Age Gender ELOVL2 PDE4C 54 Female 41.2 45.8 58 Male 35.2 27.7 45 Male 43.9 34.9 67 Male 53.6 53.3 44 Male 23.1 29.4 63 Male 37.8 33.6 28 Female 23.8 25.7 21 Female 13.5 20.5 49 Female 41.7 37.7 70 Male 55.5 51.0 50 Female 39.1 29.2 71 Female 60.3 63.5 75 Female 45.1 46.1 44 Male 29.9 30.9 54 Female 49.4 37.0 77 Male 50.5 50.5 40 Male 23.1 32.5 65 Male 43.4 38.3 43 Male 28.7 30.2 61 Male 50.3 40.6 54 Male 34.4 42.0 38 Female 34.9 30.4 78 Male 54.5 52.9 75 Female 51.0 52.3 52 Male 29.8 32.3 42 Male 34.2 27.0 57 Female 42.2 45.6 53 Female 33.9 44.9 21 Male 22.3 26.8 46 Male 34.4 31.7 74 Male 54.7 62.5 65 Male 47.4 51.3 79 Male 48.4 54.1 75 Male 53.2 39.7 46 Female 32.4 39.9 11 Male 12.7 17.5 89 Male 72.5 62.3 79 Male 45.5 45.6 69 Female 58.7 63.7 66 Female 56.6 53.6 56 Male 35.4 33.3 88 Female 67.1 63.8 55 Female 51.9 51.2 47 Female 36.3 30.0 59 Male 42.4 41.9 38 Female 36.9 40.9 81 Female 56.9 54.9 31 Male 26.7 22.8 71 Female 59.4 52.0 56 Female 46.5 47.6 44 Male 44.2 39.8 54 Female 37.7 42.1 41 Male 39.2 34.7 45 Male 17.8 20.2 51 Male 39.1 45.3 73 Female 50.6 47.4 35 Female 27.0 28.1 53 Male 36.5 36.8 72 Male 46.6 48.9 73 Female 44.9 49.6 27 Female 12.1 20.4 40 Female 24.9 18.1 80 Male 58.1 57.9 55 Female 50.9 40.1 90 Female 67.1 60.9 69 Male 48.5 46.9 60 Male 36.3 39.2 34 Male 28.4 36.0 86 Female 64.1 55.2 73 Male 50.8 61.6 11 Male 18.7 30.0 57 Female 49.1 41.4 66 Male 59.3 54.0 DNA methylation is a known biomaker for age and has been applied in forensic investigations. The aim is to construct a model which accurately predicts a person's age from DNA methylation data obtained from blood samples. The blood samples were taken from people aged between 1 year and 90 years old. The percentage of DNA methylation was measured for two genes ELOVL2 and PDE4C. The data contains the following variables: Age. Chronological age (years) Gender (Female/Male) ELOVL2% of DNA methylation at ELOVL2 PDE4C% of DNA methylation at PDE4C a)Can we improve the model of Age by including the percentage of DNA methylation at both ELOLV2 and PDE4C? We can address this question using a multiple regression model of Age where the explanatory variables are ELOVL2 and PDE4C. Assuming there is no interaction term, the PDE4C coefficient in the multiple regression model is 0.1823 years/% 0.3790 years/% 0.8791 years/% 1.2576 years/% b) Based on the multiple regression model, what is the estimated age for the person in the data whose blood sample has 41.2% DNA methylation at ELOVL2 and 45.8% DNA methylation at PDE4C? 48.787 years 54.000 years 55.669 years 57.504 years c) What is the residual in this multiple regression model for the person in the data whose blood sample has 41.2% DNA methylation at ELOVL2 and 45.8% DNA methylation at PDE4C? -3.504 years -2.586 years -1.669 years 5.213 years
|
Age |
Gender |
ELOVL2 |
PDE4C |
|
54 |
Female |
41.2 |
45.8 |
|
58 |
Male |
35.2 |
27.7 |
|
45 |
Male |
43.9 |
34.9 |
|
67 |
Male |
53.6 |
53.3 |
|
44 |
Male |
23.1 |
29.4 |
|
63 |
Male |
37.8 |
33.6 |
|
28 |
Female |
23.8 |
25.7 |
|
21 |
Female |
13.5 |
20.5 |
|
49 |
Female |
41.7 |
37.7 |
|
70 |
Male |
55.5 |
51.0 |
|
50 |
Female |
39.1 |
29.2 |
|
71 |
Female |
60.3 |
63.5 |
|
75 |
Female |
45.1 |
46.1 |
|
44 |
Male |
29.9 |
30.9 |
|
54 |
Female |
49.4 |
37.0 |
|
77 |
Male |
50.5 |
50.5 |
|
40 |
Male |
23.1 |
32.5 |
|
65 |
Male |
43.4 |
38.3 |
|
43 |
Male |
28.7 |
30.2 |
|
61 |
Male |
50.3 |
40.6 |
|
54 |
Male |
34.4 |
42.0 |
|
38 |
Female |
34.9 |
30.4 |
|
78 |
Male |
54.5 |
52.9 |
|
