A recent 10-year study conducted by a research team at the Medical School was co
ID: 3264064 • Letter: A
Question
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 57 152 No 24 67 163 No 13 58 155 No 56 86 177 Yes 28 59 196 No 51 76 189 Yes 18 56 155 Yes 31 78 120 No 37 80 135 Yes 15 78 98 No 22 71 152 No 36 70 173 Yes 15 67 135 Yes 48 77 209 Yes 15 60 199 No 36 82 119 Yes 8 66 166 No 34 80 125 Yes 3 62 117 No 37 59 207 Yes
Explanation / Answer
Answer:
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)
y = -91.7595 + 1.0767 x1 + 0.2518 x2 + 8.7399 x3
Regression Analysis
R²
0.873
Adjusted R²
0.850
n
20
R
0.935
k
3
Std. Error
5.757
Dep. Var.
Risk
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3,660.7396
3
1,220.2465
36.82
2.06E-07
Residual
530.2104
16
33.1382
Total
4,190.9500
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=16)
p-value
95% lower
95% upper
Intercept
-91.7595
15.2228
-6.028
1.76E-05
-124.0303
-59.4887
Age
1.0767
0.1660
6.488
7.49E-06
0.7249
1.4286
Blood Pressure
0.2518
0.0452
5.568
4.24E-05
0.1559
0.3477
Smoker
8.7399
3.0008
2.912
.0102
2.3784
15.1013
(c) What is the probability of a stroke over the next 10 years for Art Speen, a 67-year-old smoker who has a blood pressure of 171?
If required, round your answer to two decimal places.
Predicted y =-91.7595 + 1.0767*67+ 0.2518*171+ 8.7399*1
=32.1771
The required probability = 0.32
Regression Analysis
R²
0.873
Adjusted R²
0.850
n
20
R
0.935
k
3
Std. Error
5.757
Dep. Var.
Risk
ANOVA table
Source
SS
df
MS
F
p-value
Regression
3,660.7396
3
1,220.2465
36.82
2.06E-07
Residual
530.2104
16
33.1382
Total
4,190.9500
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=16)
p-value
95% lower
95% upper
Intercept
-91.7595
15.2228
-6.028
1.76E-05
-124.0303
-59.4887
Age
1.0767
0.1660
6.488
7.49E-06
0.7249
1.4286
Blood Pressure
0.2518
0.0452
5.568
4.24E-05
0.1559
0.3477
Smoker
8.7399
3.0008
2.912
.0102
2.3784
15.1013
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