Question

functions and lines
linear relationship and the correlation coefficient
answer the questions that follow. the same response may be the correct answer for more than one question

1. for which data set does the correlation coefficient r appear to be equal to 1?
2. which data set shows the least evidence of a linear relationship?
3. for which data set is the correlation coefficient r closest

Explanation:

Step1: Recall correlation coefficient properties

The correlation coefficient $r = 1$ indicates a perfect positive - linear relationship. Points should lie exactly on an upward - sloping straight line.

Step2: Analyze each figure

In Figure 2, the points seem to lie almost exactly on an upward - sloping straight line, so it has a correlation coefficient $r$ close to 1.

Step3: Determine least linear relationship

A data set with the least evidence of a linear relationship has points that are randomly scattered. Figure 1 has points that are very randomly distributed, showing the least linear relationship.

Step4: Re - evaluate for $r$ close to 1

Again, Figure 2 has the points most closely following an upward - sloping straight line, so its $r$ is closest to 1.

Answer:

1. Figure 2
2. Figure 1
3. Figure 2