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 5.4, Problem 49E
The paper “Population Pressure and Agricultural Intensity” (Annals of the Association of American Geographers [1977]: 384–396) reported a positive relationship between population density and agricultural intensity. The following data consist of measures of population density (x) and agricultural intensity (y) for 18 different subtropical locations:
- a. Construct a
scatterplot of y versus x. Is the scatterplot compatible with the statement of positive relationship made in the paper? - b. Construct a scatterplot that uses y and x2. Does this transformation result in a linear pattern in the scatterplot?
- c. Draw a scatterplot that uses log(y) and x. The log(y) values, given in order corresponding to the y values, are 0.95, 0.85, 0.78, 1.70, 0.70, 2.00, 0.85, 1.15, 1.15, 1.00, 1.70, 1.15, 1.70, 2.18, 1.83, 2.00, and 2.00. How does this scatterplot compare with that of Part (b)?
- d. Now consider a scatterplot that uses transformations on both x and y: log(y) and x2. Is this effective in creating a linear pattern in the plot? Explain.
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B) Theoretical (or Calculated), Numeric
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D) Theoretical (or Calculated), Categorical
1. (Prob. 11-12, p. 438) An article in the Journal of Environmental Engineering (1989, Vol. 115(3), pp.
608–619) reported the results of a study on the occurrence of sodium and chloride in surface
streams in central Rhode Island. The following data are chloride concentration y (in milligrams per
liter) and roadway area in the watershed x (in percentage).
y
4.4
6.6
9.7
10.6
10.8
10.9
0.19
0.15
0.57
0.70
0.67
0.63
y
11.8
12.1
14.3
14.7
15.0
17.3
0.47
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0.60
0.78
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y
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31.8
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1.74
1.62
a.
Draw a scatter diagram of the data. Does a simple linear regression model seem appropriate
here?
b. Fit the simple linear regression model using the method of least squares. Find an estimate of
o?.
C.
Estimate the mean chloride concentration for a watershed that has 1% roadway area.
d. Find the fitted value corresponding to x = 0.47 and the associated residual.
4.) A person's muscle mass is expected to decrease with age. To explore this relationship, a researcher randomly selected
10 persons from ages 40 to 79 years old and measured their muscle mass (unit). The result is as follows:
X (age)
Y (muscle mass)
71 64 43
67 56 73 68 56 76 65
82 91 100
68 87 73 78 80 65 84
Based on the given data, do the following:
a) Plot the scatter diagram of the given data. [3pts]
b) Obtain the regression line equation. [4pts]
c) Estimate the muscle mass when age of the person is 60 years old. [3pts]
5.) Recognize how each shape has transformed. [2pts each]
a.)
b.)
c.)
Chapter 5 Solutions
Introduction to Statistics and Data Analysis
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