The weight and systolic blood pressure of randomly selected males in age-group 2
ID: 3228251 • Letter: T
Question
The weight and systolic blood pressure of randomly selected males in age-group 25 to 30 are shown in the following table. (a) Estimate the regression coefficients. (b) Do the data support the claim that systolic blood pressure does not depend on an individual's weight? (c) If a large number of males weighing 182 pounds have their blood pressures taken, determine an interval that, with 95 percent confidence, will contain their average blood pressure. (d) Analyze the standardized residuals. (e) Determine the sample correlation coefficient.|Explanation / Answer
Answer:
a).
Regression Analysis
r²
0.584
n
20
r
0.764
k
1
Std. Error
8.872
Dep. Var.
SBP
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,992.2370
1
1,992.2370
25.31
.0001
Residual
1,416.9630
18
78.7202
Total
3,409.2000
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=18)
p-value
95% lower
95% upper
Intercept
68.5844
15.1612
4.524
.0003
36.7319
100.4370
weight
0.4164
0.0828
5.031
.0001
0.2425
0.5903
SBP=68.5844+0.4164*weight
b).
calculated F=25.31, P=0.0001 which is < 0.05 level. The model is significant.
The data support the claim.
c).
Predicted values for: SBP
95% Confidence Interval
95% Prediction Interval
weight
Predicted
lower
upper
lower
upper
Leverage
182
144.367
140.198
148.535
125.266
163.467
0.050
95% CI for weight of 182 pounds= (140.198, 148.535).
d).
Studentized
Studentized
Deleted
Observation
SBP
Predicted
Residual
Leverage
Residual
Residual
1
130.0
137.3
-7.3
0.074
-0.854
-0.847
2
133.0
138.1
-5.1
0.069
-0.598
-0.587
3
150.0
143.5
6.5
0.050
0.748
0.738
4
128.0
133.1
-5.1
0.112
-0.613
-0.602
5
151.0
156.9
-5.9
0.130
-0.708
-0.698
6
146.0
141.5
4.5
0.054
0.527
0.516
7
150.0
147.7
2.3
0.056
0.267
0.260
8
140.0
156.0
-16.0
0.120
-1.926
-2.100
9
148.0
151.9
-3.9
0.079
-0.454
-0.443
10
125.0
130.6
-5.6
0.142
-0.685
-0.674
11
153.0
140.2
12.8
0.058
1.486
1.542
12
128.0
134.8
-6.8
0.094
-0.804
-0.796
13
132.0
138.5
-6.5
0.066
-0.762
-0.753
14
149.0
141.0
8.0
0.055
0.923
0.919
15
158.0
144.8
13.2
0.050
1.529
1.592
16
150.0
158.1
-8.1
0.147
-0.989
-0.989
17
163.0
149.8
13.2
0.066
1.541
1.608
18
156.0
143.5
12.5
0.050
1.442
1.490
19
124.0
128.1
-4.1
0.180
-0.514
-0.503
20
170.0
168.5
1.5
0.347
0.207
0.201
The residuals shows that there is no outlier.
e).
correlation coefficient = 0.764
Regression Analysis
r²
0.584
n
20
r
0.764
k
1
Std. Error
8.872
Dep. Var.
SBP
ANOVA table
Source
SS
df
MS
F
p-value
Regression
1,992.2370
1
1,992.2370
25.31
.0001
Residual
1,416.9630
18
78.7202
Total
3,409.2000
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=18)
p-value
95% lower
95% upper
Intercept
68.5844
15.1612
4.524
.0003
36.7319
100.4370
weight
0.4164
0.0828
5.031
.0001
0.2425
0.5903
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