answer the following.
An article in Cancer Epidemiology, Biomarkers and Prevention journal (see attached), reported on a pilot study to assess the use of toenail arsenic concentrations as an indicator of ingestion of arsenic-containing water. Twenty-one participants were interviewed regarding use of their private (unregulated) wells for drinking and cooking, and each provided a sample of water and toenail clippings. Table below showed the data of age (years), sex of person (
1
= male,
2
= female), proportion of times household well used for drinking (1? 1 /
4
, 2 = 1 / 4,
3
= 1 / 2, 4 = 3 / 4,
5
? 3 / 4), proportion of times household well used for cooking (1? 1/4,2 = 1/4, 3 = 1/2, 4 = 3/4, 5 ? 3/4), arsenic in water(ppm), arsenic region(
0
=low arsenic, 1=high arsenic), and arsenic in toenails (ppm) respectively.
(a)Explain briefly, the objective the methodology of the research
(b)Draw a box and plot diagram for arsenic in toe concentration (y) and comment on data outliers
(c)Use the proper hypothesis test to examine if there is any difference in the arsenic toe concentration between the groups who lives in the high and low arsenic regions. Repeat the same question using ANOVA
(d) Fit a multiple linear regression model using arsenic concentration in nails as the response and age, drink use, cook use, and arsenic in the water as the regressors. Comment on model fitness validity(F-test, t-test, and R2)
(e)Use the residual Analysis procedure to check model adequacy
(f)Estimate ?2 and the standard errors of the regression coefficients.
(g)Use the model to predict the arsenic in nails when the age is 30, the drink use is category 5, the cook use is category 5, and arsenic in the water is
0.135
ppm.
age(x1)
sex(x2)
drink use(x3)
cook use(x4)
Arsenic in water(x5)
Arsenic region
Arsenic Nail(y)
44
255
0.000
8
7
1
0.119
45
245
0.00021
0
0.118
4
41
5500
0.099
66
235
0.00115
10.118
37
12500
0.277
4525500
0.358
47
155
0.00013
0
0.08
38
245
0.00069
1
0.158
412
32
0.00039
0
0.31
49
24500
0.105
72
25500
0.073
45215
0.046
1
0.832
53
155
0.0194
1
0.517
86
255
0.137
1
2.52
8255
0.0214
1
0.851
32255
0.0175
1
0.269
44155
0.0764
1
0.433
63
25500
0.141
42
155
0.0165
1
0.275
62
155
0.00012
00.135
36
155
0.0041
1
0.175
Alfaisal University
MEM 501
Extra Credit
Due December 23/2022
Use Minitab or any Statistics software to answer the following. Submit a word file to address all the
questions. Use screen shot if needed to show your results.
An article in Cancer Epidemiology, Biomarkers and Prevention journal (see attached), reported on a
pilot study to assess the use of toenail arsenic concentrations as an indicator of ingestion of arseniccontaining water. Twenty-one participants were interviewed regarding use of their private (unregulated)
wells for drinking and cooking, and each provided a sample of water and toenail clippings. Table below
showed the data of age (years), sex of person (1 = male, 2 = female), proportion of times household well
used for drinking (1≤ 1 / 4, 2 = 1 / 4, 3 = 1 / 2, 4 = 3 / 4, 5 ≥ 3 / 4), proportion of times household well
used for cooking (1≤ 1/4,2 = 1/4, 3 = 1/2, 4 = 3/4, 5 ≥ 3/4), arsenic in water(ppm), arsenic region(0=low
arsenic, 1=high arsenic), and arsenic in toenails (ppm) respectively.
(a) Explain briefly, the objective the methodology of the research
(b) Draw a box and plot diagram for arsenic in toe concentration (y) and comment on data outliers
(c) Use the proper hypothesis test to examine if there is any difference in the arsenic toe
concentration between the groups who lives in the high and low arsenic regions. Repeat the
same question using ANOVA
(d) Fit a multiple linear regression model using arsenic concentration in nails as the response and
age, drink use, cook use, and arsenic in the water as the regressors. Comment on model fitness
validity(F-test, t-test, and R2)
(e) Use the residual Analysis procedure to check model adequacy
(f) Estimate σ2 and the standard errors of the regression coefficients.
