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Bivariate data sets

Below are four bivariate data sets and the scatter plot for each. (Note that each scatter plot is displayed on the same scale.) Each data set is made up of sample values drawn from a population.

Figure 1
x y
1.0 7.7
2.0 8.7
3.0 6.9
4.0 5.7
5.0 8.5
6.0 4.9
7.0 4.5
8.0 7.3
9.0 5.9
10.0 3.8

Figure 2
u v
1.0 7.8
2.0 4.8
3.0 10.3
4.0 5.8
5.0 2.3
6.0 4.5
7.0 9.2
8.0 3.8
9.0 9.2
10.0 6.7

Figure 3
w t
1.0 8.1
2.0 6.7
3.0 7.6
4.0 6.0
5.0 7.1
6.0 4.4
7.0 5.1
8.0 3.2
9.0 4.5
10.0 3.0

Figure 4
m n
1.0 2.5
2.0 4.2
3.0 3.8
4.0 4.8
5.0 4.2
6.0 6.9
7.0 5.7
8.0 8.2
9.0 7.0
10.0 7.9

Answer the following questions about the relationships between pairs of variables and the values of , the sample correlation coefficient. The same response may be the correct answer for more than one question.
1. For which data set is the sample correlation coefficient r closest to -1? ____
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set

2. For which data set is the sample correlation coefficient r closest to 0? ____
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set

3. For which data set is the sample correlation coefficient r equal to 1? ____
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set
e. none of the data sets

4. Which data set indicates the strongest positive linear relationship between its two variables? ___
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set

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