Applied Statistics Exercise
· EXERCISE 12.12
A regional airline transfers passengers from small airports to a larger regional hub airport. The airlines data analyst was assigned to estimate the revenue (in thousands of dollars) generated by each of the 22 small airports based on two variables: the distance from each airport (in miles) to the hub and the population (in hundreds) of the cities in which each of the 22 airports is located. The data are given in the following table.
Airport
Revenue
Distance
Population
1
233
233
56
2
272
209
74
3
253
206
67
4
296
232
78
5
268
125
73
6
296
245
54
7
276
213
100
8
235
134
98
9
253
140
95
10
233
165
81
11
240
234
52
12
267
205
96
13
338
214
96
14
243
183
73
15
252
230
55
16
269
238
91
17
242
144
64
18
233
220
60
19
234
170
60
20
450
170
240
21
340
290
70
22
200
340
75
a. Produce three scatter plots: revenue vs. distance, revenue vs. population, and distance vs. population
b. For the 22 airports, is there a strong correlation between airport distance form the regional hub and city population?
c. Does there appear to be a problem with high leverage points? Justify your answer.
· EXERCISE 12.23
Refer to the kinesiology data in Example 12.6 (images below). In this example, a first- order model was fit to relate y, maximal oxygen uptake, to the explanatory variables: , weight; , age; , time to walk 1 mile; and , heart rate at the end of a 1- mile walk.
Subject
y
x1
x2
x3
x4
1
1.5
139.8
19.1
18.1
133.6
2
2.1
143.3
21.1
15.3
144.6
3
1.8
154.2
21.2
15.3
164.6
4
2.2
176.6
23.2
17.7
139.4
5
2.2
154.3
22.4
17.1
127.3
6
2.0
185.4
22.1
16.4
137.3
7
2.1
177.9
21.6
17.3
144.0
8
1.9
158.8
19.0
16.8
141.4
9
2.8
159.8
20.9
15.5
127.7
10
1.9
123.9
22.0
13.8
124.2
11
2.0
164.2
19.5
17.0
135.7
12
2.7
146.3
19.8
13.8
116.1
13
2.4
172.6
20.7
16.8
109.0
14
2.3
147.5
21.0
15.3
131.0
15
2.0
163.0
21.2
14.2
143.3
16
1.7
159.8
20.4
16.8
156.6
17
2.3
162.7
20.0
16.6
120.1
18
0.9
133.3
21.1
17.5
131.8
19
1.2
142.8
22.6
18.0
149.4
20
1.9
146.6
23.0
15.7
106.9
21
0.8
141.6
22.1
19.1
135.6
22
2.2
158.9
22.8
13.4
164.6
23
2.3
151.9
21.8
13.6
162.6
24
1.7
153.3
20.0
16.1
134.8
25
1.6
144.6
22.9
15.8
154.0
26
1.6
133.3
22.9
18.2
120.7
27
2.8
153.6
19.4
13.3
151.9
28
2.7
158.6
21.0
14.9
133.6
29
1.3
108.4
21.1
16.7
142.8
30
2.1
157.4
20.1
15.7
168.2
31
2.5
141.7
19.8
13.5
120.5
32
1.5
151.1
21.8
18.8
135.6
33
2.4
149.5
20.5
14.9
119.5
34
2.3
144.3
21.0
17.2
119.0
35
1.9
166.6
21.4
17.4
150.8
36
1.5
153.6
20.8
16.4
144.0
37
2.4
144.1
20.3
13.3
124.7
38
2.3
148.7
19.1
15.4
154.4
39
1.7
159.9
19.6
17.4
136.7
40
2.0
162.8
21.3
16.2
152.4
41
1.9
145.7
20.0
18.6
133.6
42
2.3
156.7
19.2
16.4
113.2
43
2.1
162.3
22.1
19.0
81.6
44
2.2
164.7
19.1
17.1
134.8
45
1.8
134.4
20.9
15.6
130.4
46
2.1
160.1
21.1
14.2
162.1
47
2.2
143.0
20.5
17.1
144.7
48
1.3
141.6
21.7
14.5
163.1
49
2.5
152.0
20.8
17.3
137.1
50
2.2
187.1
21.5
14.6
156.0
51
1.4
122.9
22.6
18.6
127.2
52
2.2
157.1
23.4
14.2
121.4
53
2.5
155.1
20.8
16.0
155.3
54
1.8
133.6
22.5
15.4
140.4
a. Provide the kinesiologist with an interpretation of the fitted model having an of 58.2%.
b. Fit a quadratic model to the data with the squared values of the four predictors in the model. How much of an increase in was obtained by this fitting this model?