(g) Use the model to predict the arsenic in nails when the age is 30, the drink use is category 5, the
cook use is category 5, and arsenic in the water is 0.135 ppm.
age(x1)
sex(x2)
drink use(x3)
cook use(x4)
Arsenic in
water(x5)
Arsenic region
Arsenic Nail(y)
44
45
44
66
37
45
47
38
41
49
72
45
53
86
8
32
44
63
42
62
36
2
2
1
2
1
2
1
2
2
2
2
2
1
2
2
2
1
2
1
1
1
5
4
5
3
2
5
5
4
3
4
5
1
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
2
5
5
5
5
5
5
5
5
5
5
5
5
0.00087
0.00021
0
0.00115
0
0
0.00013
0.00069
0.00039
0
0
0.046
0.0194
0.137
0.0214
0.0175
0.0764
0
0.0165
0.00012
0.0041
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0.119
0.118
0.099
0.118
0.277
0.358
0.08
0.158
0.31
0.105
0.073
0.832
0.517
2.52
0.851
0.269
0.433
0.141
0.275
0.135
0.175
MEM 501
Extra Credit
Due December 21/2022
Use Minitab or any Statistics software to answer the following. Submit a word file to address all the
questions. Use screen shot if needed to show your results.
An article in Cancer Epidemiology, Biomarkers and Prevention journal (see attached), reported on a
pilot study to assess the use of toenail arsenic concentrations as an indicator of ingestion of arseniccontaining water. Twenty-one participants were interviewed regarding use of their private (unregulated)
wells for drinking and cooking, and each provided a sample of water and toenail clippings. Table below
showed the data of age (years), sex of person (1 = male, 2 = female), proportion of times household well
used for drinking (1≤ 1 / 4, 2 = 1 / 4, 3 = 1 / 2, 4 = 3 / 4, 5 ≥ 3 / 4), proportion of times household well
used for cooking (1≤ 1/4,2 = 1/4, 3 = 1/2, 4 = 3/4, 5 ≥ 3/4), arsenic in water(ppm), arsenic region(0=low
arsenic, 1=high arsenic), and arsenic in toenails (ppm) respectively.
(a) Explain briefly, the objective the methodology of the research
(b) Draw a box and plot diagram for arsenic in toe concentration (y) and comment on data outliers
(c) Use the proper hypothesis test to examine if there is any difference in the arsenic toe
concentration between the groups who lives in the high and low arsenic regions. Repeat the
same question using ANOVA
(d) Fit a multiple linear regression model using arsenic concentration in nails as the response and
age, drink use, cook use, and arsenic in the water as the regressors. Comment on model fitness
validity(F-test, t-test, and R2)
(e) Use the residual Analysis procedure to check model adequacy
(f) Estimate σ2 and the standard errors of the regression coefficients.
(g) Use the model to predict the arsenic in nails when the age is 30, the drink use is category 5, the
cook use is category 5, and arsenic in the water is 0.135 ppm.
age(x1)
sex(x2)
drink use(x3)
cook use(x4)
44
45
44
66
37
45
47
38
41
49
72
45
53
86
8
32
44
63
42
62
36
2
2
1
2
1
2
1
2
2
2
2
2
1
2
2
2
1
2
1
1
1
5
4
5
3
2
5
5
4
3
4
5
1
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
2
5
5
5
5
5
5
5
5
5
5
5
5
Arsenic in
water(x5)
0.00087
0.00021
0
0.00115
0
0
0.00013
0.00069
0.00039
0
0
0.046
0.0194
0.137
0.0214
0.0175
0.0764
0
0.0165
0.00012
0.0041
Arsenic region
Arsenic Nail(y)
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0.119
0.118
0.099
0.118
0.277
0.358
0.08
0.158
0.31
0.105
0.073
0.832
0.517
2.52
0.851
0.269
0.433
0.141
0.275
0.135
0.175
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