75 |
Female |
51.0 |
52.3 |
|
52 |
Male |
29.8 |
32.3 |
|
42 |
Male |
34.2 |
27.0 |
|
57 |
Female |
42.2 |
45.6 |
|
53 |
Female |
33.9 |
44.9 |
|
21 |
Male |
22.3 |
26.8 |
|
46 |
Male |
34.4 |
31.7 |
|
74 |
Male |
54.7 |
62.5 |
|
65 |
Male |
47.4 |
51.3 |
|
79 |
Male |
48.4 |
54.1 |
|
75 |
Male |
53.2 |
39.7 |
|
46 |
Female |
32.4 |
39.9 |
|
11 |
Male |
12.7 |
17.5 |
|
89 |
Male |
72.5 |
62.3 |
|
79 |
Male |
45.5 |
45.6 |
|
69 |
Female |
58.7 |
63.7 |
|
66 |
Female |
56.6 |
53.6 |
|
56 |
Male |
35.4 |
33.3 |
|
88 |
Female |
67.1 |
63.8 |
|
55 |
Female |
51.9 |
51.2 |
|
47 |
Female |
36.3 |
30.0 |
|
59 |
Male |
42.4 |
41.9 |
|
38 |
Female |
36.9 |
40.9 |
|
81 |
Female |
56.9 |
54.9 |
|
31 |
Male |
26.7 |
22.8 |
|
71 |
Female |
59.4 |
52.0 |
|
56 |
Female |
46.5 |
47.6 |
|
44 |
Male |
44.2 |
39.8 |
|
54 |
Female |
37.7 |
42.1 |
|
41 |
Male |
39.2 |
34.7 |
|
45 |
Male |
17.8 |
20.2 |
|
51 |
Male |
39.1 |
45.3 |
|
73 |
Female |
50.6 |
47.4 |
|
35 |
Female |
27.0 |
28.1 |
|
53 |
Male |
36.5 |
36.8 |
|
72 |
Male |
46.6 |
48.9 |
|
73 |
Female |
44.9 |
49.6 |
|
27 |
Female |
12.1 |
20.4 |
|
40 |
Female |
24.9 |
18.1 |
|
80 |
Male |
58.1 |
57.9 |
|
55 |
Female |
50.9 |
40.1 |
|
90 |
Female |
67.1 |
60.9 |
|
69 |
Male |
48.5 |
46.9 |
|
60 |
Male |
36.3 |
39.2 |
|
34 |
Male |
28.4 |
36.0 |
|
86 |
Female |
64.1 |
55.2 |
|
73 |
Male |
50.8 |
61.6 |
|
11 |
Male |
18.7 |
30.0 |
|
57 |
Female |
49.1 |
41.4 |
|
66 |
Male |
59.3 |
54.0 |
DNA methylation is a known biomaker for age and has been applied in forensic investigations. The aim is to construct a model which accurately predicts a person's age from DNA methylation data obtained from blood samples. The blood samples were taken from people aged between 1 year and 90 years old. The percentage of DNA methylation was measured for two genes ELOVL2 and PDE4C.
The data contains the following variables:
Age. Chronological age (years)
Gender (Female/Male)
ELOVL2% of DNA methylation at ELOVL2
PDE4C% of DNA methylation at PDE4C
a)Can we improve the model of Age by including the percentage of DNA methylation at both ELOLV2 and PDE4C? We can address this question using a multiple regression model of Age where the explanatory variables are ELOVL2 and PDE4C. Assuming there is no interaction term, the PDE4C coefficient in the multiple regression model is
0.1823 years/%
0.3790 years/%
0.8791 years/%
1.2576 years/%
b)
Based on the multiple regression model, what is the estimated age for the person in the data whose blood sample has 41.2% DNA methylation at ELOVL2 and 45.8% DNA methylation at PDE4C?
48.787 years
54.000 years
55.669 years
57.504 years
c)
What is the residual in this multiple regression model for the person in the data whose blood sample has 41.2% DNA methylation at ELOVL2 and 45.8% DNA methylation at PDE4C?
-3.504 years
-2.586 years
-1.669 years
5.213 years
d)
Based on the normal probability plot of residuals for the multiple regression model fitted in Question 8, we can conclude that
the distribution of the residuals appears roughly
the distribution of the residuals is skewed to the right
the distribution of the residuals is skewed to the left
the residuals have a non-constant variance
e)
Which of the following plots could NOT be used to detect a violation of the linearity assumption for the multiple regression model?
Normal probability plot of residuals
Scatter plot of residuals against fitted values
Scatter plot of residuals against values of ELOVL2
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