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 PDE4CQuestion 1

What is the sample standard deviation of the ELOVL2 variable?

13.64 %

16.90 %

50.95 %

60.40 %

Question 2

Based on a box plot of ELOVL2, which of the following best describes the shape of its distribution?

Symmetric

Skewed to the left

Symmetric with outliers

Skewed to the right

Question 3

Which of the following best describes the relationship between Age and ELOVL2?

A strong positive linear relationship (r = 0.88)

A strong negative linear relationship (r = -0.88)

A weak positive linear relationship (r = 0.31)

A positive non-linear relationship

Question 4

What is the slope of the least-squares line for the relationship between Age and ELOVL2?

1.1842 years/%

1.3486 years/%

1.3709 years/%

6.8814 years/%

Question 5

What is the margin of error in a 95% confidence interval for the slope of the relationship between Age and ELOVL2?

0.0740 years/%

0.1233 years/%

0.1476 years/%

6.4898 years/%

Question 6

Based on the linear model, what is the estimated age of a person whose blood sample has 41.2% DNA methylation at ELOVL2?

48.79 years

54.00 years

55.67 years

57.50 years

Question 7

Based on the linear model, construct a 95% prediction interval for the age of a person whose blood sample has 41.2% DNA methylation at ELOVL2. The upper limit for this prediction interval is

53.67 years

57.67 years

66.45 years

72.86 years

Question 8

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/%

Question 9

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

Question 10

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

Question 11

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 normal

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

Question 12

Which of the following plots could NOT be used to detect a violation of the linearity assumption for the multiple regression model?

Scatter plot of residuals against values of PDE4C

Normal probability plot of residuals

Scatter plot of residuals against fitted values

Scatter plot of residuals against values of ELOVL2

Question 13

Assume that the model assumptions are satisfied. Based on the multiple regression model, you can conclude that there is

no evidence to suggest that there is an association between age and percentage of DNA methylation at PDE4C, after taking into account percentage of DNA methylation at ELOVL2 (p > 0.1)

weak evidence to suggest that there is an association between age and percentage of DNA methylation at PDE4C, after taking into account percentage of DNA methylation at ELOVL2 (p < 0.1)

moderate evidence to suggest that there is an association between age and percentage of DNA methylation at PDE4C, after taking into account percentage of DNA methylation at ELOVL2 (p < 0.05)

strong evidence to suggest that there is an association between age and percentage of DNA methylation at PDE4C, after taking into account percentage of DNA methylation at ELOVL2 (p < 0.01)

Question 14

Overall, the multiple regression model suggests that old age is associated with

Low percentage of DNA methylation at both ELOVL2 and PDE4C

Low percentage of DNA methylation at ELOVL2 and high percentage of DNA methylation at PDE4C

High percentage of DNA methylation at both ELOVL2 and PDE4C

High percentage of DNA methylation at ELOVL2 and low percentage of DNA methylation at PDE4C