Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 11.4, Problem 18E
a.
To determine
Find the values of SSE and
b.
To determine
Fit the model simple linear model to the LC50 measurements using Exercise 11.8.
Find the value of
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A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter2) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data
given in the paper and are approximate values read from a scatterplot in the paper.
BMI Change (kg/m²)
0.5 -0.5 0
0.1 0.7 0.8
1
1.5
1.2
1
0.4 0.4
Depression Score Change -1
9
4
4
5
8
13
14 17 18
12
14
The accompanying computer output is from Minitab.
Fitted Line Plot
Depression score change = 6.512 + 5.472 BMI change
20
S
5.26270
R-Sq
27.16%
R-Sq (adj) 19.88%
15-
:
10-
-0.5 0.0
1.5
Ⓡ
S
5.26270
Coefficients
Term
Coef
VIF
SE Coef
2.26
T-Value
2.88
P-Value
0.0164
Constant
6.512
BMI change
5.472
2.83
1.93
0.0823 1.00
Regression Equation
Depression score change = 6.512 + 5.472 BMI change
(a) What percentage of observed variation in depression score change can be explained by the simple linear regression model? (Round your answer to…
A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below contains a subset of the data given in the paper and are approximate values read from a scatterplot in
the paper.
BMI Change (kg/m2)
0.7 0.8 1
1.5 1.2
1
0.4 0.4
0.5
-0.5
0.1
Depression Score Change
-1
| 4
5
8
13
14| 17| 18| 12
14
The accompanying computer output is from Minitab.
Fitted Line Plot
Depression score change = 6.512 + 5.472 BMI change
5.26270
20 -
R-Sq
R-Sq (adj) 19.88%
27.16%
15-
10-.
5-
-0.5
0.0
0.5
1.0
1.5
BMI change
5.26270
27.166
Coefficients
Term
Coef
SE Coef
T-Value
P-Value
VIF
Constant
6.512
2.26
2.88
0.0164
BMI change
5.472
2.83
1.93
0.0823
1.00
Regression Equation
Depression score change = 6.512 + 5.472 EMI change
(a) What percentage of observed variation in depression score change can be explained by the simple linear regression model?…
A paper gives data on x = change in Body Mass Index (BMI, in kilograms/meter) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. The table below
contains a subset of the data given in the paper and are approximate values read from a scatterplot in the paper.
BMI Change (kg/m²)
-0.5
0.7
0.5
0.1
0.8
1
1.5
1.2
1
0.4
0.4
Depression Score Change
-1
4
4
8
13
14
16
18
12
14
The accompanying computer output is from Minitab.
Fitted Line Plot
Depression score change = 6.598 + 5.327 BMI change
20-
5.10254
R-Sq
R-Sq (adj) 20.06%
27.32%
15-
10-
5-
0-
-0.5
0.0
0.5
1.0
1.5
BMI change
R-sq
5.10254
27.32%
Coefficients
Term
Coef
SE Coef
T-Value
P-Value
VIF
Constant
6.598
2.19
3.01
0.0132
BMI change
5.327
2.75
1.94
0.0812
1.00
Regression Equation
Depression score change = 6.598 + 5.327 BMI change
(a) What percentage of observed variation in depression score change can be explained by the simple linear regression model?…
Chapter 11 Solutions
Mathematical Statistics with Applications
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