The following raw data were collected by a health an analyst from 50 smokers. It represents Risk Index (R.I.) (measured as concentration ratio of certain compounds in the blood) which is used as a strong indicator for getting a cardiovascular (CV) disease. We would like to study the effect of each of the three factors (age, mass, and No. of cigarettes) on the R.I. : Answer the following: 1. Classify the data into 3 groups according to age: Young: age < 35, Middle aged: between 36 and 59, and Old: age > 60. Then study if the Risk Index is affected by age class. 2. Classify the data into 3 groups according to body mass: regular mass <70, fat mass between 71 and 99, and obese mass above 100. Then study if the mass has an influence on the R.I. 3. Produce a linear mathematical model that can predict the R.I. based on age, mass and number of cigarettes per day. Use a confidence level of 99%. 4. Comment on your linear model. Is there an evidence that a nonlinear model shall be better? Show the evidence and comment on it. 5. Do a nonlinear fitting for the data using the following equation R.I. = co + c1*Age + c2*Mass+c3*Cig^C4 6. Compare the predicted and measured R.I. values for both linear and nonlinear fitting. Which fitting is better? Suggest a measure that can tell you quantitatively which fitting is better. Age (YRS) Mass (KG) Cigarettes (Per Day) Risk Index (R.I.) (--) 46 113 40 974.5 35 96 32 670.68 43 81 26 409.26 39 93 50 1484.5 22 66 25 500 58 55 33 631.87 60 72 15 350.75 54 93 19 347.09 32 55 12 308.78 63 115 24 580.74 30 105 20 320.5 24 90 19 381.59 55 65 15 274.25 30 115 6 322.66 40 115 21 411.11 34 80 22 396.48 31 88 22 906 70 57 33 616.87 35 116 43 1072.07 57 101 31 589.41 44 68 36 718.56 66 118 33 790.37 46 120 44 1129.84 20 72 19 487 64 63 35 665.25 30 113 3 204.26 32 70 20 312 37 68 23 299.67 52 88 26 418.76 64 70 46 1299.36 23 87 23 422.17 42 53 50 1500.5 54 64 15 299.75 35 95 49 1536.99 51 95 39 912.69 61 105 20 386.5 37 115 16 375.46 64 95 35 825.25 57 118 22 401.48 52 114 19 449.59 29 88 10 348 68 83 44 1195.34 35 114 27 554.83 24 114 17 408.13 70 103 22 410.98 48 86 16 366.96 22 52 27 768.9 28 92 19 311.59 55 90 33 736.37 46 111 48 1497.42
The following raw data were collected by a health an analyst from 50 smokers. It represents Risk Index (R.I.) (measured as concentration ratio of certain compounds in the blood) which is used as a strong indicator for getting a cardiovascular (CV) disease.
We would like to study the effect of each of the three factors (age, mass, and No. of cigarettes) on the R.I. :
Answer the following:
1. Classify the data into 3 groups according to age: Young: age < 35, Middle aged: between 36 and 59, and Old: age > 60.
Then study if the Risk Index is affected by age class.
2. Classify the data into 3 groups according to body mass: regular mass <70, fat mass between 71 and 99, and obese mass above 100. Then study if the mass has an influence on the R.I.
3. Produce a linear mathematical model that can predict the R.I. based on age, mass and number of cigarettes per day. Use a confidence level of 99%.
4. Comment on your linear model. Is there an evidence that a nonlinear model shall be better? Show the evidence and comment on it.
5. Do a nonlinear fitting for the data using the following equation
R.I. = co + c1*Age + c2*Mass+c3*Cig^C4
6. Compare the predicted and measured R.I. values for both linear and nonlinear fitting. Which fitting is better? Suggest a measure that can tell you quantitatively which fitting is better.
|
Age (YRS) |
Mass (KG) |
Cigarettes (Per Day) |
Risk Index (R.I.) (--) |
|
46 |
113 |
40 |
974.5 |
|
35 |
96 |
32 |
670.68 |
|
43 |
81 |
26 |
409.26 |
|
39 |
93 |
50 |
1484.5 |
|
22 |
66 |
25 |
500 |
|
58 |
55 |
33 |
631.87 |
|
60 |
72 |
15 |
350.75 |
|
54 |
93 |
19 |
347.09 |
|
32 |
55 |
12 |
308.78 |
|
63 |
115 |
24 |
580.74 |
|
30 |
105 |
20 |
320.5 |
|
24 |
90 |
19 |
381.59 |
|
55 |
65 |
15 |
274.25 |
|
30 |
115 |
6 |
322.66 |
|
40 |
115 |
21 |
411.11 |
|
34 |
80 |
22 |
396.48 |
|
31 |
88 |
22 |
906 |
|
70 |
57 |
33 |
616.87 |
|
35 |
116 |
43 |
1072.07 |
|
57 |
101 |
31 |
589.41 |
|
44 |
68 |
36 |
718.56 |
|
66 |
118 |
33 |
790.37 |
|
46 |
120 |
44 |
1129.84 |
|
20 |
72 |
19 |
487 |
|
64 |
63 |
35 |
665.25 |
|
30 |
113 |
3 |
204.26 |
|
32 |
70 |
20 |
312 |
|
37 |
68 |
23 |
299.67 |
|
52 |
88 |
26 |
418.76 |
|
64 |
70 |
46 |
1299.36 |
|
23 |
87 |
23 |
422.17 |
|
42 |
53 |
50 |
1500.5 |
|
54 |
64 |
15 |
299.75 |
|
35 |
95 |
49 |
1536.99 |
|
51 |
95 |
39 |
912.69 |
|
61 |
105 |
20 |
386.5 |
|
37 |
115 |
16 |
375.46 |
|
64 |
95 |
35 |
825.25 |
|
57 |
118 |
22 |
401.48 |
|
52 |
114 |
19 |
449.59 |
|
29 |
88 |
10 |
348 |
|
68 |
83 |
44 |
1195.34 |
|
35 |
114 |
27 |
554.83 |
|
24 |
114 |
17 |
408.13 |
|
70 |
103 |
22 |
410.98 |
|
48 |
86 |
16 |
366.96 |
|
22 |
52 |
27 |
768.9 |
|
28 |
92 |
19 |
311.59 |
|
55 |
90 |
33 |
736.37 |
|
46 |
111 |
48 |
1497.42 |
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