Please explain how you arrived at each answer. I tried doing it myself on excel
ID: 3204531 • Letter: P
Question
Please explain how you arrived at each answer. I tried doing it myself on excel and I'm almost positive I did it correct, but I'm not getting the right answer, could be a rounding error, but I only have 1 submission left.
A recent 10-year study conducted by a research team at the Medical School was conducted to assess how age, blood pressure, and smoking relate to the risk of strokes. Assume that the following data are from a portion of this study. Risk is interpreted as the probability (times 100) that the patient will have a stroke over the next 10-year period. For the smoking variable, define a dummy variable with 1 indicating a smoker and 0 indicating a nonsmoker.
Risk
Age
Blood
Pressure
Smoker
12
57
150
No
26
60
165
No
11
59
155
No
57
86
170
Yes
28
59
196
Yes
50
76
189
Yes
17
56
155
Yes
32
78
120
No
37
80
135
No
15
78
98
No
22
71
152
No
36
70
173
Yes
15
67
135
Yes
48
77
209
Yes
14
60
199
No
36
82
119
Yes
8
65
166
No
34
82
125
No
3
61
117
No
39
60
208
Yes
(a)
Develop an estimated multiple regression equation that relates risk of a stroke to the person's age, blood pressure, and whether the person is a smoker.
Let x1 represent the person's age.
Let x2 represent the person's blood pressure.
Let x3 represent whether the person is a smoker.
If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)
= + x1 + x2 + x3
(b)
Is smoking a significant factor in the risk of a stroke? Explain. Use a 0.05 level of significance.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(c)
What is the probability of a stroke over the next 10 years for Art Speen, a 66-year-old smoker who has a blood pressure of 168?
If required, round your answer to two decimal places.
What action might the physician recommend for this patient?
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(d)
What other factors could be included in the model as independent variables?
(i)
Family History of Stroke
(ii)
Weight/obesity
(iii)
Gender
(iv)
All of the above
- Select your answer -Option (i)Option (ii)Option (iii)Option (iv)
Risk
Age
Blood
Pressure
Smoker
12
57
150
No
26
60
165
No
11
59
155
No
57
86
170
Yes
28
59
196
Yes
50
76
189
Yes
17
56
155
Yes
32
78
120
No
37
80
135
No
15
78
98
No
22
71
152
No
36
70
173
Yes
15
67
135
Yes
48
77
209
Yes
14
60
199
No
36
82
119
Yes
8
65
166
No
34
82
125
No
3
61
117
No
39
60
208
Yes
Explanation / Answer
Let dependent variable is risk and independent variables are age, blood pressure, and smoker.
Develop an estimated multiple regression equation that relates risk of a stroke to the person's age, blood pressure, and whether the person is a smoker.
This we can done in MINITAB.
steps :
ENTER data into MINITAB sheet --> Stat --> Regression --> Regression --> Response : risk --> Predictors : age, blood pressure and smoker --> Results :select second option --> ok --> ok
The regression equation is
risk = - 97.1987 + 1.2095 age + 0.2369 blood pressure + 7.4401 smoker
Is smoking a significant factor in the risk of a stroke? Explain. Use a 0.05 level of significance
Here we have to test the hypothesis that,
H0 : B = 0 Vs H1 : B not= 0
where B is population slope for smoking.
Assume alpha = level of significance = 0.05
Predictor Coef SE Coef T P
Constant -97.20 16.55 -5.87 0.000
age 1.2095 0.1657 7.30 0.000
blood pressure 0.23694 0.05623 4.21 0.001
smoker 7.440 3.413 2.18 0.045
S = 6.46240 R-Sq = 84.6% R-Sq(adj) = 81.8%
Analysis of Variance
Source DF SS MS F P
Regression 3 3683.8 1227.9 29.40 0.000
Residual Error 16 668.2 41.8
Total 19 4352.0
Here the test statistic follows t-distribution.
ANd we see that the smoking has test statistic 2.18 with P-value = 0.045.
P-value < alpha
Reject H0 at 5% level of significance.
Conclusion : The population slope for smikong is differ than 0.
Smoking is significant factor.
What is the probability of a stroke over the next 10 years for Art Speen, a 66-year-old smoker who has a blood pressure of 168?
Here we have to predict risk when age = 66, blood pressure = 168 and smoking = 1
This we can find by using regression equation.
risk = - 97.2 + 1.21 age + 0.237 blood pressure + 7.44 smoker
risk = - 97.1987 + 1.2095*66 + 0.2369*168 + 7.4401*1 = 29.88
What other factors could be included in the model as independent variables?
Here we include weight/obesity in the model because this variable affects the risk.