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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

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

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