Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305115347
Author: Roxy Peck; Chris Olsen; Jay L. Devore
Publisher: Brooks Cole
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Textbook Question
Chapter 5, Problem 65CR
The article “Reduction is Soluble Protein and Chlorophyll Contents in a Few Plants as Indicators of Automobile Exhaust Pollution” (International Journal of Environmental Studies [1983]: 239–244) reported the following data on x = Distance from a highway (in meters) and y = Lead content of soil at that distance (in parts per million):
- a. Use a statistical computer package to construct
scatterplots of y versus x, y versus log(x), log(y) versus log(x), and - b. Which transformation considered in Part (a) does the best job of producing an approximately linear relationship? Use the selected transformation to predict lead content when distance is 25 m.
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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
-0.5
0.1
0.7 0.8
1
1.5
1.2 1
0.4
0.4
Depression Score Change
-1
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
5.26270
20-
R-Sq
R-Sq (adj) 19.88%
27.16%
15-
10-
5-
0-
-0.5
0.0
0.5
1.0
1.5
BMI change
R-są
5.26270
27.16%
Coefficients
Term
Coef
SE Coef
T-Value
P-Value
VIF
6.512
5.472
Constant
2.26
2.88
0.0164
BMI change
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…
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)
-0.5
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 5 Solutions
Introduction to Statistics and Data Analysis
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