Question

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.

x   y
1.0   4.1
2.0   6.1
3.0   7.0
4.0   4.0
5.0   5.2
6.0   8.1
7.0   5.5
8.0   6.9
9.0   9.0
10.0   7.3
x1234567891011y12345678910110
Figure 1
  
u   v
1.0   8.1
2.0   7.4
3.0   8.1
4.0   6.1
5.0   7.4
6.0   4.5
7.0   4.6
8.0   3.4
9.0   3.8
10.0   2.9
u1234567891011v12345678910110
Figure 2
w   t
1.0   8.4
2.0   5.1
3.0   9.6
4.0   5.8
5.0   1.9
6.0   4.7
7.0   9.2
8.0   4.0
9.0   9.5
10.0   7.0
w1234567891011t12345678910110
Figure 3
  
m   n
1.0   1.0
2.0   2.0
3.0   3.0
4.0   4.0
5.0   5.0
6.0   6.0
7.0   7.0
8.0   8.0
9.0   9.0
10.0   10.0
m1234567891011n12345678910110
Figure 4
Answer the following questions about the relationships between pairs of variables and the values of r, 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 equal to -1?  
2. Which data set has an apparent positive, but not perfect, linear relationship between its two variables?  
3. Which data set indicates the strongest positive linear relationship between its two variables?  
4. For which data set is the sample correlation coefficient r closest to 0?  

Answer 1

1. For which data set is the sample correlation coefficient r equal to -1?  

Figure 2
2. Which data set has an apparent positive, but not perfect, linear relationship between its two variables?  

Figure 1
3. Which data set indicates the strongest positive linear relationship between its two variables?  

Figure 4
4. For which data set is the sample correlation coefficient r closest to 0?  

Figure 3

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