Question

linear relationship and the correlation coefficient
figure 1
figure 2
figure 3
figure 4

1. which data set indicates the strongest linear relationship between its two variables?
2. which data set has an apparent negative, but not perfect, linear relationship between its two variables?
3. for which data set does the correlation coefficient r appear to be equal to 1?

Explanation:

1. The data points in Figure 3 are most closely clustered around a line, indicating the strongest linear relationship.
2. In Figure 4, the data points show a downward - sloping trend but are not perfectly aligned, indicating an apparent negative, but not perfect, linear relationship.
3. A correlation coefficient $r = 1$ indicates a perfect positive linear relationship. None of the given figures show a perfect positive linear relationship where all points lie exactly on an upward - sloping straight line.

Answer:

1. The data set in Figure 3
2. The data set in Figure 4
3. None of the above figures