Bivariate data: Correlation

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

x y = Figure 1
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1.0 8.0
2.0 4.8
3.0 9.8
4.0 6.2
5.0 2.0
6.0 4.8
7.0 8.9
8.0 4.0
9.0 9.7
10.0 6.7

u v = Figure 2
--- ---
1.0 7.4
2.0 8.5
3.0 7.0
4.0 5.3
5.0 7.8
6.0 4.8
7.0 4.0
8.0 7.1
9.0 5.9
10.0 4.2

w t = Figure 3
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1.0 10.0
2.0 9.0
3.0 8.0
4.0 7.0
5.0 6.0
6.0 5.0
7.0 4.0
8.0 3.0
9.0 2.0
10.0 1.0
m n = Figure 4
---- ----
1.0 2.8
2.0 4.0
3.0 3.7
4.0 5.5
5.0 4.7
6.0 6.8
7.0 5.7
8.0 7.7
9.0 6.7
10.0 8.0

Answer the following questions. The same response may be the correct answer for more than one question.

1. 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

2. Which data set has an apparent positive, but not perfect, 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
e. none of the data sets

3. Which data set indicated the strongest negative 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

4. 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