· EXERCISE 12.32
The following artificial data are designed to illustrate the effect of correlated and uncorrelated explanatory variables.
y
x
w
v
17
1
1
1
21
1
2
1
26
1
3
2
22
1
4
2
27
2
1
3
25
2
2
3
28
2
3
4
34
2
4
4
29
3
1
5
37
3
2
5
38
3
3
6
38
3
4
6
Locate the 95% prediction interval. Explain why Minitab gave the very extreme X values warning
· EXERCISE 12.35
After sewage is processed through sewage treatment plants, what remains is a dried product called sludge. Sludge contains many minerals that are beneficial to the growth of many farm crops, such as corn, wheat, and barley. Thus, large corporate farm purchase sludge from big cities to use as fertilizer for their crops. However, sludge often contains varying concentrations of heavy metals, which can concentrate in the crops and pose health problems to the people and animals consuming the crops. Therefore, it is important to study the amount of heavy metals absorbed by plants fertilized with sludge. A crop scientist designs the following experiment to study the amount of mercury that may be accumulated in the crops if mercury was contained in sludge. The experiment studied corn, wheat, and barley plants with one of six concentrations of mercury added to the planting soil. There were 90 growth containers used in the experiment with each container having the same soil type. The 18 treatments (three crops types and six mercury concentrations) were randomly assigned five containers each. At a specified growth stage, the mercury concentration in parts per million (ppm) was determined for the plants in each container. The 90 data values are given here. Note that there are 5 data values for each combination of type of crop and mercury concentration in the soil.
SoilMerCon
Crop
PlantMerCon
1
Corn
33.3
1
Corn
25.8
1
Corn
24.6
1
Corn
15.1
1
Corn
18.0
1
Wheat
17.4
1
Wheat
9.2
1
Wheat
10.0
1
Wheat
25.9
1
Wheat
8.6
1
Barley
1.1
1
Barley
23.1
1
Barley
9.6
1
Barley
4.5
1
Barley
8.2
2
Corn
31.4
2
Corn
35.7
2
Corn
14.5
2
Corn
40.9
2
Corn
22.9
2
Wheat
10.5
2
Wheat
34.6
2
Wheat
23.4
2
Wheat
18.4
2
Wheat
24.9
2
Barley
21.2
2
Barley
4.3
2
Barley
9.6
2
Barley
6.4
2
Barley
23.2
3
Corn
40.4
3
Corn
35.2
3
Corn
52.1
3
Corn
30.7
3
Corn
46.9
3
Wheat
27.1
3
Wheat
13.5
3
Wheat
30.3
3
Wheat
19.3
3
Wheat
33.6
3
Barley
30.8
3
Barley
22.0
3
Barley
12.9
3
Barley
3.5
3
Barley
27.9
4
Corn
65.6
4
Corn
74.7
4
Corn
77.3
4
Corn
64.2
4
Corn
71.3
4
Wheat
50.6
4
Wheat
53.9
4
Wheat
55.2
4
Wheat
48.6
4
Wheat
35.2
4
Barley
36.6
4
Barley
34.2
4
Barley
6.8
4
Barley
27.7
4
Barley
39.5
5
Corn
94.4
5
Corn
94.9
5
Corn
88.1
5
Corn
100.1
5
Corn
104.8
5
Wheat
84.9
5
Wheat
77.6
5
Wheat
93.3
5
Wheat
64.3
5
Wheat
74.2
5
Barley
56.7
5
Barley
42.8
5
Barley
49.0
5
Barley
47.9
5
Barley
45.2
6
Corn
123.4
6
Corn
158.6
6
Corn
137.3
6
Corn
156.7
6
Corn
133.5
6
Wheat
107.5
6
Wheat
91.9
6
Wheat
87.7
6
Wheat
106.2
6
Wheat
108.1
6
Barley
70.8
6
Barley
75.7
6
Barley
100.3
6
Barley
64.6
6
Barley
70.1
a. Graph the above data with separate symbols for each crop
b. Does the relationship between oil mercury content and plant mercury content appear to be linear? Quadratic?
c. Does the relationship between soil mercury content and plant mercury content appear to be the same for all three crops?
· EXERCISE 12.40
A quality control engineer studied the relationship between years of experience as a system control engineer and the capacity of the engineer to complete within a given time complex control design including debugging of all computer programs and control devices. A group of 25 engineers having widely differing amounts of experience (measured in months of experience) was given the same control design project. The results of the study are given in the following table with y = 1 if the project was successfully completed in the allocated time and y=0 if the project was not successfully completed.
Experience
Success
2
0
4
0
5
0
6
0
7
0
8
1
8
1
9
0
10
0
10
0
11
1
12
1
13
0
15
1
16
1
17
0
19
1
20
1
22
0
23
1
24
1
27
1
30
0
31
1
32
1
a. Determine whether experience is associated with the probability of completing the task.
b. Compute the probability of successfully completing the task for an engineer having 24 months of experience. Place a 95% confidence interval on your estimate.
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