recent 10-year study conducted by a research team at the Great Falls Medical Sch
ID: 3178962 • Letter: R
Question
recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic 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.
1. Interpret the regression constant and regression coefficient. Forecast a value for the dependent variable,
2. Test the overall significant of the regression model and interpret the coefficient of determination.
3. Are there any indications of multicollinearity.
Risk 13 28 31 37 15 36 15 48 15 Age 58 86 59 78 67 Systolic Blood Pressure 163 196 189 120 135 98 173 209 1990 166 125 207 Smoker Yes Yes Yes YesExplanation / Answer
Result:
recent 10-year study conducted by a research team at the Great Falls Medical School was conducted to assess how age, systolic 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.
1. Interpret the regression constant and regression coefficient. Forecast a value for the dependent variable,
Regression line = -91.7595 + 1.0767*age + 0.2518*SBP + 8.7399 *smoker
Regression coefficient for age =1.0767. When age increases by 1, ,risk increases by 1.0767.
Regression coefficient for SBP = 0.2518 . When SBP increases by 1, ,risk increases by 0.2518.
Regression coefficient for smoker = 8.7399 .. When the person is smoker, ,risk increases by 8.7399 .
Regression constant is -91.7595 , there is no meaning in interpreting the constant in this case.
2. Test the overall significant of the regression model and interpret the coefficient of determination.
Calculated F=36.82, P=0.000 which is < 0.05 level.
The regression model is significant.
R square =0.873.
87.3% variation is Risk is explained by the model.
3. Are there any indications of multicollinearity.
Correlation Matrix
Age
SBP
smoker
Age
1.000
SBP
-.309
1.000
smoker
.411
.167
1.000
20
sample size
± .444
critical value .05 (two-tail)
± .561
critical value .01 (two-tail)
The correlation between independent variables are not high. There are no indications of multicollinearity
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
SBP
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
Correlation Matrix
Age
SBP
smoker
Age
1.000
SBP
-.309
1.000
smoker
.411
.167
1.000
20
sample size
± .444
critical value .05 (two-tail)
± .561
critical value .01 (two-tail)
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