Question

functions and lines
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:

Step1: Recall correlation - coefficient concept

The correlation coefficient \(r = 1\) indicates a perfect positive - linear relationship. In a scatter - plot, the points of a perfect positive - linear relationship lie exactly on a straight line with a positive slope.

Step2: Analyze each figure

Looking at Figure 1, the points are scattered with no clear linear pattern. Figure 2 has a negative but not perfect linear relationship. Figure 3 has a strong positive linear relationship but not all points lie exactly on a line. For a correlation coefficient \(r = 1\), all points must lie exactly on a straight line with a positive slope. None of the given figures show this.

Answer:

None of the given figures