Assignment Paper

 EXERCISE 12.12

A regional airline transfers passengers from small airports to a larger regional hub airport. The airline’s 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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