
0
|
2
|
2
|
|
76
|
1
|
1
|
3
|
1
|
|
67
|
1
|
0
|
2
|
3
|
|
57
|
1
|
0
|
4
|
2
|
|
55
|
1
|
1
|
3
|
2
|
|
54
|
1
|
0
|
5
|
2
|
|
69
|
1
|
0
|
3
|
3
|
|
82
|
1
|
0
|
5
|
1
|
|
94
|
1
|
0
|
1
|
1
|
|
74
|
1
|
1
|
5
|
2
|
|
75
|
1
|
1
|
4
|
3
|
|
69
|
1
|
0
|
2
|
2
|
|
71
|
1
|
0
|
4
|
4
|
|
79
|
1
|
0
|
5
|
2
|
|
80
|
1
|
0
|
1
|
4
|
|
91
|
1
|
0
|
4
|
1
|
|
92
|
1
|
0
|
1
|
4
|
|
46
|
1
|
1
|
4
|
3
|
|
72
|
1
|
0
|
5
|
2
|
|
85
|
1
|
0
|
5
|
1
|
a. Develop the estimated regression equation using all of the independent variables.
b. Did the estimated regression equation developed in part (a) provide a good fit? Explain.
c. Develop a scatter diagram showing Delay as a function of Finished. What does this scatter diagram indicate about the relationship between Delay and Finished?
d. On the basis of your observations about the relationship between Delay and Finished, develop an alternative estimated regression equation to the one developed in (a) to ex-plain as much of the variability in Delay as possible.
Detailed Question: I need these questions completed step by step using excel and the details on how to find the solutions.